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NEW UPDATE: An analytic expression x is redefined as any expression of language verified as completely true (or false) entirely on the basis that x (or ~x) is derived by applying truth preserving operations to other expressions of language axioms.

An axiom is a proposition regarded as self-evidently true without proof. https://mathworld.wolfram.com/Axiom.html

A text based artificial intelligence would have to rely on an axiomatic model of the world so that it would have the same basis as human minds. Each of the elements of this model precisely meet the rewritten definition of analytic.

Is the above an unequivocal way to make an analytic v synthetic distinction, that would address Quine's objections?

PRIOR POST

“Analytic” sentences, such as “Pediatricians are doctors,” have historically been characterized as ones that are true by virtue of the meanings of their words alone and/or can be known to be so solely by knowing those meanings. They are contrasted with more usual “synthetic” sentences, such as “Pediatricians are rich,” (knowledge of) whose truth depends also upon (knowledge of) the worldly fortunes of pediatricians. https://plato.stanford.edu/entries/analytic-synthetic/

I am taking the above definition to mean that analytic truth is simply a body of semantic tautologies within a model of the world so the definition of analytic seems to remain the same.

This seems at least somewhat consistent with Quine's holism where the model of the world is construed as Quine's "whole theory"

In philosophy of science, confirmation holism, also called epistemological holism, is the view that no individual statement can be confirmed or disconfirmed by an empirical test, but rather that only a set of statements (a whole theory) can be so. https://en.wikipedia.org/wiki/Confirmation_holism

"Dogs are animals" would be formalized as a relation between finite strings specifying a relation between semantic categories DOGS ⊆ ANIMALS.

From the above we divide off synthetic as: Synthetic truth [new] is the set of expressions of language that cannot be verified as true entirely within a model of the world and additionally require sense data from the sense organs: {Example: There is a dog in my living room right now}

Quine's definition of the analytic v Synthetic distinction:
"truths which are analytic, or grounded in meanings independently of matters of fact, and truth which are synthetic, or grounded in fact." Two Dogmas of Empiricism Willard Van Orman Quine

The expression: "dogs are animals" would seem to be synthetic under the Quine definition, because it is a fact that dogs are animals. Under the revised definitions facts of the world are encoded as natural language axioms. This constructs a model of the world. Thus {dogs are animals} becomes analytical.

When analytic truth is verified entirely on the basis of its meanings then it remains true in the model of the world even if untrue within the actual world.

One thing that is useful about this distinction is this definition of analytic draws a sharp boundary between what a text based AI mind could and could not do.

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  • The definitions you give for analytic and synthetic are not correct. What you gave are (more or less) the definitions of a priori and a posteriori. Quine's definitions are correct. Whether analytic is the same as a priori and synthetic is the same as a posteriori is a matter of some controversy in philosophy. Apr 20, 2023 at 17:08
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    Your re-definitions do not address Quine's objections and would not work for Carnap's purposes, which is what the point of Quine's objections was. Carnap and Quine were not concerned with "analytic" in a specific language, where one is free to stipulate as they please, he was asking for a general explication of "analytic in L", where the language L is a variable. In other words, for spelling out the underlying idea that supposedly guides "stipulation" of some expressions as analytic and others not in Carnap's "linguistic frameworks". Quine argued that no satisfactory explication exists.
    – Conifold
    Apr 21, 2023 at 5:00
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    Those are meaning postulates, i.e. conditions that the explication of "analytic" is supposed to satisfy. Quine's point was that there is no cogent concept of "analytic in L" satisfying these conditions.
    – Conifold
    Apr 21, 2023 at 6:26
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    L could be anything coherent. What Carnap needs for his paradigm of linguistic frameworks is to explain how he will identify analytic expressions in any language someone else (scientists, say) comes up with. Those do not come with analytic 'stipulations', he needs to discriminate what is "analytic" there and what isn't based on some consistent rule. "Grounded in meanings independently of matters of fact" seemed like such a rule. Until Quine picked it apart.
    – Conifold
    Apr 21, 2023 at 7:50
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    Let us continue this discussion in chat.
    – polcott
    Apr 27, 2023 at 16:36

6 Answers 6

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Your proposed definitions would not address Quine's objections at all. For one thing, Quine is just as opposed to the concept of a priori knowledge as he is to analytic truth. For another, he rejects the claim that there can be truth by convention: this is the subject of his paper of that name.

Facts are not created by stipulation. With the exception of some special terminology that is introduced within scientific and technical disciplines, words have natural meanings. Nobody stipulates what they mean. Compilers of dictionaries are not in the business of stipulating meanings either; rather, they are in the business of documenting how the speakers of a language use the words it contains.

