Laws of Thought and Kant's Synthetic A Priori

philosophy

The three traditional ''laws of thought'' in philosophy include:

(1) The Law of Identity: ''Whatever is, is.''
(2) The Law of Non-Contradiction: ''Nothing can both be and not be.''
(3) The Law of Excluded Middle: ''Everything must either be or not be.''

Kant distinguished between a priori and a posteriori propositions.

An a priori proposition is one for which experience plays no role in justifying the proposition. For example, ''All triangles have three sides.''

An a posteriori proposition is one for which experience does play a role in justifying the proposition. For example, ''All triangles induce headaches.''

Kant further distinguished between analytic and synthetic propositions.

An analytic proposition is one which is true by virtue of the meaning of its terms. More technically, an analytic proposition is one whereby the concept of the predicate is contained within the concept of the subject. Negation of an analytic proposition results in a contradiction. For example: ''All bachelors are unmarried.''

A synthetic proposition is one which is true by virtue of the meaning of its terms and facts about the world. More technically, a synthetic proposition is one whereby the concept of the predicate is not contained within the concept of the subject. Negation of a synthetic proposition does not result in a contradiction. For example: ''All triangles are red.''

All analytic propositions are a priori. There are no analytic propositions which are a posteriori. It is clear that there are synthetic propositions which are a posteriori.

But, Kant further argued that there are synthetic a priori propositions. That is to say, Kant argued that there are propositions which are true a priori but not in virtue of the meaning of their terms.

Would Kant consider the aforesaid laws of thought to be examples of his so-called synthetic a priori? If so, do you think he was right in thinking this?

It seems to me that the laws of thought are synthetic, since they are not true by virtue of the meaning of their terms, and they are a priori, given that one does not need to rely on experience in order to justify them.

MindForged

A synthetic proposition is one which is true by virtue of the meaning of its terms and facts about the world — philosophy

I think you typoed. Synthetic propositions are *not* true in virtue of meaning.

In any case, calling these the "laws of thought" is and has always been kind of dumb. Not only do they not correspond to the limits of thought - people have inconsistencies in their beliefs all the time, and occasionally don't seem to hold to Excluded Middle - but they're just one possible set of axioms a logic can adopt. There are logics without each of these axioms.

That aside, this idea is full of holes. I'd have to go check what exactly it was, but even this "in virtue of" relationship has faced technical roadblocks in the past.

Moreover, these axioms are not true in virtue of some kind of indisputable way. Consider the Law of Non-contradiction: a proposition cannot be true and untrue or equivalently the negation of a conjunction of a proposition and it's negation is always true. It's clear this is an exclusivity condition for propositions and the truth-value they relate to. But mathematically we know that this type of setup is not all that exists. We can go beyond functions and use broader relations. If we take truth-valuation to be a relation between proposition and any number of truth-values then it's clear that Non-contradiction no longer holds necessarily since the technical machinery exists in that logic to violate it coherently. Some proposition 'P' could relate to truth and relate to falsity, and so it's clear this logic lacks that exclusivity condition since the semantics of truth value assignment has changed. Of course, you'd need to find something that can fill the overlap which is pretty controversial.

So clearly there's more going on here than meaning establishing truth. The terms employed in the definition give away the assumptions that seem to guarantee the truth, but those assumptions could be attacked it questioned anyway. There's broader issue with the analytic-synthetic distinction but since others are likely to mention them I went a different route.

philosophy

@MindForged

Thanks. I'd be curious to hear what your views on Nietzsche are regarding this. Nietzsche essentially argues that we simplify the world by means of logic, reason, number, etc. and, in so doing, falsify it. Logic distorts the world by creating entities that do not actually refer to anything in the world (e.g. ''things'', ''identity'', ''permanence'', etc.), but we have to rely on logic in order to live at all. In other words, Nietzsche argues that we falsify the world in order to live, hence his questioning the value of truth in Beyond Good and Evil.

I think you typoed. Synthetic propositions are *not* true in virtue of meaning.

I thought that was the definition of a synthetic proposition though? A synthetic proposition is true by virtue of the meaning of its terms and due to facts about the world, whereas analytic propositions are true by virtue of the meaning of their terms alone?

MindForged

↪philosophy

I'm not knowledgeable on Nietzsche but based on what you said it sounds in part correct but it ends at the wrong conclusion. It's true that what we essentially do is create models of the world and that there's some simplification. But that doesn't make the enterprise false, it just means we need to speak more carefully. There's a reason statements like "All models are false but some are useful" exists. Based on how well they perform on various theoretical virtues we think it more likely that we are getting closer to the truth.

I thought that was the definition of a synthetic proposition though? A synthetic proposition is true by virtue of the meaning of its terms and due to facts about the world, whereas analytic propositions are true by virtue of the meaning of their terms alone? — philosophy

Nah, just check the SEP:

An “analytic” sentence, such as “Ophthalmologists are doctors,” has historically been characterized as one whose truth depends upon the meanings of its constituent terms (and how they’re combined) alone, as opposed to a more usual “synthetic” sentence, such as “Ophthalmologists are rich,” whose truth depends also upon the facts about the world that the sentence represents, e.g., that ophthalmologists are rich.

Mww

The three laws of thought, as put forth by Aristotle, are analytic propositions, not because of their content, but because they are true necessarily, which just means their negation is impossible. From a Kantian point of view, the laws of thought are analytical propositions because the predicate contains no conceptions that are not explicit in the subject. He would call the use of these pure transcendental logic because they serve as the form of a proposition and will therefore be true no matter what particulars are used as subject.

All that being said, why do we need synthetic a priori propositions anyway?

MindForged

The three laws of thought, as put forth by Aristotle, are analytic propositions, not because of their content, but because they are true necessarily, which just means their negation is impossible — Mww

Is this something you believe? Because intuitionistic logic alone has existed for nearly a century now so it feels like a strange view to me. Logical operations such as negation are defined by a logical formalism, they don't stand independently of them, and so how they function is not something we can say works a particular way outside of a logical system. In intuitionistic logic, Excluded Middle is not necessarily true because negation is defined differently and so Excluded Middle cannot be asserted within a universal quantifier. It's not that the negation of Excluded Middle is true, but that EM is not a true in all models.

Mww

Logical operations (...) don't stand independently (.....) outside of a logical system. — MindForged

Understood. An epistemological theory grounded in rules should adhere to that system of rules sufficient to regulate it.

Because intuitionistic logic alone has existed for nearly a century now — MindForged

First I heard about it. Call me old-fashion that way, I guess. Can you tell me why a plain ol’ guy on the street like me would need anything but plain ol’ propositional logic?

Laws of Thought and Kant's Synthetic A Priori

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