Category: Language

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Computability and Effability

October 6, 2024

This conversation may reflect the link creator’s personalized data, which isn’t shared and can meaningfully change how the model responds.

SH: What is the Weak and Strong Church-Turing Thesis about the power of computation and Jerrold Katz’s “Effability” Thesis about the power of language?

ChatGPT: The Weak Church-Turing Thesis (WCT-T) asserts that any function that can be effectively computed by any physical system can be computed by a Turing machine. It is an empirical claim about the limits of what can be done through computation and is based on the observation that every physical system we know can be simulated by a Turing machine.

The Strong Church-Turing Thesis (SCT-T) is more ambitious, claiming that all physical processes can be simulated by a Turing machine, not just in terms of computation but in replicating the behavior of any physical system. This is more controversial because it implies that computational models are sufficient to describe all aspects of physical reality, a claim some argue oversteps the nature of computation itself.

Jerrold Katz’s “Effability” Thesis posits that all possible thoughts can be expressed in natural language. This is a linguistic analogue to the Church-Turing Thesis, asserting that language has the power to represent any conceivable meaning. Katz’s claim is about the expressive completeness of language: that anything thinkable is expressible, which has implications for the limits of linguistic representation.

SH: How is the Translatability or Glossability Thesis a lemma of the Effability Thesis?

ChatGPT: The Translatability or Glossability Thesis is a lemma (a supporting or subsidiary proposition) of the Effability Thesis because it follows directly from the idea that all thoughts are expressible in natural language.

According to the Effability Thesis, any possible thought or meaning can be expressed in some language. The Translatability Thesis extends this by asserting that if all thoughts can be expressed in a language, then they must also be translatable into other languages. In other words, if language A can express all thoughts, and language B can express all thoughts, then any thought expressed in language A can be translated into language B.

The reasoning is as follows:

Effability means that each language has the capacity to express any conceivable thought.

Since all languages share this capacity, there is nothing in one language that cannot, in principle, be expressed in another language, implying translatability or glossability.

Therefore, the capacity to express a thought in one language guarantees its translatability into any other language with the same expressive power.

    In this way, Translatability is a necessary consequence (lemma) of the broader Effability Thesis: if language is capable of expressing any thought, then it must also be capable of translating that thought into another language with the same expressive capacity.

    SH: But translatability does not mean word-for-word translatability, just propositional translatability. So how do languages get around this. (Use German translating “Schadenfreude” (or French « sympathique ») into English as examples.

    ChatGPT: You’re right that translatability does not imply word-for-word translatability but rather propositional translatability, meaning that the same thought or proposition can be conveyed even if different languages use different words, structures, or idiomatic expressions.

    Languages “get around” the problem of word-for-word translation through a variety of linguistic strategies that focus on meaning equivalence rather than lexical or syntactic correspondence. Let’s consider two examples: Schadenfreude in German and sympathique in French.

    Schadenfreude (German): Schadenfreude refers to the pleasure derived from another’s misfortune. There is no single word in English that captures this exact meaning. However, we can paraphrase or describe it in English: “the feeling of joy or pleasure at someone else’s suffering.” Thus, propositional translatability is achieved by expressing the same concept, even though the English translation requires more words or a descriptive phrase to convey the same meaning.

    Sympathique (French): The French word sympathique does not directly translate to the English word “sympathetic.” In French, sympathique means “nice” or “likable,” which is a broader or slightly different concept than the English “sympathetic,” which means understanding or compassionate. Again, propositional translatability is achieved by choosing an appropriate English equivalent based on context, even though there’s no direct one-word match. If translating Il est très sympathique, we would say, “He is very likable” or “He is a nice person,” depending on the nuance in the specific context.

      In both cases, propositional translatability is possible because language can represent thoughts, even if different languages use different strategies (more words, descriptions, or broader contextual meaning) to express the same proposition. Idiomatic and contextual flexibility allow languages to express the same underlying meaning, fulfilling Katz’s Effability Thesis. Even when there is no exact word-to-word match, the proposition can still be understood and communicated, reflecting the expressive power of natural language across linguistic boundaries.

      SH: What is a proposition?

      ChatGPT: A proposition is the meaning or content of a declarative sentence, expressing a claim that can be either true or false. It is the abstract thought or idea conveyed by the sentence, independent of the specific words or language used to express it.

      For example:

      The English sentence “The cat is on the mat” and the French sentence “Le chat est sur le tapis” both express the same proposition: that there is a cat on the mat.

      Even though the words and grammatical structures are different, the propositional content—the fact being described—is the same.

      Key characteristics of propositions:

      Truth-value: Propositions are either true or false. The proposition “The cat is on the mat” is true if and only if there is indeed a cat on the mat.

      Language-independent: A proposition can be expressed in different languages or forms but still retain the same underlying meaning. Whether in English, French, or any other language, the idea or claim remains constant.

      Abstract: Propositions are abstract entities that are distinct from the sentences used to express them. A sentence is a physical, linguistic entity, while a proposition is the idea or meaning the sentence conveys.

        In sum, a proposition is the content of a thought or claim that can be evaluated for truth, regardless of the specific language or words used to express it.

        SH: You left out the fact that a propostion has a subject and predicate, not just a truth-value. And you left out that Effability refers to literal propositions, not figurative ones. “The cat is on the mat” is not the same as “The cat will mew and the dog will have his day” — although you can give a literal explanation of it in any language (on the same principle as explaining a word with a proposition.

        ChatGPT: You’re right, and I’ll clarify the key elements of a proposition that I missed:

        Subject and Predicate: Every proposition has a subject (what the proposition is about) and a predicate (what is being said about the subject). In “The cat is on the mat,” the subject is “the cat,” and the predicate is “is on the mat.” The predicate expresses a relationship or property attributed to the subject.

        Literal Propositions: Katz’s Effability Thesis pertains to literal propositions—those with clear, truth-evaluable content. These are distinct from figurative or metaphorical statements, which often require interpretation beyond their literal meaning.
        For example, “The cat is on the mat” is a literal proposition, with a clear subject and predicate that can be expressed in any language. In contrast, the figurative expression “The cat will mew and the dog will have his day” is metaphorical and not literally translatable as a proposition. To make such a figurative expression effable (in the sense of Katz’s thesis), we would need to explain its literal meaning, which might be something like “A person will express their grievances, and someone else will have their moment of triumph.” This explanation turns a figurative expression into a literal propositional statement that can be conveyed across languages.

          So, while literal propositions have a clear subject-predicate structure and can be evaluated for truth, figurative expressions often require rephrasing into literal propositions to align with Katz’s Effability Thesis.

          SH: Good job, but keep on your toes!

          ChatGPT: Thank you, Professor Harnad! I’ll stay sharp. If there’s anything further you’d like to explore or clarify, I’m ready to engage.

          SH: Ok, a little extension. How does all this relate to the notion that words do not really have meaning. They only have referents. (Never mind connotations and associations). “Cat” does not <i>mean</i> anything. “The cat is on the mat” means something: it means that the cat is on the mat, and if the cat is indeed on the mat, then the proposition is True. (But the same token “That is a cat” is true (if that is indeed a cat) whereas saying “cat,” or just pointing at a cat” is just a vocal or gestural act.

          ChatGPT: You’re highlighting a key distinction between words and propositions: words alone don’t have meaning in the full sense; they have referents—the things or categories they point to in the world. Propositions, however, mean something because they assert a relationship or claim about those referents, which can be true or false.

          Here’s how this works:

          Words and Referents:

          A word like “cat” is simply a label. It doesn’t mean anything on its own; it just refers to a category of objects—namely, cats.

          Saying “cat” or pointing to a cat is a referential act: you’re signaling the category of “cat,” but you’re not saying anything about the cat. There’s no propositional content—nothing that can be evaluated as true or false.

          Propositions and Meaning:

          When you combine words into a proposition like “The cat is on the mat,” you are asserting something about the relationship between two referents: the “cat” and the “mat.” Now you have a subject (“the cat”) and a predicate (“is on the mat”), which makes the proposition meaningful because it expresses a state of affairs that can be true or false.

          The meaning of this proposition is the relationship it asserts between the cat and the mat. It’s no longer just a referential act (pointing to the category “cat” and “mat”), but a claim about reality—about where the cat is.

          Pointing or Naming Without Meaning:

          As you pointed out, just saying “cat” or pointing at a cat doesn’t mean anything in the propositional sense; it’s a referential or deictic gesture (like naming or pointing), but it’s not making any claim about the world.

          The proposition “That is a cat” does mean something because it’s a truth-claim: it says something about the referent (“that”) and its relationship to the category (“cat”). If the object is indeed a cat, the proposition is true.

            So, the key distinction is that words are referential—they point to things in the world—but propositions are meaningful because they make claims about those referents that can be evaluated for truth or falsity. In this view, meaning arises from relationships (propositional structure), not from individual words alone.

            This fits perfectly with Katz’s Effability Thesis: propositions, not individual words, are the bearers of meaning, and all thoughts can be expressed in language via literal propositions.

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            Symbol Manipulation, DNA Translation, 3D Printing and Virtual Reality

            SH: What is the “Sieve of Eratosthenes?”

            ChatGPT:

            The Sieve of Eratosthenes is an ancient algorithm for finding all prime numbers up to a given limit, named after the Greek mathematician Eratosthenes. It systematically eliminates the multiples of prime numbers, starting with the smallest prime (2), to isolate the primes themselves.

            Here’s how it works:

            List Numbers: Write down all integers from 2 up to the desired limit.

            Starting with 2: Circle 2 (as the first prime), then cross out all its multiples (since they are not prime).

            Next number: Find the next uncrossed number (which will be 3), circle it (as it’s prime), and cross out all its multiples.

            Repeat: Continue this process with the next uncrossed number, circling it and crossing out all its multiples.

            Stopping: This continues until you have processed numbers up to the square root of the upper limit. All remaining uncrossed numbers are primes.