The proposition that dogs are animals is not true by stipulation and is not analytic. There are good empirical reasons to believe that dogs are animals. We observe that they reproduce, grow, die, eat, excrete, respire, move around, and interact with their environment. We classify dogs as animals for this reason, not as the result of an arbitrary stipulation.

Quine would say that "dogs are animals" is deeply entrenched in our web of belief and well protected from revision in the light of experience, but not immune to revision. Biologists can and do make revisions to the classification of living things, and they do so for empirical reasons. Not so long ago it was believed that giant pandas were raccoons, but after their DNA was sequenced it was discovered that they are in fact bears. Similarly, fungi were once classified as plants but they are now considered to be a kingdom in their own right. These classifications are neither analytic nor a priori but based on empirical facts, which are in turn based on observation.

One of the most foolish mistakes that beginners in philosophy make is to suppose that truths are created by definitions or by stipulations. At the end of the day definitions are redundant: they are just a convenient shorthand. What makes propositions true is that they form part of our best scientific theories. And for Quine, the truth of a proposition (or sentence, as he prefers) cannot be assessed on a sentence-by-sentence basis but by consideration of the entire theory or chunk of beliefs of which the sentence is a part. This is why, for Quine, no sentence is analytic. A sentence inherits empirical content from the empirical theory of which it is a part.

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  • "Facts are not created by stipulation." Facts and tautologies are encoded in language as stipulated relations between finite strings. Disagreeing with these stipulated relations is the same as disagreeing with a tautology, necessarily incorrect. The only way that we know that dogs are animals and not ten story office buildings is stipulated relations between finite strings that encode facts.
    – polcott
    Apr 20, 2023 at 23:35
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    Facts are different from tautologies and are not true by stipulation. Two people may disagree about whether a proposition is true and this does not entail that one of them is using the language incorrectly. A person may change their mind about whether a proposition is true and this does not entail that they previously misunderstood the language. All beliefs about propositions are open to revision in the light of empirical experience...
    – Bumble
    Apr 21, 2023 at 0:19
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    And even tautologies are not stipulations. In the logical sense of the term, tautologies exist only in formal systems and not in natural language. The tautologies of classical logic are different from those of intuitionistic logic and from those of relevance logic, etc. Nobody stipulates that a given logic and its tautologies are correct and nobody is necessarily incorrect if they choose to use a different logic.
    – Bumble
    Apr 21, 2023 at 0:19
  • " In the logical sense of the term, tautologies exist only in formal systems and not in natural language." That would mean that the expression: "existence exists" is possibly a misconception and the truth is that actually nothing has ever existed. Any expression of formal or natural language such that its negation is unsatisfiable seems to sum it up. (this excludes self-contradictory expressions that are necessarily not truth bearers).
    – polcott
    Apr 21, 2023 at 1:28
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    But there are lots of formal systems and they differ. And people disagree about lots of things without misunderstanding each other. As to the sentence "existence exists" I have no idea what that means. It does not seem to me to parse correctly. If it means, "the universe is non-empty" then I would agree that is true, but not that its negation is unsatisfiable.
    – Bumble
    Apr 21, 2023 at 1:31
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Short answer: no.

Analytic truth is the set of expressions of language that can be verified as completely true without any sense data from the sense organs: Example {Dogs are animals}

I think the inherent contradiction with the alternative definition prevented is that most people come to understand the use and mention of 'dog' and 'animal' by appealing to the senses intuitionally (SEP) and fundamentally. A dog is an often fluffy-to-touch, visibly four-legged, animal that smells peculiar when wet, and barks loudly. An animal is generally a moving, breathing, frequently visibly-legged thing with a bumpy backbone, laps up wet water, (insert additional sensory description here).

Thus, the determination of natural kinds (SEP) is inherently folk psychological precisely because it relies on the senses ot make sense of the world:

Scientific disciplines frequently divide the particulars they study into kinds and theorize about those kinds. To say that a kind is natural is to say that it corresponds to a grouping that reflects the structure of the natural world rather than the interests and actions of human beings. We tend to assume that science is often successful in revealing these kinds; it is a corollary of scientific realism that when all goes well the classifications and taxonomies employed by science correspond to the real kinds in nature. (Emphasis mine)

That is, for most people "the structure of the natural world" is dictated by the senses rather than operational definitions, mathematical physics, psychometrics, etc. People make sense of the world initially through their senses and only develop a more language-like analytical capacity through extensive socialization and education.

This is presumably why the analytic-synthetic distinction appeals to the explicit sentence that expresses the proposition:

analytic proposition: a proposition whose predicate concept is contained in its subject concept
synthetic proposition: a proposition whose predicate concept is not contained in its subject concept but related

This "closeness" of subject to predicate is precisely a linguistic distinction because propositions themselves are adjacent to language use. From a nominalist's perspective, linguistic labels are just a tool for describing and communicating experience, and all language, ultimately to be meaningful has to have some grounding in the senses, a perspective that begins with British empiricism and is defended contemporaneously by physicalists in various philosophical arguments such as van Fraasen's constructive empiricism (SEP) and 2nd-generation cognitive science's embodied cognition (SEP).

