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(1) Every bachelor is unmarried.

I know this is one of the most famous examples (intensionally) denoting analytic and a priori propositions. No problems yet.

(2) Every apple is a fruit.

This one is a bit more confusing. At first glance, I thought it was analytic, but after a while I’ve come to notice that I can’t be very convinced because of the following sentence:

(3) Every apple is molecular.

This appears to be obviously a posteriori; no one would know if this is true like in the 8th century. I knew Kripke made a distinction among necessity, analyticity, and a priority. So I was like “this may be something like an a posteriori analytic proposition or whatnot.” (Is it?)

But the real question I haven’t given an answer to myself yet is that if the last sentence is a posteriori, what about the first one? Can it still be considered a priori? It seems it is still widely assumed so, but I can’t see the differences among those three sentences. I would really appreciate it if you would answer me.

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"S is P" ( S for subject, P for predicate) is analytic iff its negation is contradictory ( due to the fact that the concept of the predicate is contained, as says Kant, in the concept of the subject).

" Some bachelor is married" is clearly contradictory.

Is " Some apple is not a fruit" contradictory. Can we conceive of a possible world in which something actually is what we call an apple in english while not being a fruit? If there is a possible world in which an " apple" is not a fruit, then, in this world, the word " apple" has not the same sense, it does not express the same concept. I think in all possible worlds " being an apple" ( with the concept that is expressed in english by this word) logically implies" being a fruit".

Is " some apple is not molecular" contradictory? Is there a possible world in which some objects have all the biological properties of apples, although the structure of matter is not the same in this world as in ours, so that these fruits are not made out of molecules? It is hard to imagine, but I think one can conceive this. So, I would tend to say that this claim is not a priori. " Apple" is a biological concept and " being molecular" is a physical concept that is not contained ( logically) in the concept " apple".

Is " all husbands have a wife" analytic ? If I lived in Poland I would tend to say that it is. But I would have to imagine possible countries in which gay marriage is legal. And surely there are possible countries in which a man can be a husband without having a wife ( for there are actually countries in which it is the case).

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    Thanks for comment. I have deleted my answer (a) because I don't want to be constrained by Kant and (b) because the more I think about the a priori the more puzzling and unclear I find it. Btw: in a gay marriage one partner may be referred to as the 'husband' and the other as the 'wife'. This usage while not universal is not uncommon. I offer this as an item of a posteriori knowledge. – Geoffrey Thomas Nov 10 at 15:42
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    Thank you for the answer! I think I can think of a possible world where every apple is a vegetable. In this regard, “apple” doesn’t seem to me to imply [being a fruit]. – Tzetachi Nov 10 at 16:16
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Welcome, Tzetachi.

While (1) is widely regarded as analytic, i.e. true by virtue of the meaning of words, I don't think it is a priori, known or knowable independently of or prior to experience. For one thing, you need to know the English language in order to understand it, and that knowledge is not a priori. More than that, the concepts of 'bachelor' and 'ummarried man' and the fact that they are co-referring terms also has to be learnt.

In saying this I can use 'analytic' in its wide current sense above, untied to Kant, and also satisfy Kant's two criteria for analyticity: (a) the denial of an analytic proposition involves a contradiction and (b) the concept of the predicate is 'contained' in the concept of the subject.

In Kant an a priori proposition is one of which, if we understand its terms, we can establish - ascertain, know - its truth without reference to experience. Analyticity is about truth merely, whether known or not, and is a semantic notion; the a priori is about knowledge and thus is an epistemological notion concerned with what can be known to be true without reference to experience.

In brief, then (1) is an analytic truth and is knowable a priori. Your (2) and (3) are a posteriori. You can know what a fruit is without knowing that an apple is a fruit or even that there are apples; that requires empirical investigation. Also it is a factual matter whether an apple is molecular. Once you understand what a molecule is, and what an apple is, you cannot (except dogmatically) know without reference to experience that an apple is molecular. So (2) and (3) are neither analytic nor a priori.

  • GeoffreyThomas.- The question " is the konowledge that : S is P, a priori knowledge ? ", in the traditional kantian sense, does not refer, I believe, to the acquisition process of meanings nor to the formation process of concepts. I tend to interpret it as " being admitted that one grasps the concepts of S and of P, can one know, without any additional experience, that : S is P?". – Ray LittleRock Nov 10 at 13:22
  • Thank you for your reply! This is just my intuition, but I feel like (1) is somewhat different from (2) and (3) even though you said you don’t think (1) is a priori. Could I ask where you think this difference comes from? – Tzetachi Nov 10 at 16:32
  • I have revised and restored my answer, perhaps it will answer your question. Let me know if it doesn't. Best - Geoff – Geoffrey Thomas Nov 10 at 16:37
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1: Analytic: a bachelor is by definition an unmarried man; an unmarried man is by definition a bachelor. As you can see, there is nothing we can see that might render the sentence as a function of external state of affairs.

Perhaps these examples are easier to grasp: 1+1=2 or i²=-1; they are true by virtue of meaning within their respective framework.

2: Synthetic: We don't know exactly what a fruit is unless, of course, we refer to some facts about the real word.

3: Synthetic: since "molecular" is meaningless without contemporary physics which implies this sentence also depends on fact about the real world.

3: Analytic: alternatively we can take contemporary physics as a framework, and not an empirical investigation which would render "Apple is molecular" true by virtue of meaning. That is, ∀x(x∈D->x∈M) where D is an arbitrary subet of the universe, and M is the set of everything which is Molecular. Therefore, if we take Contemporary physics as a framework, then ∀x(x∈D->x∈M) becomes definitionally; consequently, "Apple is molecular" becomes true by definition since apple is an element of D, then, by definition, everything in D is molecular so apple is molecular.

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