October 6, 2024<\/p>\n\n\n\n
This conversation may reflect the link creator\u2019s personalized data, which isn\u2019t shared and can meaningfully change how the model responds.<\/em><\/p>\n\n\n\n SH<\/strong>: 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?<\/p>\n\n\n\n ChatGPT:<\/strong> The\u00a0Weak Church-Turing Thesis (WCT-T)<\/strong>\u00a0asserts 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.<\/p>\n\n\n\n The Strong Church-Turing Thesis (SCT-T)<\/strong> is more ambitious, claiming that all<\/strong> 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.<\/p>\n\n\n\n Jerrold Katz’s “Effability” Thesis<\/strong> posits that all possible thoughts can be expressed in natural language<\/strong>. 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<\/strong> of language: that anything thinkable is expressible, which has implications for the limits of linguistic representation.<\/p>\n\n\n\n SH<\/strong>: How is the Translatability or Glossability Thesis a lemma of the Effability Thesis?<\/p>\n\n\n\n ChatGPT:<\/strong> The\u00a0Translatability or Glossability Thesis<\/strong>\u00a0is a\u00a0lemma<\/strong>\u00a0(a supporting or subsidiary proposition) of the\u00a0Effability Thesis<\/strong>\u00a0because it follows directly from the idea that all thoughts are expressible in natural language.<\/p>\n\n\n\n According to the Effability Thesis<\/strong>, any possible thought or meaning can be expressed in some language. The Translatability Thesis<\/strong> extends this by asserting that if all thoughts can be expressed in a language, then they must also be translatable into other<\/strong> 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<\/strong>.<\/p>\n\n\n\n The reasoning is as follows:<\/p>\n\n\n\n Effability<\/strong>\u00a0means that each language has the capacity to express any conceivable thought.<\/p>\n\n\n\n Since all languages share this capacity, there is nothing in one language that cannot, in principle, be expressed in another language, implying\u00a0translatability<\/strong>\u00a0or\u00a0glossability<\/strong>.<\/p>\n\n\n\n Therefore, the capacity to express a thought in one language guarantees its translatability into any other language with the same expressive power.<\/p>\n\n\n\n In this way, Translatability<\/strong> is a necessary consequence (lemma) of the broader Effability Thesis<\/strong>: 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.<\/p>\n\n\n\n SH:<\/strong> 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 \u00ab sympathique \u00bb) into English as examples.<\/p>\n\n\n\n ChatGPT:<\/strong> You’re right that\u00a0translatability<\/strong>\u00a0does not imply\u00a0word-for-word<\/strong>\u00a0translatability but rather\u00a0propositional translatability<\/strong>, meaning that the same thought or proposition can be conveyed even if different languages use different words, structures, or idiomatic expressions.<\/p>\n\n\n\n Languages “get around” the problem of word-for-word translation through a variety of linguistic strategies that focus on meaning equivalence<\/strong> rather than lexical or syntactic correspondence. Let’s consider two examples: Schadenfreude<\/em> in German and sympathique<\/em> in French.<\/p>\n\n\n\n Schadenfreude (German)<\/strong>:\u00a0Schadenfreude<\/em>\u00a0refers to the pleasure derived from another’s misfortune. There is no\u00a0single word<\/strong>\u00a0in English that captures this exact meaning. However, we can\u00a0paraphrase<\/strong>\u00a0or describe it in English: \u201cthe feeling of joy or pleasure at someone else’s suffering.\u201d Thus,\u00a0propositional translatability<\/strong>\u00a0is achieved by expressing the same concept, even though the English translation requires more words or a descriptive phrase to convey the same meaning.