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  • What does it mean that a "proposition is adjacent to language use"?
    – Frank
    Apr 20, 2023 at 19:43
  • Propositions (if you believe they exist) and utterances/sentences obey dualism. A proposition is an imputed mental artifact, whereas an utterance is the concrete communication that conveys it. Synonymy and substitutativity in philosophy of language presumes that multiple utterances can have the same content (proposition). We can use use-mention to exemplify. 'Der Schnee ist weiß' and 'The snow is white' are two utterances with the same mental content and even the same decompositionality. 'Schnee' means 'snow', 'ist' means 'is', etc...
    – J D
    Apr 20, 2023 at 21:11
  • The nature of propositions is that they convey belief and desire generally, but given mind-body duality, we cannot directly inspect someone's propostions, their mental content. We can only infer the meaning from the statement or utterance. Such an act is interpretation, and interpretation, like translation and belief attribution more generally, is underdetermined. In a broad epistemological sense, we can only infer mental content of others through our subjective lens. This is related to the easy and hard problems of consciousness, which is to
    – J D
    Apr 20, 2023 at 21:15
  • @Frank provide explanations for why what appears to be regarding mind-body duality actually is.
    – J D
    Apr 20, 2023 at 21:15
  • Think of it is as ISO OSI.... propositions are application layer communications whereas sentences are physical layer communications.
    – J D
    Apr 20, 2023 at 21:18
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I think your question has prompted several objections it might have avoided if you had cast it in a different way. I sense from your own answer that what you were trying to do was draw a distinction between truths that could be recognised by AI without any sensory inputs and truths that could not. If you had made that the sole focus of your question, you would have got a more helpful response, I suspect. As it is, by conflating that objective with another of trying to dodge Quine's assertion that all statements are really synthetic, you have triggered a lot of antibodies.

Yes, you can if you wish develop your own idiosyncratic definition of analytic and synthetic, but that doesn't change the validity of Quine's position, since that was directed at the original position of the goalposts before your attempt to move them.

To put my point another way, you might have received a different response had you substituted 'an' for 'the' in the headline question.

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  • It seems that Quine is saying that hardly anything is synthetic: In philosophy of science, confirmation holism, also called epistemological holism, is the view that no individual statement can be confirmed or disconfirmed by an empirical test, but rather that only a set of statements (a whole theory) can be so. It is attributed to Willard Van Orman Quine en.wikipedia.org/wiki/Confirmation_holism (I changed "the" to "an")
    – polcott
    Apr 27, 2023 at 13:53
  • I am trying to unravel how these things can be coherently understood which may require them to be redefined to remove any incoherence. If we say that all analytical truth only exists within an abstract model of the world then this may be a totally coherent way of viewing it. This certainly seems consistent with the SEP definition of analytical: "true by virtue of the meanings of their words alone and/or can be known to be so solely by knowing those meanings."
    – polcott
    Apr 28, 2023 at 2:11
  • I understand that, and it is fine. If you create a model of the world, in that model you can make stipulations such as cats are animals, and you can define analytical statement to be those that are true on the basis of the stipulations alone. That all seems consistent to me. Apr 28, 2023 at 6:02
  • So I am thinking that this might be construed as a new and improved definition of analytical. It can be converted into a consistent formal system that is not incomplete and True(L, x) can be defined.
    – polcott
    Apr 28, 2023 at 6:21
  • I think you are missing a point here, which is that it is your personal definition. Whether it is new I cannot say, since others might already have thought of it. Whether it is improved is a matter of opinion and perspective. Apr 28, 2023 at 8:28
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As I pointed out in my comment, what you are proposing to do is essentially to replace the analytic/synthetic distinction with the a priori/a posteriori distinction. Kant distinguished these two categories in the eighteenth century, and ever since, it has been controversial whether one pair can replace the other or not.

Kant claimed that the pairs are not identical; that there is synthetic a priori knowledge. He pointed to arithmetic as an example. You can know that 2+3=5 without examining objects in the real world to know if it's true, but most philosophers believe that 2+3=5 is not analytic. This is controversial, though; some philosophers called neo-Fregeans would say that is analytic.

Broadly, those who would say that your reduction is correct (that is, that you can replace the traditional analytic/synthetic distinction with a priori/a posteriori are called empiricists. Another example Kant gave to show that the two pairs are different is geometry. For example, it seems that we don't need to actually examine the real world to know that you can connect any two points with a line segment. Empiricists would generally disagree, and claim that this can only be known from experience.