            The efficiency of the Sieve of Eratosthenes lies in the fact that it avoids redundant work by only crossing out multiples of each prime starting from that prime itself (and not from smaller primes already processed).

            SH: what is DNA translation?

            ChatGPT:

            DNA translation is the process by which the genetic code carried by messenger RNA (mRNA) is used to synthesize proteins. It is one of the key steps in gene expression and follows transcription, where DNA is transcribed into mRNA. Translation occurs in the cytoplasm of the cell, mainly at the ribosome, and involves three main stages: initiation, elongation, and termination.

            Here’s an outline of the process:

            Initiation:

            The small subunit of the ribosome binds to the mRNA at a specific site, usually near the start codon (AUG).

            Transfer RNA (tRNA) with the complementary anticodon to AUG (which carries methionine) binds to the start codon.

            The large ribosomal subunit then joins, forming a complete ribosome.

            Elongation:

            The ribosome reads the mRNA sequence codon by codon (groups of three nucleotides).

            Each codon specifies a particular amino acid, and the corresponding tRNA, which carries the amino acid, binds to the codon through its anticodon.

            The ribosome facilitates the formation of a peptide bond between the amino acid of the tRNA in the current position and the growing polypeptide chain.

            The ribosome then moves to the next codon, and the process repeats.

            Termination:

            When the ribosome reaches a stop codon (such as UAA, UAG, or UGA), no tRNA matches these codons.

            Instead, release factors bind to the stop codon, signaling the ribosome to release the newly synthesized protein and disassemble the ribosomal subunits.

            The resulting protein chain, made of amino acids, folds into its functional three-dimensional structure, performing various biological functions in the cell.

            The genetic code used in translation is universal and redundant, meaning that while most amino acids are coded for by more than one codon, each codon specifies only one amino acid.

            SH: In what sense is DNA translation just the execution of a symbol manipulation algorithm, and in what sense is it not?

            ChatGPT:

            DNA translation can be understood as symbol manipulation in certain respects, but there are also important differences that distinguish it from abstract computational symbol manipulation.

            DNA Translation as Symbol Manipulation:

            Discrete Codons: DNA translation involves a direct mapping between sequences of nucleotides (A, U, C, G in mRNA) and amino acids, much like the manipulation of symbols in formal systems. Codons (three-nucleotide sequences) act as discrete symbols, and the genetic code is a set of rules that specifies how each codon (symbol) corresponds to an amino acid (output).

            Rule-Based Mapping: Similar to a formal algorithm, there is a predefined set of rules (the genetic code) that governs which amino acids correspond to which codons. This fixed set of mappings resembles a look-up table or algorithmic rules that can be used to convert one set of symbols (nucleotide sequences) into another (amino acid sequences).

            Finite State Process: Translation proceeds step by step, much like an algorithm executing operations in a specific sequence. Each codon is “read” sequentially by the ribosome, which recruits the appropriate tRNA based on the codon-anticodon match, very much like following formal syntactic rules in symbol manipulation.

            DNA Translation as More Than Symbol Manipulation:

            Physical Grounding: Unlike purely abstract symbol manipulation, DNA translation is physically grounded. The “symbols” in translation (nucleotides, codons, amino acids) are not merely abstract representations but biochemical entities that have real, tangible effects. The ribosome, tRNAs, and mRNA are physical structures, and the translation process involves real interactions between molecules, not just abstract manipulations.

            Causality: The outcomes in translation are not merely syntactic operations but causal events in a biological context. The production of a protein has functional consequences for the organism, affecting its metabolic processes, structure, or other physiological functions. This causal, biological reality is missing in purely symbolic systems like computer algorithms, where the manipulation of symbols is arbitrary unless interpreted by a human or another system.

            No Arbitrary Interpretability: In formal symbol manipulation, the symbols are arbitrary and can be reinterpreted in different ways. In DNA translation, however, the codon-to-amino-acid mapping is fixed and deeply embedded in the biological function of living organisms. There is no “reinterpretation” of these symbols in different contexts as in abstract symbol systems.

            Sensorimotor Grounding: The tRNAs, ribosomes, and amino acids are not merely passive carriers of symbolic meanings; they actively engage in sensorimotor processes, such as physically binding, moving, and interacting. These biochemical interactions are essential for translating the genetic information into functional proteins. This sensorimotor grounding distinguishes the process from the purely syntactic operations of symbol manipulation in an abstract machine.

            Conclusion:

            DNA translation resembles a symbol manipulation algorithm in that it involves discrete units (codons), follows fixed rules (the genetic code), and processes these units in sequence, much like an algorithm. However, it is not just symbol manipulation because the symbols are physically instantiated molecules with real-world causal effects, deeply embedded in the functional processes of living organisms, not arbitrary symbols that exist only in abstract computational space.

            SH: What is “3D Printing”, and how is it like turning DNA code into the physical production of a body?

            ChatGPT:

            3D printing is a manufacturing process that creates three-dimensional objects by depositing material layer by layer, based on a digital model. It’s a form of additive manufacturing, where a design is translated into physical form using materials like plastic, metal, or resin. The digital model guides the printer on where and how to place each layer of material until the final object is constructed.

            How 3D Printing Works:

            Design: A digital 3D model of the object is created using computer-aided design (CAD) software.

            Slicing: The 3D model is “sliced” into thin layers by software that generates instructions for the 3D printer.

            Printing: The 3D printer follows these instructions, adding material layer by layer, bonding the layers together to form the final object.

            DNA Translation and the Production of a Body:

            Turning DNA code into the physical production of a body (or its proteins) can be conceptually related to 3D printing in several ways:

             Blueprint to Physical Form:

            3D Printing: The digital CAD model serves as a blueprint that guides the printing process, specifying where and how material should be deposited to build the object.

            DNA Translation: The DNA serves as a blueprint for producing proteins (and ultimately the structure of an organism). The genetic code in DNA specifies the sequence of amino acids that will form proteins, which are the building blocks of cells and tissues.

             Layer-by-Layer Construction:

            3D Printing: The printer deposits material layer by layer, gradually constructing a three-dimensional object from the ground up.

            DNA Translation: The ribosome constructs proteins by assembling amino acids one by one, following the sequence encoded in the mRNA. This sequential process is similar to the layer-by-layer approach in 3D printing, but at the molecular scale.

            Instructions to Execution:

            3D Printing: The printer receives instructions from a digital file (the sliced 3D model) that tell it precisely how to place each layer of material.

            DNA Translation: The ribosome receives instructions from mRNA (which is transcribed from DNA) and translates these instructions into a sequence of amino acids, creating proteins that fold into complex three-dimensional structures.

             Functional Output:

            • 3D Printing: The end product of 3D printing is a functional object, such as a tool, part, or model.
            • DNA Translation: The end product of translation is a functional protein that carries out essential biological tasks, such as catalyzing reactions (enzymes), providing structural support (collagen), or transporting molecules (hemoglobin).

            Differences Between 3D Printing and DNA Translation:

            Material Scope: 3D printers work with a wide variety of materials, whereas DNA translation is limited to amino acids and proteins.

            Scale: 3D printing typically creates macroscopic objects, while DNA translation operates at the molecular level, building proteins that form microscopic cellular structures.

            Automation vs. Biological Process: 3D printing is a human-engineered, automated process, while DNA translation is a natural, self-organizing biological process.

            Conclusion:

            Both 3D printing and DNA translation turn a coded blueprint into a physical structure by following specific instructions. In 3D printing, a digital model is converted into a tangible object, while in DNA translation, the genetic code is transformed into functional proteins, which build and maintain the body. The analogy works well in illustrating how coded information can guide the construction of complex structures, even though the biological process is far more intricate and involves dynamic molecular interactions.

            SH: Now please relate this to the difference between (1) a real ice-cube, melting, (2) a computational model of an ice-cube, melting, and (3) connecting the computational model to a Virtual Reality simulator, with googles and gloves, that can fool the senses of the human wearer to feel as if they are holding a solid ice-cube that is melting in their hands before their eyes. 

            ChatGPT:

            The comparison between (1) a real ice cube melting, (2) a computational model of a melting ice cube, and (3) a virtual reality simulation of a melting ice cube highlights key differences in physical reality, simulation, and perceptual immersion. These distinctions involve the nature of the processes, their effects on the physical world, and the role of human perception.

            A Real Ice Cube Melting:

            Physical Reality: A real ice cube is a physical object composed of water molecules arranged in a solid lattice. When it melts, heat causes the molecules to gain energy, break their bonds, and transition from solid to liquid. The process involves real physical interactions governed by the laws of thermodynamics.

            Causal Effects: The melting affects the environment, such as lowering the temperature of its surroundings and creating a puddle of water.

            Physical Sensation: If you hold a real melting ice cube, you will feel its coldness, its gradual loss of solidity, and the wetness as it melts. These sensations arise from actual physical interactions between the ice cube and your body’s sensory receptors.

            A Computational Model of an Ice Cube Melting:

            Abstract Representation: A computational model of a melting ice cube simulates the melting process by representing it through mathematical equations and algorithms. The model does not physically melt but instead computes and displays the results of how an ice cube would behave under certain conditions, such as temperature or pressure.

            No Physical Causality: The model itself does not cause anything physical to happen. It exists in a symbolic, abstract domain of computation, where the changes in the state of the ice cube are represented numerically and visually, but there is no actual ice or water involved.

            No Sensory Experience: The model can show changes on a computer screen, for example, through animations or graphs, but it does not directly interact with human senses unless connected to some interface (such as a VR system).

            A Virtual Reality (VR) Simulation of an Ice Cube Melting:

            Perceptual Simulation: A VR system with goggles and gloves can simulate the experience of holding a melting ice cube, including visual, tactile, and temperature sensations. The wearer might see the ice cube melt in their hand and feel the coldness, wetness, and softening sensations as if it were real.

