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.