Also, you go a little off the standard definition of a posteriori by referring to sense impressions. Aren't there things you can learn from experience that aren't directly related to sense impressions? For example, can't you be imagining a story in your head and decide that you don't like one of the characters, even though no sense impressions are involved? According to your definitions, this fact which you learned from experience would be known analytically, which doesn't seem right.

Incidentally, pretty much everyone would agree that "a dog is an animal" is analytic. It's practically a canonical example of an analytic sentence. To see this, ask whether you could ever empirically find a dog that isn't an animal. Obviously, you couldn't, because anything that isn't an animal would not count as a dog. Being an animal is part of what you mean by calling something a dog.

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  • I will sum it up differently and more succinctly, analytic truth is defined as expressions of language that have been stipulated to be true (the whole set of facts) and expressions that are a semantic consequence of these expressions. This leaves synthetic truth as expressions of language requiring sense data from the sense organs to verify their truth.
    – polcott
    Apr 20, 2023 at 19:35
  • @polcott Before "semantic consequence", maybe you could also consider "formal logic consequences", since formal logic is not supposed to add anything new to the starting point of the deduction.
    – Frank
    Apr 20, 2023 at 19:42
  • @polcott, you are confusing things by continuing to refer to your definitions as definitions of analytic/synthetic when they aren't. They aren't conceptually identical to the standard definitions, and there is good reason to believe that they aren't practically equivalent either. If you want to be understood, you need to word things the way I did in my answer. Take the traditional definitions of analytic/synthetic and ask whether your new definitions have the same practical effect. This isn't redefining the existing concepts; it is asking whether a new pair of concepts is equivalent. Apr 20, 2023 at 20:11
  • @Frank I am implicitly referring to formalized semantics of formal or natural language both anchored in set theory. I have the Semantic Necessity operator: ⊨□ as a replacement for logical implication. This guarantees semantic relevance.
    – polcott
    Apr 20, 2023 at 20:11
  • @DavidGudeman I am not aiming for equivalence because sufficient equivalence would have the same ambiguity issues. New_Analytic is stipulated to mean any expression of language that can be determined to be true on the basis of relations between finite strings.
    – polcott
    Apr 20, 2023 at 20:15
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It seems that I am defining analytic in the same way that the Logical positivists do, and merely adding a nuance of criteria to their same definition of synthetic.

Logical positivist definitions Thus the logical positivists drew a new distinction, and, inheriting the terms from Kant, named it the "analytic-synthetic distinction".[7] They provided many different definitions, such as the following:

(1) analytic proposition: a proposition whose truth depends solely on the meaning of its terms

(2) analytic proposition: a proposition that is true (or false) by definition

(3) analytic proposition: a proposition that is made true (or false) solely by the conventions of language

(While the logical positivists believed that the only necessarily true propositions were analytic, they did not define "analytic proposition" as "necessarily true proposition" or "proposition that is true in all possible worlds".)

Synthetic propositions were then defined as: synthetic proposition: a proposition that is not analytic

My intention was to unequivocally divide expressions of language into

(a) Those requiring sense data from the sense organs to verify their truth: "there is a dog in my living room right now". SYNTHETIC

(b) Those that can be verified as true on the basis of their relation to other expressions within a model of the world. "cats are animals" is stipulated to be true within a model of the world. ANALYTICAL

This division specifies the limits of a text based artificial intelligence that has no sense organs or sense data.

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Regarding your new proposal: By applying truth-preserving operations you aren't able to distinguish meanings (intensions) - obviously, because all true sentences are equivalent (coextensive), although they don't have the same meaning (if we were able to specify what meanings are, of course, which Quine denies). This simply doesn't work.

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  • I included that we can and do stipulate the meanings of terms and then derive the set of true or false expressions of language x or ~x by applying truth preserving operations to expressions comprised of these semantic meanings. The stipulated meanings of terms are like axioms and the expressions derived from them comprise the entire body of analytic expressions.
    – polcott
    Feb 4 at 17:54
  • @polcott Then you beg the question against Quine.
    – user71009
    Feb 4 at 18:04
  • Within my redefinition of {analytic} when Quine says that facts are synthetic he is simply wrong. That {dogs} <are> {animals} is an axiom anchored in the stipulated meaning of these terms.
    – polcott
    Feb 4 at 18:33
  • @polcott But Quine asks if there is any good criterion of that. I don't see how your proposal resolves his issue.
    – user71009
    Feb 4 at 18:40
  • Any expression of language that can be resolved as true or false entirely on the basis of other expressions of language that stipulate the meaning of its terms seems to be airtight to me. (Analytical expressions are resolved to true or false by pure analysis) Can you come of with a counter-example where this does not work?
    – polcott
    Feb 4 at 18:46

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