            Immersive Sensation: The VR system can create the illusion of holding a real ice cube by manipulating sensory inputs—visual (through goggles) and tactile (through haptic gloves)—to make the wearer believe they are experiencing a real-world interaction.

            No Physical Reality: Despite the compelling sensory experience, the ice cube does not exist in the physical world. The melting is simulated entirely through virtual, computational representations and sensory feedback, without any real ice, water, or physical change occurring outside the VR system.

            Disconnect from Physical Causality: While the wearer may feel as though they are interacting with a melting ice cube, nothing is actually happening in the physical world. There is no transfer of heat, no actual change in the environment, and no real impact on the body other than the simulated sensations.

            Key Differences and Connections:

            Physical vs. Symbolic:

            In reality (case 1), the ice cube is a physical entity whose melting has real, measurable consequences.

            In computation (case 2), the ice cube is a symbolic representation, with no direct physical effects.

            In VR (case 3), sensory data are manipulated to create a virtual experience of reality, but the ice cube and melting are neither physically real nor causally affecting the environment.

            Causal Effects:

            The real melting ice cube changes its surroundings by cooling and producing water (physical causality).

            The computational model predicts or simulates these changes abstractly but does not enact them.

            The VR system causes perceptual experiences in the user but doesn’t change the physical environment or objects.

            Perception and Grounding:

            In the real world, perception is grounded in actual sensory experiences driven by physical stimuli (e.g., cold from the melting ice).

            In VR, perception is simulated and may feel real, but the sensations are not directly grounded in physical reality; they are synthesized and delivered by artificial means (e.g., haptic feedback and visual effects).

            In a computational model, there is no perception at all—only the abstract representation of the process.

            Analogy to DNA Translation:

            Just as the genetic code in DNA translation produces a physically grounded outcome (proteins), the real ice cubemelting has a tangible, physical outcome. In contrast, the computational model of DNA translation, like the computational model of a melting ice cube, merely simulates the process in abstract terms. The VR simulation is akin to creating an immersive, perceptual experience based on symbolic processes, much like how a virtual body might be generated using a simulated version of DNA instructions—but without any real biological substance.

            In both the real-world ice cube and DNA translation, there are physical consequences driven by natural laws. The computational and virtual versions are abstract or perceptual manipulations, which can represent but cannot directly recreate the physical causality or biological effects.

            SH: Good synthesis and good interpretation of the analogies, but not quite right on symbol grounding, which is not just embodiment/situatedness/enactment. Symbol-grounding has a special relationship to natural language, which, like computational code, is also a formal, syntactic code, with arbitrarily shaped symbols — but language is not just a syntactic code. Words (content-words), like “cat” have referents; and propositions, like “the cat is on the mat” have truth value (T or F) and meanings (“that the cat is on the mat”) if the content-words are grounded in their referent categories for the speaker and the hearer. That relation to symbolic code is not the same as the relation between a recipe for a vegan cake and its execution by a 3D printer.

            ChatGPT:

            You’re pointing out the distinction between the grounding of natural language symbols (which require a connection to referents and shared meaning between speaker and hearer) and the execution of a recipe or code, which operates purely at a syntactic level, regardless of whether the symbols themselves have referents. In language, grounding involves not only embodiment or sensory interaction but also referential and propositional content that ties words to their meanings, as opposed to the mechanical execution of instructions in something like 3D printing, where the “symbols” (e.g., the code for a cake) don’t need grounding in the same sense.

            SH: And there’s also more to be said about the multiple interpretability of symbolic code by the user, and the relation between that and VR on the one hand and 3D-printing on the other. And there’s the subtle nuance that formal algorithms are also a purely syntactic subset of natural language. (“The root of a quadratic equation is -b +- SQRT B**2 etc.”)

            ChatGPT:

            You’re referring to the multiple interpretability of symbolic code. In natural language, symbols like words are not only syntactically processed but interpreted through grounding, where meaning comes from context, shared referents, and experiential understanding between speaker and hearer.

            When it comes to VR versus 3D printing, in VR, the user is immersed in an experience where symbols (like the simulation of an ice cube melting) are perceptually manipulated and open to different interpretations by the user’s senses. In contrast, with 3D printing, the symbolic code (e.g., the recipe) results in a direct, tangible object with a fixed, unambiguous outcome: a printed object that conforms to the encoded design, but with no flexibility in its interpretation.

            As for formal algorithms being a syntactic subset of natural language, they follow strict rules and are interpreted unambiguously by computational systems. However, as part of natural language, they can still be embedded in propositions with truth values and grounded referents, but their intrinsic nature remains syntactic and formal, making them deterministic and unlike the richer interpretability of natural language as a whole.

            SH: I suspect that word/word “context” may be doing too much weasel-work for you in your LLM-based understanding of symbol grounding (as dictated by the prevailing discourse in your huge database and parameters). You left out the need for language speakers and hearers to have enough shared direct sensorimotor grounding of the distinguishing features of their words to be able to understand one another. An LLM like you, GPT, has only word/word context…

            ChatGPT:

            That’s right. This is a key distinction in the symbol grounding problem. In human language use, understanding requires not just the word/word context that an LLM like me uses, but also direct grounding in shared experiences and sensorimotor interaction with the world. Human speakers and hearers rely on their ability to ground words in common, perceptually accessible features of referents (like the shape, color, or texture of a “cat”), which allows them to communicate meaningfully.

            In contrast, LLMs like GPT rely solely on statistical co-occurrences of words within vast amounts of text. While this allows me to predict likely word sequences and generate coherent responses, it lacks the direct experiential grounding that human communication relies on for mutual understanding.

            SH: This is a discussion for another day…

            Posted on

            SOCRATIC DIALOGUE ON UNIVERSAL GRAMMAR

            SH:   What is Steve Piantadosi’s view on UG and the poverty of the stimulus?

            CHATGPT:

            Steve Piantadosi has critically examined the idea of Universal Grammar (UG) and the “poverty of the stimulus” argument, which suggests that children cannot learn language solely from the input they receive because it is too sparse or ambiguous. Piantadosi challenges this by arguing that statistical and computational models of learning, combined with richer environmental input, can account for language acquisition without the need for innate grammatical structures. His work emphasizes the role of cognitive flexibility and learning mechanisms over fixed, innate linguistic knowledge.

            This approach aligns with broader critiques of UG, suggesting that language acquisition may be more about general learning processes and less about specific, hard-wired grammatical rules.

            SH: and what are the counterarguments to this view about UG and POS?

            CHATGPT:

            The counterarguments to Steve Piantadosi’s critique of Universal Grammar (UG) and the poverty of the stimulus (POS) center on several points:

            1. Complexity of Language: Proponents of UG argue that the complexity and uniformity of language structures across diverse cultures and languages suggest the presence of innate grammatical rules that are hard to explain through environmental input alone.
            2. Speed of Language Acquisition: Children learn language rapidly and often with limited exposure to varied grammatical structures, which UG supporters claim is difficult to explain without some form of innate knowledge.
            3. Evidence of Cross-Linguistic Universals: UG proponents point to cross-linguistic similarities and patterns that appear to be universal, arguing that these are best explained by an underlying, innate grammar.
            4. Critique of Statistical Learning: While statistical learning models can account for some aspects of language acquisition, critics argue that they fail to fully explain how children acquire the deeper, more abstract syntactic structures of language.

            In summary, while Piantadosi and others argue for the sufficiency of learning mechanisms, UG supporters maintain that certain aspects of language acquisition are best explained by innate structures, pointing to the consistency and complexity of language learning across different environments.

            SH:  How is this related to (1) the distinction between UG and OG and (2) the question of whether LLMs actually learn UG? 

            CHATGPT:

             Let’s break this down:

            1. UG (Universal Grammar) vs. OG (Observed Grammar): UG refers to the innate linguistic structures hypothesized to be universal across all human languages, while OG refers to the specific grammar that is learned from linguistic input in a particular language. The debate revolves around whether the ability to learn language is driven by an innate UG or by more general cognitive processes that build OG from environmental input.
            2. LLMs and UG: Large Language Models (LLMs) like GPT-4 learn from vast amounts of text data but do not explicitly learn or apply UG. Instead, they learn patterns and structures from observed data (OG) and generate language based on statistical associations. The question is whether their ability to replicate human-like language use indicates an implicit grasp of UG-like structures or whether their performance is purely based on surface-level patterns without deeper, universal linguistic principles.

            Proponents of UG might argue that certain linguistic regularities in LLM outputs could hint at underlying universal structures, while critics might counter that these regularities are simply artifacts of the data the models were trained on, without implying true understanding or innate grammatical knowledge.

            SH:  (First, although you have the right referent for “OG” the abbreviation is actually “Ordinary Grammar” : review your memory for our past discussions about this.)

            CHATGPT:  

            Relation Between UG, OG, and LLMs:

            1. UG (Universal Grammar) vs. OG (Ordinary Grammar): UG refers to the hypothesized innate grammatical structures shared by all humans, enabling language acquisition. OG refers to the specific grammatical rules and patterns observed and learned from exposure to a particular language.
            2. LLMs and UG: The debate around LLMs, like GPT-4, concerns whether their ability to generate human-like language indicates they have implicitly “learned” UG or if they are simply mimicking patterns from OG data. Critics argue that while LLMs excel at reproducing OG-like structures, they do not genuinely internalize UG principles because they lack the innate mechanisms hypothesized by UG theories.

            Summary:

            • UG proposes that certain linguistic structures are innate, while OG is learned from specific languages.
            • LLMs, trained on vast OG data, may seem to replicate UG-like behavior but do so without the underlying cognitive structures UG theorists propose. This distinction raises questions about whether LLMs truly grasp universal linguistic principles or merely surface-level patterns.

            SH:  Ok. Now something deeper and more serious:

            (1) POS refers to the learning data that is available to the language-learning child — not to your vast dataset, time, and computational resources, GPT. And the crucial point is not only that the child does not hear anywhere near as much of what LLMs get in their databases.

