Understanding the difference between analytic/synthetic vs necessary/contingent

Question

I was listening to a lecture by John Searle on philosophy of language and he mentions the classifications: analytic/synthetic and necessary/contingent. I am not sure what the difference is but using my background from mathematical logic, I guess that the analytic/synthetic classification is syntactic and similar to the notion of "whether a proposition is provable from no axioms or not" while necessary/contingent is similar to the notion of "Wether a proposition is true in all possible worlds or not", if I am guessing right, then probably mathematical logicans borrowed these notions from philosophers, no ?

Answer 1

There are actually three different distinctions in play here. Analytic vs. synthetic, necessary vs. contingent, and a priori vs a posteriori.

Analytic/synthetic is a linguistic distinction. It aims to distinguish between propositions that are true in virtue of the meanings of their terms, and those that aren't. In fact, there are at least four different ways of characterising analyticity, but this is the most common one. The original Kantian definition was a proposition in subject-predicate form where the predicate is contained within the subject. Another version is a proposition that is true in virtue of linguistic convention. Another, due to Frege, is a proposition that can be derived from a logical truth by substitution of terms that are definitionally equivalent.

Necessary/contingent is a metaphysical distinction. It aims to distinguish propositions that must be true from those that might or might not be true depending on how things are in the actual world. True in all possible worlds is one way of describing necessity, though it can get more complex than this.

A priori/a posteriori is an epistemological distinction. It aims to distinguish those propositions that are knowable independently of empirical experience, from those that can only be known by checking how the world is. Being knowable independently of empirical experience is usually understood to make allowance for whatever experience is needed to understand what a proposition means.

It is important to keep these distinctions separate, because for many philosophers, the whole point of making them is to understand the relationships between them. For example, the logical positivists believed we could explain, or even explain away, necessary truths and a priori knowledge by claiming that only analytic propositions are necessary and only analytic propositions are a priori knowable. This is a substantial reductive thesis that would be made trivial if we confused 'analytic' with 'necessary' or with 'a priori'.

All three distinctions are the subject of philosophical dispute. The analytic/synthetic distinction was rejected by Quine and remains controversial. Kripke provided an influential account of necessity that breaks the connection between necessary and a priori, i.e. it allows for propositions that are a priori contingent and a posteriori necessary.

Answer 2

The distinction between analytical propositions & synthetic propositions DOES NOT come from Kant. KANT used his own definition which almost no one followed. It is certainly not used today without specifically mentioning Kant. If Kant is not mentioned his definition is not used.

A new context was given to those terms. When Philosophy textbooks speak on analytic propositions they mean how truth of propositions are determined. Analytic propositions fall under two kinds: logically necessary or self contradictory. They are not based on our knowledge the world around us. We know a proposition is analytic by definition alone & how language is used. "All bachelors are unmarried" is an analytic proposition because we do not need any real world knowledge like experience to determine it's truth. All we need is knowledge of the English language. We know how this language works. The language requires the proposition to be true always. In this case there is no possibility of the proposition being false. In this way the proposition is called logically necessary. Math people usually use the term tautology in a specific context for this idea in those classes.

On the other hand, "All circles have four sides" is self contradictory. The language of English does not allow us to use the term circle in that way. Circles can't have any corners and still be a pure circle. The self contradictory propositions are always false by definition. There is no possibility of that type of analytic proposition to be true. It is always false. Math people usually use the term contradiction in a context in place of this idea in those classes.

Synthetic propositions are based on knowledge of the world. You need more knowledge than the premises given to determine the truth. "The capital of France is Paris" is not determined by our knowledge of a particular language. We can say we know that Paris is the actual capital of France by real world interactions. It could be true or false. It could be the capital changes over time. These propositions can be temporarily true. Contingent propositions are those propositions that have a truth value that alternate from true to false depending on the content of the propositions. "All roads lead to Rome" was true at some point. We would need to use experience to discover if the proposition is true still today. It is not necessary that all roads lead to Rome. Some road may lead somewhere else. If we found some roads lead elsewhere we would not be surprised today. Laws of a specific country would be expressed as synthetic propositions. We also know that laws can change based on location. How do we KNOW that? It is not any LANGUAGE that tells us different locations can have different laws. How the world actually is tells us this knowledge. We need experience directly or we learn from the experience of someone else. So all synthetic propositions can be contingent. For instance, there is no laws of Physics requiring certain propositions to be true outside of a language.