<\/p>\n\n\n\n Sympathique (French)<\/strong>: The French word\u00a0sympathique<\/em>\u00a0does not directly translate to the English word “sympathetic.” In French,\u00a0sympathique<\/em>\u00a0means “nice” or “likable,” which is a broader or slightly different concept than the English “sympathetic,” which means understanding or compassionate. Again,\u00a0propositional translatability<\/strong>\u00a0is achieved by choosing an appropriate English equivalent based on context, even though there’s no direct one-word match. If translating\u00a0Il est tr\u00e8s sympathique<\/em>, we would say, “He is very likable” or “He is a nice person,” depending on the nuance in the specific context.<\/p>\n\n\n\n In both cases, propositional translatability<\/strong> is possible because language can represent thoughts<\/strong>, even if different languages use different strategies (more words, descriptions, or broader contextual meaning) to express the same proposition. Idiomatic<\/strong> and contextual flexibility<\/strong> allow languages to express the same underlying meaning, fulfilling Katz’s Effability Thesis<\/strong>. Even when there is no exact word-to-word match, the proposition can still be understood and communicated, reflecting the expressive power<\/strong> of natural language across linguistic boundaries.<\/p>\n\n\n\n SH:<\/strong> What is a proposition?<\/p>\n\n\n\n ChatGPT:<\/strong> A\u00a0proposition<\/strong>\u00a0is the\u00a0meaning or content of a declarative sentence<\/strong>, expressing a claim that can be either true or false. It is the abstract\u00a0thought or idea<\/strong>\u00a0conveyed by the sentence, independent of the specific words or language used to express it.<\/p>\n\n\n\n For example:<\/p>\n\n\n\n The English sentence “The cat is on the mat” and the French sentence\u00a0“Le chat est sur le tapis”<\/em>\u00a0both express the same\u00a0proposition<\/strong>: that there is a cat on the mat.<\/p>\n\n\n\n Even though the words and grammatical structures are different, the\u00a0propositional content<\/strong>\u2014the fact being described\u2014is the same.<\/p>\n\n\n\n Key characteristics of propositions:<\/p>\n\n\n\n Truth-value<\/strong>: Propositions are either\u00a0true or false<\/strong>. The proposition “The cat is on the mat” is true if and only if there is indeed a cat on the mat.<\/p>\n\n\n\n Language-independent<\/strong>: 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.<\/p>\n\n\n\n Abstract<\/strong>: Propositions are\u00a0abstract entities<\/strong>\u00a0that are distinct from the sentences used to express them. A sentence is a physical, linguistic entity, while a proposition is the\u00a0idea<\/strong>\u00a0or\u00a0meaning<\/strong>\u00a0the sentence conveys.<\/p>\n\n\n\n In sum, a proposition<\/strong> is the content of a thought<\/strong> or claim<\/strong> that can be evaluated for truth, regardless of the specific language or words used to express it.<\/p>\n\n\n\n SH:<\/strong> 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.<\/p>\n\n\n\n ChatGPT:<\/strong> You’re right, and I\u2019ll clarify the key elements of a\u00a0proposition<\/strong>\u00a0that I missed:<\/p>\n\n\n\n Subject and Predicate<\/strong>: Every\u00a0proposition<\/strong>\u00a0has a\u00a0subject<\/strong>\u00a0(what the proposition is about) and a\u00a0predicate<\/strong>\u00a0(what is being said about the subject). In “The cat is on the mat,” the\u00a0subject<\/strong>\u00a0is “the cat,” and the\u00a0predicate<\/strong>\u00a0is “is on the mat.” The predicate expresses a\u00a0relationship<\/strong>\u00a0or\u00a0property<\/strong>\u00a0attributed to the subject.<\/p>\n\n\n\n Literal Propositions<\/strong>: Katz’s\u00a0Effability Thesis<\/strong>\u00a0pertains to\u00a0literal<\/strong>\u00a0propositions\u2014those with clear, truth-evaluable content. These are distinct from\u00a0figurative<\/strong>\u00a0or metaphorical statements, which often require interpretation beyond their literal meaning. So, while literal propositions<\/strong> 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.<\/p>\n\n\n\n SH:<\/strong> Good job, but keep on your toes!<\/p>\n\n\n\n ChatGPT:<\/strong> Thank you, Professor Harnad! I’ll stay sharp. If there\u2019s anything further you\u2019d like to explore or clarify, I\u2019m ready to engage.<\/p>\n\n\n\n SH:<\/strong> 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.