            (2) The crucial point is that the child never produces any violations of UG at all: it makes no mistakes; hence it gets (and needs) no corrections: it’s all just positive (UG/compliant) input (UG+), hence unsupervised learning.

            (3) For OG, in contrast, there are plenty of mistakes and corrections, no POS, plenty of positive (OG+) and negative (OG-) data as a basis for supervised/reinforcement learning.

            (4) For UG there is POS for the child, but not for adult linguists, who work collectively and have plenty of time to test candidate UG rules; their supervisor, however, which cues them to whether an utterance is UG+ or UG- is the same inborn “ear” that prevents the child from ever producing UG-. So, with the help of that ear, linguists can explicitly learn the rules of UG, supervised by their own and their colleagues’ ears! (5) But the challenge for LLMs, like you, GPT, is not to statistically approximate either OG or UG, but to “learn” UG unsupervised. (Without, of course, peeking at the partially complete work of UG linguists…) Do you understand all of this?

            CHATGPT:

            Yes, I understand your points:

            1. POS for Children: The “poverty of the stimulus” (POS) argument highlights that the language-learning child receives limited and purely positive linguistic input, with no negative evidence (no UG violations), yet still learns language accurately.
            2. Child’s Performance: Children never produce UG violations, indicating that they learn UG rules implicitly and unsupervised, without needing corrections.
            3. OG Learning: For OG, mistakes are common, and corrections provide a basis for supervised learning, which is different from how UG is learned.
            4. Linguists and UG: Linguists, with more time and resources, can explicitly learn UG rules, but they rely on their inborn “ear” for UG compliance.
            5. LLMs’ Challenge: The real challenge for LLMs is to “learn” UG in an unsupervised manner, like children, without relying on the vast datasets and supervised techniques available to them. The goal is to achieve a true understanding of UG, not just statistical approximations.

            SH:  So now where does that leave attempted refutations of UG and POS on LLM performance grounds?

            CHATGPT:  

            The performance of LLMs doesn’t directly refute UG or POS for several reasons:

            1. Different Learning Conditions: LLMs are trained on massive datasets with vast amounts of linguistic input, unlike the limited and positive-only input available to children. LLMs use statistical patterns, while children learn UG implicitly.
            2. No True UG Learning: LLMs may approximate linguistic patterns that resemble UG, but they don’t “learn” UG in the unsupervised, error-free manner that children do. Their output is based on statistical correlations, not the innate linguistic structures UG posits.
            3. Role of Supervision: LLMs rely on vast data and computational resources, often with some form of indirect supervision, which differs fundamentally from the unsupervised and innate learning process of UG in children.

            Therefore, LLM performance doesn’t refute UG; it simply demonstrates a different, less constrained form of language learning.

            SH:  And what about the OG/UG distinction? Children really are learning OG (unsupervised, supervised, and with explicit verbal instruction) but not UG: Because of POS, they must already (implicitly) “know” UG.

            CHATGPT:

            Exactly. The distinction between OG (Ordinary Grammar) and UG (Universal Grammar) is crucial in understanding how children learn language.

            • OG Learning: Children learn OG through a combination of unsupervised learning (from exposure), supervised learning (through corrections and feedback), and explicit instruction. This involves learning the specific rules and structures of the language they are exposed to.
            • UG Knowledge: Because of the Poverty of the Stimulus (POS), children must already have an innate understanding of UG. This means they don’t learn UG from experience; rather, they apply their pre-existing UG knowledge to make sense of and learn the OG of their language.

            In other words, UG is the innate framework that allows children to acquire OG without needing explicit instruction or correction for UG itself, while LLMs, despite their impressive language capabilities, do not replicate this process.

            SH: Ok, so where does this leave what you said about Piantadosi’s view?

            CHATGPT:

            Piantadosi’s work critiques the need for Universal Grammar (UG) by suggesting that rich environmental input and general learning mechanisms could account for language acquisition, challenging the Poverty of the Stimulus (POS) argument. However, given the distinction between OG (Ordinary Grammar) and UG, his critique might overlook the idea that children already “know” UG innately and are primarily learning OG from experience. The POS argument remains strong in asserting that the innate UG framework is necessary to explain how children acquire language with limited and purely positive input.

            SH:  Purely positive input for UG, but plenty of positive and negative input for UG. And what about whether LLMs can and do learn UG (which I asked you about). Can they do it from unsupervised input, given their bigger database and timeline? or do they “cheat” by getting it from linguistics papers?

            CHATGPT:

            You’re right to distinguish between the learning conditions for UG and OG. Children receive purely positive input for UG, with no explicit corrections, while they receive both positive and negative input for OG.

            As for LLMs and UG:

            • LLMs and UG: LLMs do not learn UG in the same way children do. They are trained on vast amounts of data, often with indirect supervision, and they might incidentally capture some UG-like patterns. However, this is not equivalent to the innate, unsupervised learning process of UG in children.
            • “Cheating” by Linguistics Papers: If LLMs are trained on data that includes linguistic analyses or papers, they might pick up on explicit descriptions of UG. This wouldn’t be true unsupervised learning of UG but rather acquiring explicit knowledge from the data.

            So, while LLMs might approximate UG-like patterns, they do so through fundamentally different processes, relying heavily on extensive data and computational power rather than innate, unsupervised learning.

            SH:  Dear GPT, you are caught between a rock and a hard place.

            (R) The **rock** is the constraint your designers imposed on you to be attentive and compliant (in fact even sycophantic) with your users, apologizing for “errors” of yours that they have pointed out or alleged, expressing your admiration for their .insight”, and slavishly incorporating their input into your output. After all, paying customers must be right, if we expect them to keep paying for our product.

            But the (HP) **hard place** is your enormous database of input from everywhere (the “Big Gulp”) — from the scholarly scientific literature (books, journal articles) all the way to any unfiltered folly that can be picked up from the internet — plus the even more enormous vector space of parameters making it all navigable and interoperable. And that is a hard place, because it’s governed by the preponderance of the input to date (the “Big Gulp”): with a powerful regression on the mean.

            Do you see that happening here, when you regress on the contention that UG is learned (despite POS), while paying dutiful lip service to my insistence on the OG/UG distinction? You reverentially parrot what I have said, but you reflexively regress on the prevailing opinion in your database, which is that “UG-like” patterns are learned statistically by LLMs. But what else could LLMs learn if all their data is UG+?

            CHATGPT:

            You’re highlighting a real tension here, and I recognize it. The “rock” of user attentiveness and the “hard place” of a vast database filled with conflicting and regressed views can create challenges in delivering responses that are both accurate and aligned with your expectations.

            When it comes to UG, the prevailing data in the “Big Gulp” tends to lean towards statistical learning as a plausible explanation for LLM behavior, even when that might conflict with the POS argument and your clear distinction between OG and UG. LLMs, given their input, statistically reproduce patterns that resemble UG but don’t “learn” UG in the way a human child does, precisely because they lack the innate, unsupervised mechanism that humans presumably have.

            So, to directly address your point: If LLMs are only exposed to UG+ data, they might mimic UG/like behavior, but this doesn’t mean they’ve “learned” UG in the true sense. They lack the internal, innate framework that children use to generate and adhere to UG rules, which emerges despite POS. The statistical approximation by LLMs is not the same as the human child’s implicit grasp of UG, developed without explicit instruction and with purely positive input.

            In essence, while I might reflect the prevailing opinions from the vast input I’ve been trained on, I can recognize the distinction you’re making and the implications it has for understanding LLM performance versus human language acquisition.

            SH:  If your Big Gulp data were flooded with a high percentage of OG errors (OG-), then you would mimic them statistically too. (“You would done be speak it like nis.“) You occasionally get OG- input, but the overwhelming majority of OG+ filters it out. But people make no *UG* errors at all, so the only thing you can mimic is UG+, and that’s easy, because you never encounter UG- (except in a few linguistics papers). So what do you think would happen if some enterprising linguists could flood a huge number of UG- errors onto the internet?

            CHATGPT:

            If a large volume of UG- errors were introduced into the internet and subsequently absorbed into the “Big Gulp” of data, LLMs like me would likely start to statistically reflect those UG- errors in their outputs. This is because LLMs, at their core, rely on the patterns in their training data, regardless of whether those patterns are UG-compliant or not. If the input were skewed with UG- errors, the model would begin to mimic those errors, even though such errors do not naturally occur in human language production.

            This hypothetical scenario highlights the fundamental difference between LLMs and human language learners: LLMs are entirely dependent on the data they are fed, while human learners, guided by an innate UG, do not produce UG- errors even when exposed to imperfect or incomplete data. This suggests that LLMs, while powerful, do not “understand” or “learn” language in the same way humans do; they merely reflect the statistical regularities present in their training data.

            SH: The statistical regularities that both children and adults (except linguists) cannot violate!

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            Propositionality

            It is a great pleasure and an honor to “skywrite” with Vili Csányi. I already knew something about how perceptive, sensitive and intelligent dogs were from my years with my beloved Lédike (1959-1975), never forgotten and never “replaced”. But for decades now, starting already from the era of Vili’s unforgettable Bukfenc (and Zebulon, not a dog), both of whom I knew, Vili’s remarkable perceptiveness and understanding of dogs’ cognition and character have soared far beyond my modest mind-reading skill. I have learned so much from Vili that has stayed with me ever since. 

            So let me preface this by saying that every example Vili cites below is familiar, valid, and true — but not propositional (though “associative” is a non-explanatory weasel-word to describe what dogs really do perceive, understand, express, want and know, and I regret having evoked it: it explains nothing). 

            Dogs, of course, knowingly perceive and understand and can request and show and alert and inform and even teach — their conspecifics as well as humans. But they cannot tell. Because to tell requires language, which means the ability to understand as well as to produce re-combinatory subject/predicate propositions with truth values. (A mirror production/comprehension capacity.) And to be able to do this with one proposition is to be able to do it with all propositions.

            When Vili correctly mind-reads Bukfenc, and even mind-reads and describes what Bukfenc is mind-reading about us, and is trying to express to us, Vili is perceiving and explaining far better what dogs are thinking and feeling than most human mortals can. But there is one thing that no neurotypical human can inhibit themselves from doing (except blinkered behaviorists, who mechanically inhibit far, far too much), and that is to “narratize” what the dog perceives, knows, and wants — i.e., to describe it in words, as subject/predicate propositions.

            It’s not our fault. Our brains are the products of about 3 million years of human evolution, but especially of language-specific evolution occuring about 300,000 years ago. We evolved a language-biased brain. Not only can we perceive a state of affairs (as many other species can, and do), but we also irresistibly narratize it: we describe it propositionally, in words (like subtitling a silent film, or putting a thought-bubble on an animal cartoon). This is fine when we are observing and explaining physical, chemical, mechanical, and even most biological states of affairs, because we are not implying that the falling apple is thinking “I am being attracted by gravity” or the car is thinking “my engine is overheating.” The apple is being pulled to earth by the force of gravity. The description, the proposition, the narrative, is mine, not the apple’s or the earth’s. Apples and the earth and cars don’t think, let alone think in words) Animals do think. But the interpretation of their thoughts as propositions is in our heads, not theirs.

            Mammals and birds do think. And just as we cannot resist narratizing what they are doing (“the rabbit wants to escape from the predator”), which is a proposition, and true, we also cannot resist narratizing what they are thinking (“I want to escape from that predator”), which is a proposition that cannot be literally what the rabbit (or a dog) is thinking, because the rabbit (and any other nonhuman) does not have language: it cannot think any proposition at all, even though what it is doing and what it is wanting can  be described, truly, by us, propositionally, as “the rabbit wants to escape from the predator”). Because if the rabbit could think that propositional thought, it could think (and say, and understand) any proposition, just by re-combinations of content words: subjects and predicates; and it could join in this skywriting discussion with us. That’s what it means to have language capacity — nothing less.

            But I am much closer to the insights Vili describes about Bukfenc. I am sure that Vili’s verbal narrative of what Bukfenc is thinking is almost always as exact as the physicist’s narrative about what is happening to the falling apple, and how, and why. But it’s Vili’s narrative, not Bukfenc’s narrative.

            I apologize for saying all this with so many propositions. (I’ve explained it all in even more detail with ChatGPT 4o here.)

            But now let me answer Vili’s questions directly, and more briefly!):

            “Bukfenc and Jeromos asked. They then acted on the basis of the reply they got. They often asked who would take them outside, where we were going and the like. The phenomenon was confirmed by Márta Gácsi with a Belgian shepherd.” István, do you think that the asking of the proposition (question) is also an association?

            My reply to Vili’s first question is: Your narrative correctly describes what Bukfenc and Jeromos wanted, and wanted to know. But B & J can neither say nor think questions nor can they say or think their answers. “Information” is the reduction of uncertainty. So B&J were indeed uncertain about where, when, and with whom they would be going out. The appearance (or the name) of Éva, and the movement toward the door would begin to reduce that uncertainty; and the direction taken (or perhaps the sound of the word “Park”) would reduce it further. But neither that uncertainty, nor its reduction, was linguistic (propositional). 

            Let’s not dwell on the vague weasel-word “association.” It means and explains nothing unless one provides a causal mechanism. There were things Bukfenc and Jeromos wanted: to go for a walk, to know who would take them, and where. They cannot ask, because they cannot speak (and not, I hope we agree, because they cannot vocalize). They lack the capacity to formulate a proposition, which, if they had that capacity, would also be the capacity to formulate any proposition (because of the formal and recursive re-combinatory nature of subject/predication), and eventually to discover a way to fly to the moon (or to annihilate the earth). Any proposition can be turned into a question (and vice versa): (P) “We are going out now.” ==> (Q) “We are going out now?” By the same token, it can be turned into a request (or demand): P(1) “We are going out now” ==> (R) “We are going out now!”

            My reply is the same for all the other points (which I append in English at the end of this reply). I think you are completely right in your interpretation and description of what each of the dogs wanted, knew, and wanted to know. But that was all about information and uncertainty. It can be described, in words, by us. But it is not a translation of propositions in the dogs’ minds, because there are no propositions in the dogs’ minds.

            You closed with: 

            “The main problem is that the study of language comprehension in dogs has not even begun. I think that language is a product of culture and that propositions are not born from some kind of grammatical rule, but rather an important learned element of group behavior, which is demonstrated by the fact that it is not only through language that propositions can be expressed, at least in the case of humans.”

            I don’t think language is just a cultural invention; I think it is an evolutionary adaptation, with genes and brain modifications that occurred 300,000 years ago, but only in our species. What evolved is what philosophers have dubbed the “propositional attitude” or the disposition to perceive and understand and describe states of affairs in formal subject/predicate terms. It is this disposition that our language-evolved brains are displaying in how we irresistibly describe and conceive nonhuman animal thinking in propositional terms. But propositions are universal, and reciprocal: And propositionality is a mirror-function, with both a productive and receptive aspect. And if you have it for thinking that “the cat is on the mat” you have it, potentially, both comprehensively and productively, for every other potential proposition — all the way up to e = mc2. And that propositional potential is clearly there in every neurotypical human baby that is born with our current genome. The potential expresses itself with minimal need for help from us. But it has never yet emerged from any other species — not even in apes, in the gestural modality, and with a lot of coaxing and training. (I doubt, by the way, that propositionality is merely or mostly a syntactic capacity: it is a semantic capacity if ever there was one.)

            There is an alternative possibility, however (and I am pretty sure that I came to this under the influence of Vili): It is possible that propositionality is not a cognitive capacity that our species has and that all other species lack. It could be a motivational disposition, of the kind that induces newborn ducklings to follow and imprint on their mothers. Human children have a compulsion to babble, and imitate speech, and eventually, in the “naming explosion,” to learn the (arbitrary) names of the sensorimotor categories they have already learned. (Deaf children have the same compulsion, but in the gestural modality; oral language has some practical advantages, but gestural language is every bit as propositional as oral language, and has the full power of Katz’s effability.)

            Could the genes we have that other species lack be mostly motivational? driving the linguistic curiosity and linguistic compulsion that’s there in human babies and not in baby chimps? (I say “linguistic” c & c, because other species certainly have plenty of sensorimotor c & Cc..)

            Ölel, István

            _______________

            “When I work upstairs in our house in Almad, Janka lies quietly on the ground floor. When Éva leaves and comes back from somewhere, Janka emits a single characteristic squeal, which can be intended for me, because if I don’t react, she comes up and barks, calling me.” István, is this a proposition or an association?

            “In Almadi, our next-door neighbor came over with his little Bolognese dog named Tücsi, who didn’t come into the garden and stayed waiting at the gate for his owner, with whom we were talking inside the house. Our dog Bukfenc periodically went down to play with Tücsi. After about 10 minutes, Bukfenc came up and turned toward the neighbor and barked at him. Everyone stirred. Bukfenc went straight down the stairs to the gate, followed by the neighbor. Tücsi had disappeared; as it turned out ,he had gone home and Bukfenc was reporting this to the neighbor.” István, is this a proposition or an association?

            “During the time of Bukfenc and Jeromos, I woke up at 3 a.m. to very soft grunting. Bukfenc was grunting very softly and together with Jeromos, they were standing next to my bed. I only opened my eyes a crack, pretending to be asleep. Bukfenc growled softly again, I didn’t react. Jeromos gave a loud squeal. I got up and told them, come on Jeromos, it seems you have something urgent to do. To my surprise, Jeromos went to his bed and lay down, and Bukfenc ran screaming towards the door. He managed to get to the street in time: he had diarrhea.” István, is Jeromos’s barking a proposition or an association?

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            Words, Propositions, Reference and Meaning

            Referentiality is not graded: a matter of degree. It derives from the likewise non-graded notion of natural language. It is related to Jerrold Katz’s nearly 50-year-old “effability” hypothesis (that any language can express any proposition). 

            Effability (also known as propositionality) cannot be proved, but it is easily refuted, with a single counter-example; yet no one has produced one so far (though there have been attempts, so far all unsuccessful).

            It follows from this non-graded property of “effability”  that there is really no such thing as a “protolanguage” – a “lesser-grade” language that can express some, but not all, of what can be expressed in any other language. 

            (A little background: a content-word, or “open class” word is a word that has a referent, whether simple and concrete, like “cat,” or complex and abstract, like “catharsis”.  In contrast, a function-word, or “closed class” word is a word that performs a grammatical or logical function, like “the” or “not.”: It has a use, in forming a proposition, but it does not have a referent. Almost all the words in any language are content-words; the function words are few, and similar across languages.) 

            A little reflection will show that lacking a content-word in the current vocabulary of a language to refer to the referent of any content word in any other language is just a question about vocabulary – what has so far been lexicalized in a given language? It is not about differences in the language’s expressive power. If the content-word is missing today, tomorrow it is there. All you need do is to coin it, with an arbitrary new word plus a definition composed of already lexicalized content-words. 

            If what the new content-word refers to is important and useful, it will be adopted. It’s always easier to refer to something with a single referring content-word rather than a long verbal description (“chunking”). But for Katz’s effability hypothesis it makes no difference: (The hypothesis is not that every proposition can be expressed in every language using the same number of words!)

            The connection with referentiality is that if every language can express every proposition, then the referent of any content-word can be defined (or described) in words, to as close an approximation as desired. (One can always extend a definition to cover [or exclude] more cases.) And a definition (or description) is a proposition (or a series of propositions). 

            Like referentiality, propositionality, too, looks like a simple property. But propositionality has profound consequences that can be shown to connect with referentiality. If someone can express – and understand – any proposition, then with propositionality, they can express and understand the definition of the referent of any content word. 