<\/p>\n\n\n\n ChatGPT:<\/strong> You’re highlighting a key distinction between\u00a0words<\/strong>\u00a0and\u00a0propositions<\/strong>: words alone don’t have\u00a0meaning<\/strong>\u00a0in the full sense; they have\u00a0referents<\/strong>\u2014the things or categories they point to in the world. Propositions, however,\u00a0mean<\/strong>\u00a0something because they assert a relationship or claim about those referents, which can be\u00a0true or false<\/strong>.<\/p>\n\n\n\n Here\u2019s how this works:<\/p>\n\n\n\n Words and Referents<\/strong>:<\/p>\n\n\n\n A\u00a0word<\/strong>\u00a0like “cat” is simply a label. It doesn\u2019t\u00a0mean<\/strong>\u00a0anything on its own; it just refers to a category of objects\u2014namely, cats.<\/p>\n\n\n\n Saying “cat” or pointing to a cat is a\u00a0referential act<\/strong>: you\u2019re signaling the category of “cat,” but you\u2019re not saying anything\u00a0about<\/em>\u00a0the cat. There\u2019s no\u00a0propositional content<\/strong>\u2014nothing that can be evaluated as true or false.<\/p>\n\n\n\n Propositions and Meaning<\/strong>:<\/p>\n\n\n\n When you combine words into a\u00a0proposition<\/strong>\u00a0like “The cat is on the mat,” you are\u00a0asserting<\/strong>\u00a0something about the relationship between two referents: the “cat” and the “mat.” Now you have a\u00a0subject<\/strong>\u00a0(“the cat”) and a\u00a0predicate<\/strong>\u00a0(“is on the mat”), which makes the proposition\u00a0meaningful<\/strong>\u00a0because it expresses a state of affairs that can be\u00a0true<\/strong>\u00a0or\u00a0false<\/strong>.<\/p>\n\n\n\n The meaning of this proposition is the\u00a0relationship<\/strong>\u00a0it asserts between the cat and the mat. It\u2019s no longer just a referential act (pointing to the category “cat” and “mat”), but a claim about reality\u2014about\u00a0where<\/strong>\u00a0the cat is.<\/p>\n\n\n\n Pointing or Naming Without Meaning<\/strong>:<\/p>\n\n\n\n As you pointed out, just saying “cat” or pointing at a cat doesn\u2019t\u00a0mean<\/strong>\u00a0anything in the propositional sense; it\u2019s a\u00a0referential<\/strong>\u00a0or\u00a0deictic<\/strong>\u00a0gesture (like naming or pointing), but it\u2019s not making any claim about the world.<\/p>\n\n\n\n The proposition “That is a cat” does\u00a0mean<\/strong>\u00a0something because it\u2019s a\u00a0truth-claim<\/strong>: it says something\u00a0about<\/strong>\u00a0the referent (“that”) and its relationship to the category (“cat”). If the object is indeed a cat, the proposition is\u00a0true<\/strong>.<\/p>\n\n\n\n So, the key distinction is that words<\/strong> are referential<\/strong>\u2014they point to things in the world\u2014but propositions<\/strong> are meaningful<\/strong> because they make claims<\/strong> about those referents that can be evaluated for truth or falsity. In this view, meaning arises from relationships<\/strong> (propositional structure), not from individual words alone.<\/p>\n\n\n\n This fits perfectly with Katz\u2019s Effability Thesis<\/strong>: propositions, not individual words, are the bearers of meaning<\/strong>, and all thoughts can be expressed in language via literal propositions<\/strong>.<\/p>\n","protected":false},"excerpt":{"rendered":" October 6, 2024 This conversation may reflect the link creator\u2019s personalized data, which isn\u2019t 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\u00a0Weak Church-Turing Thesis (WCT-T)\u00a0asserts that any function … <\/p>\n<\/ol>\n\n\n\n
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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\u00a0literally translatable<\/strong>\u00a0as a proposition. To make such a figurative expression\u00a0effable<\/strong>\u00a0(in the sense of Katz’s thesis), we would need to explain its\u00a0literal<\/strong>\u00a0meaning, 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\u00a0literal propositional statement<\/strong>\u00a0that can be conveyed across languages.<\/p>\n\n\n\n<\/ol>\n\n\n\n
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