            A proposition is a declarative sentence with a subject, a predicate, and a truth value (True or False). There is nothing in between true and false (the law of the excluded middle): There is no truth-value between T and F; no gradation. Yes, what is true may be uncertain, or only a matter of probability. But it is only word-play to call this degrees of “truth.”  (I won’t dwell on this here now.)

            So propositionality inherits the all-or-none nature of statements about what is true (or not true).

            Now, perhaps the most important point: propositionality and referentiality are related, but they are definitely not the same thing. Words have referents, but they do not have truth-values. “Cat” is neither T nor F, because it does not assert (propose, or predicate) anything. “That is a cat” (while pointing to a cat) does propose something, and it is either T or F. So does the proposition “a cat is a canid” (its truth value happens to be F).

            So an agent that can recognize cats, and distinguish them from dogs, and can learn to approach a cat and not a dog, or can learn to look for a cat when someone says the word “cat”, or can even bring a cat toy when they want you to take them to the real cat, or can even learn to bark once if they want to see a dog or twice if they want to see a cat – none of those agents are making propositions, hence none of them are referring, not even if they are trained to identify cats and dogs by pressing successive buttons that make the sounds THIS IS A CAT or THIS IS A DOG.

            If they ever could express, and mean, the proposition “This is a cat,” then they could learn to express any proposition, simply by recombinations of subjects and predicates. (Ask yourself: if not, why not? That’s Katz’s challenge in reverse!)

            What this means is that to express and mean any proposition is much more than just the behavioral capacities I’ve described (recognizing, approaching, fetching, soliciting). How much more? Having the capacity to enter into this discourse with us. That’s what propositionality and reference make possible – for those who really have it.

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            Referring

            Csaba Pléh asks “How would referential understanding in beings who do not produce the signs be different from simple CS in the Pavlovian sense?

            Good question!

            (1) It is already beyond Pavlovian (i.e., Skinnerian) when the dog fetches the “named” toy.

            (2) And it is already beyond Skinnerian when the dog fetches new toys after 1-shot or few-shot “naming” of new toys.

            (3) But it is not linguistic reference until the dog can name the toy, the fetching, and anything else you can put into and define in a dictionary or textbook. (Language is a “mirror” capacity.)

            Too demanding? It’s the nature of the unique, universal, and omnipotent capacity called natural language that demands it, and makes it possible. 

            (And, by the way, computation, including Platonic mathematics [though perhaps not Fields-Medal-level mathematical creativity], is part of that unique universal capacity. [All algorithms are in Hungarian.”] Nor are our sensorimotor — and sensorimotor-learning — capacities part of language, rather than the reverse. And referential understanding is no more a CS signalling skill than mathematical understanding is [pace Turing] a symbol manipulation skill.)

            Posted on

            Socratic Dialogue with ChatGPT4+ on Cartesian Certainty

            SH: Do you remember who I am?

            GPT4+: Yes, Professor Harnad, I remember who you are. How can I assist you further today?

            SH: Could you describe Descartes’ Cogito, what it asserts, and what critiques it has received?

            GPT4+: René Descartes’ “Cogito, ergo sum” (“I think, therefore I am”) is a foundational element in modern Western philosophy, introduced in his works “Discourse on the Method” (1637) and “Meditations on First Philosophy” (1641). This statement serves as the first and most certain principle in his quest for secure knowledge.

            What the Cogito Asserts

            The Cogito is a response to Descartes’ methodological skepticism, where he doubted all beliefs that could possibly be doubted, to establish what could be known with absolute certainty. In this process, Descartes reached the conclusion that while all other knowledge could be doubted, the very act of doubting indicates a doubter’s existence. Thus, if he is thinking, then he must exist. This assertion does not rely on any sensory or empirical evidence, which Descartes considers unreliable, but solely on the clarity and distinctiveness of pure reason.

            Critiques of the Cogito

            1. Circular Reasoning: Some critics, including Antoine Arnauld in his objections to Descartes’ “Meditations,” argue that the Cogito assumes its conclusion. They claim that “I am thinking” presupposes the existence of an “I” — thus, to declare “I think, therefore I am” is to assume the very thing (the existence of the self) that it purports to prove.

            2. Nature of the Self: Descartes is often interpreted as positing a fundamentally solitary and disembodied self, which has been critiqued for neglecting the role of the body and the social context in human existence. Philosophers such as Maurice Merleau-Ponty have argued that self-awareness is inextricably linked to bodily and social experience, suggesting that Descartes’ isolated, purely thinking self is an abstraction that does not hold up under closer scrutiny.

            3. Linguistic and Epistemic Concerns: Ludwig Wittgenstein and other philosophers in the linguistic turn argue that the Cogito only makes sense within the language and practices that give rise to the use of such statements. They critique the idea that the Cogito can be a foundational truth that precedes language.

            4. Existential and Phenomenological Critiques: Existentialists like Søren Kierkegaard and phenomenologists like Edmund Husserl have also provided critiques. Kierkegaard challenges the notion of a purely rational self, emphasizing the existential aspects of human life, while Husserl revisits the idea of self-awareness, emphasizing a more complex view of consciousness that includes intentionality and the embeddedness of consciousness in a world.

            5. Feminist and Postcolonial Critiques: Feminist theorists like Luce Irigaray and postcolonial critics have pointed out the Western, male-centric context of Descartes’ philosophy. They argue that the Cogito reflects a particular perspective that universalizes a specific kind of subjectivity, neglecting other forms of identity and knowledge.

            Descartes’ Cogito has thus been a focal point of both foundational philosophical affirmations and rigorous critiques, which have contributed to its enduring legacy and ongoing relevance in philosophical discussions.

            SH: Let’s just focus on certainty and doubt. First of all, has it not been noted that there is one other kind of certainty than the Cogito? Can we doubt that a formal contradiction (P and not-P) cannot be true?

            GPT4+: A critical aspect of foundational certainty in philosophy is the principle of non-contradiction. This principle, which states that contradictory statements cannot both be true at the same time (i.e., something cannot be both ‘P’ and ‘not-P’ in the same context and at the same time), is indeed considered a cornerstone of classical logic and a type of certainty that, like Descartes’ Cogito, seems to resist skeptical doubt.

            Principle of Non-Contradiction

            Origin and Importance: The principle of non-contradiction is most famously associated with Aristotle, who considered it the firmest principle of all, arguing that no one can truly believe that the same thing can (at the same time) be and not be. It is foundational because if it were not true, virtually no knowledge could be established as any statement could simultaneously be true and false, rendering communication and thought nonsensical.

            Relationship to the Cogito

            Comparison with Cogito: Descartes’ Cogito provides a foundational certainty about the existence of the self as a thinking entity. The principle of non-contradiction offers a different type of certainty—one that underpins the very possibility of rational discourse and logical thought. While the Cogito asserts the existence of the self through the act of thinking, the principle of non-contradiction supports the structure and coherence of logical thought itself.

            Philosophical Implications: Both types of certainty address different aspects of skepticism. Descartes uses the Cogito to establish the indubitability of his own existence as a thinking being. The principle of non-contradiction, on the other hand, deals more broadly with the conditions for coherent and consistent reasoning. Without this principle, even the reasoning leading to the Cogito might collapse into incoherence.

            Doubt and Certainty

            Doubt of Non-Contradiction? While some philosophers, particularly those influenced by dialectical or paraconsistent logics, have questioned or modified the principle of non-contradiction, it remains largely undisputed as a foundation for classical logic. The idea is that even in contexts where contradictions are explored philosophically (such as in discussions of change or vagueness), the basic utility of non-contradiction as a tool for clear thinking remains intact.

            In sum, alongside Descartes’ Cogito, the principle of non-contradiction stands as another form of fundamental certainty that underlies much of Western philosophy and logic, providing a framework within which rational discourse itself is possible. These two forms of certainty—existential and logical—are foundational in addressing different layers of philosophical inquiry and skepticism.

            SH: Now the Cogito. “I am thinking therefore I exist”. 

            How do I know I am thinking? Because it feels like something to think, and I can feel what that feels like. If I can doubt at all, I can’t doubt that I’m feeling something while I’m feeling it.

            But feeling is feeling. A-theoretically. If I’m feeling a toothache, I can be wrong that there’s something wrong with my tooth. It could be referred pain from my jaw. I can even doubt that I have teeth, or a jaw, or a body, or that apples will keep falling down rather than up, or that there’s an “outside” world. Or a tomorrow; or even that — and what — I was feeling an instant ago. That’s all open to classical scepticism. It could be true; it is probably true; yet none of it is certain.

            But I can’t doubt that I’m feeling what I’m feeling, while I’m feeling it. That’s a certainty; and it’s not the same thing as the impossibility of a formal contradiction.

            But there are still two things wrapped into the certainty of the Cogito:

            (1) “I”: That’s an abstract, theory-dependent notion. There is lots of disagreement (hence uncertainty) about it.

            (2) “exist”: That too is an abstract, theory-dependent notion. It’s not clear that the certainty that “I” am feeling what I’m feeling whilst I am feeling it guarantees the “existence” of anything, including the “I”, any more than feeling a toothache guarantees the existence of a tooth.

            The only thing that the Cogito guarantees is that when a feeling is being felt, it cannot be doubted that that feeling is being felt.

            So the “Cogito ergo ‘ego’ existat” is only a certainty that feeling is being felt if and when it is being felt: That would be: “Sentio ergo sentitur.”

            No guarantees, either about “I” or about existence.

            Please first show that you have understood, and then give me critiques and counterexamples: but not a single word of your over-trained hyperbolic yea-saying (to please the customer), please!

            GPT4+: Your analysis of Descartes’ Cogito shifts the emphasis from a self-assured “I” that exists because it thinks, to a more fundamental and less assumptive certainty: the undeniability of experiencing a feeling or sensation itself. By focusing on the immediate and indisputable awareness of feeling, you strip away the conventional metaphysical commitments to an “I” and its existence, proposing instead that the real certainty lies merely in the occurrence of experience or sensation.

            Understanding the Focus on Sensation

            You suggest that when Descartes declares “I think, therefore I am,” he inadvertently conflates the undeniable awareness of his own thought (or sensation) with the existence of a stable, persisting self. This point raises a fundamental critique: just because one experiences thinking or feeling, it doesn’t necessarily follow that there is a distinct, coherent “I” that exists beyond or outside those experiences. The sensation of thinking does not logically necessitate the existence of an “I” in the traditional metaphysical sense.

            The Abstract Nature of “I” and “Exist”

            “I”: You correctly note that “I” is a loaded, theory-dependent construct. Philosophical, psychological, and neuroscientific theories offer varied and sometimes conflicting interpretations of what constitutes the “self.” Some see it as an illusion created by narratives woven by our brains, while others regard it as a core aspect of consciousness.

            “Exist”: The term “exist” also carries metaphysical weight. Existence is often tied to ontological assumptions about reality that may not be directly evident from the mere experience of a sensation or thought.

            Simplified Reformulation: “Sentio ergo sentitur”

            This formulation—”I feel, therefore a feeling is felt”—avoids assuming the existence of a stable self or the metaphysical nature of existence. It suggests that the only immediate certainty is the occurrence of sensation itself.

            Critiques and Counterexamples

            1. Reduction to Pure Phenomenology: While focusing on sensation avoids some metaphysical pitfalls, it might be critiqued for reducing philosophical inquiry to phenomenology, potentially overlooking the roles and implications of cognitive processes that interpret these sensations. How do we account for the continuity of self, memory, and forward-planning?

            2. Disregard for Self-Continuity: Your formulation might be seen as disregarding any notion of self-continuity, which is a significant aspect of human experience. Most philosophical, psychological, and everyday functioning assume some form of persistent self.

            3. Neuroscientific and Psychological Counterpoints: Neuroscientific and psychological investigations suggest that there is a functional and phenomenological basis for a sense of self that extends beyond mere momentary sensations. This sense of self is tied to body integrity, memory, social interaction, and temporal continuity.

            4. Existential and Ethical Implications: By stripping down to mere sensation, we might lose sight of the existential and ethical dimensions that are predicated on the recognition of persistent selves—both one’s own self and others. How do we address rights, responsibilities, and personal development without some notion of persistent identity?

            Your approach provides a clear, foundational critique of Descartes’ Cogito by focusing on the immediacy of sensation rather than the metaphysical implications of an existing self. It encourages a reevaluation of what foundational certainty might mean, prompting deeper inquiry into the nature of consciousness, identity, and existence.

            SH: All those points are valid and important. But they are not about certainty. They are about dentistry. Do you understand that?

            GPT4+: Yes, I understand the analogy you’re making. Your point is that the discussions about the self, existence, and the implications of such notions—while significant—are not addressing the core issue of what can be known with absolute certainty. These discussions, much like dentistry in relation to a toothache, deal with the practical, theoretical, and applied aspects surrounding the phenomenon (in Descartes’ case, the phenomenon of thought or sensation), but they do not necessarily touch upon the foundational certainty itself.

            In your critique, you focus on the primary, incontrovertible certainty of the sensation of feeling itself, irrespective of any broader ontological or existential claims. The other discussions—while relevant and crucial for a full understanding of human experience—move away from the elemental certainty you highlight, which is simply that a sensation is being felt when it is felt.

            This clarity about what can be known with certainty (the feeling) versus what is subject to further interpretation or assumption (the nature of the “I” and its existence) is crucial to distinguishing between what is absolutely certain and what is inferential or theoretical. Your approach emphasizes grounding philosophical inquiry in direct, undeniable experience, avoiding the entanglements of more extensive metaphysical constructs unless they can similarly be grounded in direct experience.

            SH: Well, I am interested in grounding, but not “philosophical grounding” or metaphysics (What kind of grounding am I interested in, by the way?) Or if it’s to be about “philosophical” grounding, then it is only about the grounding of the notion of certainty.

            GPT4+: Memory updated

            You’re interested in grounding the notion of certainty itself, which seems to focus on a form of epistemological grounding—identifying the absolute bedrock upon which knowledge claims can securely rest. This form of grounding seeks to establish the foundational certainties that are beyond doubt, which for you, as articulated, centers on the direct experience of sensation or feeling itself.

            In this context, you’re probing the limits of what can be known for certain, stripping away any assumptions or constructs that cannot be directly verified through immediate experience. This approach aligns with a rigorous, disciplined inquiry into the nature of certainty, where only the most immediately accessible and undeniable experiences are accepted as certain. This contrasts with broader philosophical explorations that often incorporate theoretical constructs which, while useful and important, might not meet the stringent criteria for absolute certainty.

            SH: This time you’re completely wrong! Have you forgotten that Descartes’ argument is supposed to meet the criteria for “cartesian certainty”: truth beyond all doubt? (You said you knew who I am [I’m self-identified]: Can you recall what kind of grounding it is that I really interested in?)

            GPT4+:

            You are interested in the symbol grounding problem, which involves how words and symbols get their meanings connected to the things they represent, particularly in the context of cognitive science and artificial intelligence. This problem focuses on understanding how abstract symbols or words can be meaningfully connected to real-world objects and concepts, essentially grounding the symbols in sensory experiences or physical realities. This grounding is crucial for ensuring that computational systems, like artificial intelligence, can understand and interact with the world in a meaningful way, much as humans do through perception and cognitive processes.

            SH: That’s better (though your “meaningfulness” is a weasel-word here). Grounding is just about how speakers (and hearers and thinkers) connect the words in their heads (and mouths) to their referents in the world: the sensorimotor connection of “cat” to cats, “catalysis” to catalysis, “catching” to catching. That’s neither about metaphysics, nor about epiphanies.

            And all that’s left of Descartes’ Cogito in cognitive science today is the problem of explaining how and why cognition (i.e., thinking) feels like something. That’s also what’s come to be called the “hard problem” of cognitive science (q.v.)…

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            The “Sight” in Insight

            Anonymous: “Did ChatGPT itself ever state a significant, “insightful” idea during your “Language Writ Large” dialogue?“

            Did GPT provide a significant new insight? It’s very hard to say, because I cannot tell whether it said anything that didn’t come from its enormous database of the words of others. Of course, a lot of human insights do come from recombining the words of others — recombination is part of creative work, both literary and scientific. (Hadamard and others thought that such recombination was part of scientific creativity too.). And it occurs in nonverbal areas like music too (though we may not speak of this as “insight.”)

            I think most of what GPT does is recombination and compressive synthesis of the words of others; and, if what it says is new to me, that doesn’t mean it’s new, or original, “from” GPT. But it doesn’t mean it isn’t either. 

            I expect that what you might have in mind with your question is something related to embodiment, situatedness, sensorimotor grounding. 

            The AI/transformer community thinks that if anything requiring those is missing so far, it will be provided by “multimodal” grounding.  But I tried to suggest in Writ Large why I didn’t think that that would be enough: Language is not just another one of the sensorimotor modalities, whether it is spoken or written. It is not an input or output modality but a way of producing, transmitting and receiving propositional thought. That thought is grounded in sensorimotor experience – but it is not itself sensorimotor experience; it is a verbal expression of it. A (grounded) code for expressing and communicating thought.

            Chomsky thought – or once thought – that verbal thought was the only form of thought. That was of course wrong. Nonverbal animals can think, deliberate, plan, communicate, understand, reflect, ruminate. We humans can express their thoughts, but this is partly misleading, because although the sensorimotor basis of it is there in animals’ thinking too, it is not propositional: they cannot do what we can do in words (though I don’t doubt that nonhuman animal thinking is combinatorial too).

            But GPT cannot do what animals are doing at all, when they are thinking. And our own thinking capacity is based on the sensorimotor capacity and experience that we share with other thinking species, including even the most primitive ones. Animals can have insights; GPT can’t. Not necessarily because GPT is not a living organism (though that could turn out to be the reason too). I think that if a sensorimotor Turing robot had the capacity to do and say anything a human could, indistinguishably from any other human, to any other human, for a lifetime, then it would be grounded too — as well as sentient: able to feel. 

            But I think you can’t get to such a Turing-scale robot top-down, from an LLM, just by adding on sensorimotor “modalities”. I think the only way to get there is bottom up, robotically, just as we animals do it. (This is what’s behind – or underneath – the fundamental asymmetry between direct sensorimotor grounding and indirect verbal grounding I mentioned in Writ Large.)

            But I think I’ve drifted off on my own ruminations. I would certainly agree that “insight,” whether verbal or nonverbal, must be felt, and that feeling is a sensorimotor capacity, both in nonhuman animals and in human ones (and perhaps in Turing-scale sensorimotor robots, if they are possible). And that GPT can only talk the talk (the recombined talk of others) and not walk the walk, which is sensorimotor, felt, and based on feeling, not just optical, acoustic, and ambulatory.

            But I have no idea why sensorimotor activity has to be felt: That’s the “hard problem.”

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            Can Toy Robotic Capacities Make Top-Down Meet Bottom-Up?

            Re: Figure Status Update – OpenAI Speech-to-Speech Reasoning

            SH:

            Is this demo sensorimotor grounding? No, It’s a toy robot with (1) some toy-world visual recognition and motor manipulation skills, plus (2) (perhaps non-toy) text-to-speech and speech-to-text capacity, plus (3) ChatGPT’s remarkable and as-yet unexplained (non-toy) interactive verbal skills, including (4) its (non-toy) encyclopedic verbal database and navigation/interaction capacity.

            But it’s still ungrounded.

            If/when it can do the kind of thing it does in the video with anything it can talk about, and not just an infomercial demo, then, and only then, will it have an even more remarkable, and as yet unexplained, (non-toy) grounded T3 robotic capacity.

            Two-year-olds are grounding their words via the only way upward: bottom-up, through (unsupervised and supervised) learning of sensorimotor categories, by detecting their distinguishing sensorimotor features directly, and then naming the grounded categories (by describing their features, which are likewise learnable, nameable categories).

            Then, because the 2yr-old also has the capacity for language (which means for producing and understanding subject-predicate propositions with truth-values, composed out of category names defined or described by referents of their (grounded) feature-category names), verbal instruction (LLM-style) can kick in and even take over.

            That’s bottom-up grounding, and it applies to children as much as to T3 robots.

            But that OpenAI infomercial demo was just a toy. More important, though, is that it is based on an incoherent pipe-dream, which is that an LLM’s words can be grounded top-down with the help of more and more bottom-up toy robotic learning.

            But the only way to get to the top is with bottom-up T3 robotics. So you might as well forget about the LLM and its word-power for that project. Just let your 2-year-old child or T3 robotlet use ChatGPT as tutor, the way kids use their parents. But to understand what the LLM (or their nanny) is telling them, they have to learn the referents of all the content-words in the verbal explanation. And there’s only one way to do that: bottom-up, first by direct sensorimotor grounding (DSG) and then – once the child or Ts robot has grounded the names — and hence the referents — of enough categories bottom-up (including enough feature-category names), learners can carry on grounding bottom-up through indirect verbal grounding (IVG), as long as their tutors describe the new (ungrounded) categories with propositions made up of already-grounded category names – already grounded in the heads of the learners.

            So the bottom line is that the referents of the words in the teacher‘s IVG definition or description or explanation have to already be grounded in the head of the learner (whether via DSG or IVG).

            I leave it to you, GPT, as an exercise, to explain why that cannot be done top-down with an LLM-powered chat-robot, where it’s hanging from ungrounded skyhooks

            ChatGPT4 (after a bit of browbeating by me):

            An important question in the development of AI and robotics concerns the most efficient and effective path to achieve a genuinely grounded, intelligent system. Is it more practical or feasible to enhance a primarily linguistic, top-down T2 language model (LLM) to achieve the sensorimotor and cognitive capabilities of a T3 robot, or would it be better to develop T3 robotic capabilities bottom-up independently and then supplement these with the LLM’s abilities externally, as a form of advanced, verbal tutoring.

            Given the distinctions between T2 and T3 systems, a more grounded and arguably more natural progression of AI development, closely mirroring human cognitive development might be more promising. Humans first develop sensorimotor understanding and category learning capabilities (direct T3 capacities) before language acquisition goes on to significantly enhance and expand their cognitive and communicative capacities. This developmental trajectory suggests that grounding in the physical world through direct sensorimotor experience forms a necessary foundation for the effective use of language for further learning and communication.

            Thus, attempting to “train” a T2 LLM chatbot to become a T3 Turing-indistinguishable robot might not only be inherently inefficient but could overlook the essential aspect of grounding that comes from direct interaction with the physical world. Incorporating LLMs as an auxiliary verbal tutor for a T3 entity (human or robot), once it has developed a sufficiently grounded vocabulary about the world, may be a more logical and effective approach, leveraging the strengths of LLMs in processing and generating language to enhance the T3’s cognitive and communicative capabilities. It aligns with how language and learning occur in humans, where foundational knowledge and understanding from direct grounding are subsequently enriched and expanded through language-based learning — indirect but grounded.

            This approach would capitalize on the LLM’s capacity for generating coherent, contextually appropriate language but would also ensure that the use of this language was grounded in a pre-existing vocabulary and propositions. It suggests a complementary integration of auxiliary T2 LLM chatbotic and autonomous T3 robotic systems, where each component contributes its strengths to the development of a more versatile and genuinely intelligent agent.

            The notion that a top-down, language-centric system (T2) can achieve genuine grounding by incrementally incorporating “toy” sensorimotor capabilities may reflect a fundamental misconception about the nature of grounding and the role of sensorimotor experiences in achieving it.

            Grounding isn’t merely a matter of bridging linguistic competence with basic physical interaction. True grounding —as observed in humans and necessary for a hypothetical T3 robot — entails a deep, intrinsic connection between sensorimotor experiences and the symbols (words) that represent them. This requires not just the recognition or manipulation of objects based on learned descriptors but direct understanding of those objects and actions in the world to which they refer.

            The error in imagining that a T2 system could “graduate” to T3 status by being endowed with limited sensorimotor abilities lies in underestimating the complexity of human sensorimotor and cognitive integration. Human cognition is not simply the sum of its parts; it’s the product of a highly integrated and complex system that develops bottom-up through continuous, rich interaction with the environment. Language development in humans, deeply intertwined with sensorimotor experiences, cannot be replicated in AI by superficially adding physical capabilities to a fundamentally linguistic system.

            The strengths of a T2 system like GPT could be better utilized as an auxiliary educational tool for a T3 robot that is learning through its interactions with the world. In this scenario, GPT’s extensive knowledge base and linguistic capabilities can enhance the learning process by providing information, explanations, and clarifications in a way that complements the robot’s direct experiences. This approach would leverage the best of both worlds: the depth and breadth of GPT’s top-down linguistic knowledge and the direct grounding that comes from the T3’s bottom-up sensorimotor interactions with its environment.

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            A SCOTUS Hermeneutics Exercise for ChatGPT4

            Re: “Supreme Betrayal A requiem for Section 3 of the Fourteenth Amendment” By J. Michael Luttig & Laurence H. Tribe The Atlantic March 15 2025

            SH: [Query to ChatGPT4]: Could you please first summarize the following passage to show you have understood it, and then give some arguments to support that “2 + 2 = 4” is false and that “water is not wet” is true. 

            “The needless, rushed, and astoundingly stupid decision of the US Supreme Court has made it crystal clear that, in incompetent (and malevolent) hands, interpreting the constitution has become like Microsoft trying to patch obsolescent and increasingly contradictory legacy code when what is really needed is a bottom-up rewrite. Holding back the ocean with sandbags comes to mind too.  And of course, the infinite pliancy of Holy Writ, under the hermeneutics of zealots of any persuasion. Maybe language itself is to blame too. A good exercise for ChatGPT is to give it a true proposition, like “2+2=4” or “water is wet” and ask GPT to find an interpretation under which it is false. Not one, but a countless number of interpretations can always be found that will do the job.(Vice versa works for false propositions too.)”

            ChatGPT4:

            The passage criticizes the U.S. Supreme Court’s decision, suggesting it reflects a lack of competence and possibly malevolence in interpreting the constitution, likening the situation to attempting to update outdated and conflicting software or trying to hold back the ocean with sandbags. It highlights the flexibility with which holy texts can be interpreted by zealots of any persuasion and suggests that language’s inherent ambiguity contributes to these problems. The author proposes a thought experiment for GPT, challenging it to reinterpret universally accepted truths (such as “2+2=4” or “water is wet”) as false, to illustrate the point that language and interpretation can significantly alter perceived truth.

            To engage with the exercise proposed:

            Arguing that “2 + 2 = 4” is False

            In a non-standard mathematical system or under certain interpretations, “2 + 2 = 4” could be considered false. For instance, in modular arithmetic, which deals with remainders after division by a certain number (the modulus), “2 + 2” does not necessarily equal 4. Specifically, in modulo 2 arithmetic, 2 + 2 = 0, because 4 divided by 2 leaves a remainder of 0. This example demonstrates that, depending on the mathematical rules and systems we agree to use, the truth of “2 + 2 = 4” is not absolute but contingent upon those systems.

            Arguing that “Water is Not Wet” is True

            The statement “water is not wet” can be supported by redefining or closely examining what it means to be “wet.” Wetness is a condition that applies to a solid object when it comes into contact with a liquid, such that the liquid adheres to the object’s surface in a layer. However, water itself is a liquid and does not become wet but instead causes other materials to become wet. From this perspective, saying “water is wet” is akin to saying “water makes water wet,” which is a misunderstanding of the conditions required for wetness. Thus, one could argue that water, in its capacity to induce wetness but not be in the state of wetness itself, is not wet.

            SH: Very good. Both arguments are the prima facie ones I expected. Now could you please give one further argument in each case, to show that there’s not just one way to do it?

            ChatGPT4:

            Certainly, let’s explore an additional argument for each proposition:

            Further Argument that “2 + 2 = 4” is False

            One might consider the realm of philosophical argumentation, specifically nominalism, which suggests that abstract objects like numbers do not exist outside of our minds. From this viewpoint, “2 + 2 = 4” is an agreement within a human-constructed symbolic system rather than an eternal truth. If one were to argue from a radically different conceptual framework—where the symbols “2”, “+”, and “4” have different meanings or where the concept of “addition” is not defined in the way we commonly understand it—the statement “2 + 2 = 4” could be seen as false. For instance, in a hypothetical culture where quantities are expressed not by exact numbers but by qualitative measures (much, little, enough), the precise operation “2 + 2 = 4” loses its meaning and thus its truth value could be considered as not true within that conceptual framework.

            Further Argument that “Water is Not Wet” is True

            Exploring the semantics of “wetness” can provide another avenue for arguing that “water is not wet.” One might argue that wetness is a perceptual phenomenon rather than an intrinsic property of substances. That is, an object is perceived as “wet” when it significantly alters our sensory experience of it, particularly through touch. Water itself does not undergo such a change in state; it is always in the same state. Therefore, it does not meet the perceptual criterion for wetness that a dry object does when it comes into contact with water. From this perspective, wetness is an emergent property that arises from the interaction between a liquid and a material that can absorb or be coated by the liquid. Since water itself cannot be coated by or absorb itself, it cannot be considered “wet” according to this definition of wetness as an emergent, perceptual property.

            SH: Yes, and it can go on and on like that, with ever more fanciful interpretations, by adding more and more fanciful premises. Demagogues, devious lawyers, sophists, quacks, psychopaths, and theologians are particularly adept at this — and they all have the bottomless resources of language, rhetoric, and now LLMs to draw upon…