Analytic is a conceptual term, meaning roughly that the rules of a language, or of its interpretation, guarantee that a certain sentence or thought is true (or false). For something to be analytically true is for the truth of it to be contained within the meaning of the thing that expresses it. If you're competent with the rules of the language or rules of thought, you'll be able to recognize it as true just by looking at it.

A priori is an epistemological term, which means that something is known, or knowable, without experience, by means of reason alone. This need not be in virtue of its being analytic – for example, you might think 'I exist' is in some way a priori, even though it's contingent and so not analytic.

To expand on @The Great Whatever's concise answer...

I have trouble distinguishing between analytic and a priori for example. Do they just have the same meaning with 2 different ways of saying it or is there some other distinction? — ladyphoenix86

Good question. Some philosophers have believed analytic and a priori to be coextensive, and the same goes for synthetic and a posteriori. From this empiricist point of view, whatever is analytic is a priori and whatever is synthetic is a posteriori, and vice versa.

But they have different meanings. Analytic-synthetic is semantic, and a priori-a posteriori is epistemological.

Analytic-synthetic is about what makes a proposition true. Analytic propositions are true by virtue of what their words mean, and synthetic propositions are not true merely by virtue of what their words mean. One of Kant's ways of thinking about the difference is that analytic truths don't tell us very much, i.e., they are explicative, whereas synthetic truths can tell us something new, i.e., they are ampliative.

A priori-a posteriori is about how we know things or how we justify our knowledge. A priori knowledge is known independently of experience. A posteriori, or empirical, knowledge is known from experience. The thing to note about a posteriori knowledge is that because it is confirmed or disconfirmed by experience, it tells us what happens to be the case, and not what must be the case, i.e., this kind of knowledge is about what is contingent. In contrast, a priori knowledge is neither confirmed nor disconfirmed by experience, and so concerns what must be the case, i.e., this kind of knowledge is about what is necessary.

As you've noticed, some philosophers think there is synthetic a priori knowledge.

why is 'synthetic a priori' different to 'analytic a posteriori'? — ladyphoenix86

To know a synthetic proposition a priori is to know something that is not true merely due to the definitions of the terms involved, and to know it independently of experience too. This is important because, if such knowledge is possible, then we can have substantial, ampliative knowledge (from the synthetic component) that does not depend on experience, i.e., that we attain using our own reason unaided by experiential confirmation.

Analytic a posteriori knowledge, on the other hand, seems impossible. It doesn't make much sense to say a sentence that's true by virtue of the meaning of the constituent words can be known from experience. If you understand it then you know it's true already, without any perception or investigation of the world.

The main thing I haven't really addressed here is what "independently of experience" precisely means, because it can be interpreted strictly or loosely.

Kripke makes an interesting case for the necessary a posteriori and the contingent a priori. Scott Soames' history of AP rocks at explaining succinctly 20th Century ponderings on the subject.

Yeah, I don't know of any philosopher who defends the existence of the analytic a posteriori. I suppose it could be possible if you hold a view such that knowledge of the operations of a language is impossible without world-knowledge. For example, to know the meaning of a referential expression might be to know its referent, which would in turn requiring having empirical knowledge of how the language community uses it to refer.

I find the 'synthetic/analytic' distinction impossibly woolly. I have never encountered a definition that can achieve both clarity and internal consistency while still enabling Kant's conclusion that
'All bachelors are unmarried'
is analytic while
'7+5=12'
is synthetic.

I wonder how Kant would class the following true proposition:
'If P is a bachelor at time T then (if P marries at time T2 then if (T2<T) it is the case that 1+1=3)'

And if that's still analytic, how about:
'If P is a bachelor at time T then (if P was born at time T2 then if (T2>T-5 years) it is the case that 1+1=3)'

I don't really get what you are getting at in the examples.
I do get why Kant thinks 7+5 = 12 is synthetic, whilst all bachelors are unmarried is analytic. So if you elaborate a little I may understand.

This notion that bachelors being unmarried is analytic - it drives me crazy. These are just words that pass. It tests nothing.

Bachelor = unmarried: analytic because true in virtue of the meanings of the words.
7+5 = 12: not analytic because '7+5' does not mean '12'. Synthetic because 7+5 can be shown by counting in various ways that are self-evidently beyond question to equal 12.

Interesting cases, along the kind of lines you seem to be indicating, of fact that are at least quasi-analytic is exampled by "Paris is the capital of France". It is not a merely empirical proposition because there doesn't seem to be any imaginable way to falsify it.

No, that sounds like a plain old empirical proposition to me.

Great, so how would you imagine it could be falsifiable, as all the other "plain old empirical propositions" such as "the sun is shining here and now" "Plato wrote the republic" "John F Kennedy was assasinated by Lee Harvey Oswald" and so on, can easily can be imagined to be ?

...If France had a capital other than Paris? I don't understand what you're asking.

Are you seriously suggesting that France could have a capital other Paris?

...Yes?

There is no possible world that contains the thing we've named "France" which has a capital that isn't Paris.

That's Kripke's necessary aposteriori in a nutshell.

'Bachelor --> Unmarried' is NOT true in virtue of the words.

The definition of bachelor is not 'an object that is unmarried'. It is something like 'An adult, male, live, human that has never been married.' To get from there to the Theorem 'If X is a bachelor then X is unmarried' requires several steps of logical deduction.

For example one such step, but by no means the only one, is that, given ' X AND Y', we can conclude 'X'. This involves applying the rule of inference in Natural Deduction that is usually called either 'Simplification' or 'AND elimination'.

Similarly, to get '7+5=12' from the axioms of arithmetic requires a series of steps of logic. The series is longer than the series required to prove that from 'X is a bachelor' we can conclude 'X is not married'. I can see no other material difference between the two cases.

Is it then the length of the proof that determines whether deducing B from A is analytic or synthetic?

If so, what is the maximum number of steps before something can no longer be considered analytic?

I introduced the two propositions about bachelors in my above post because they are theorems that require longer proofs than 'if X is a bachelor then X is not married'. They are also not immediately obvious, yet they are true. I am trying to explore the boundary between analytic and synthetic, to see what the maximum length of proof is.

Sure there is. For example, the world in which the capital is Cannes instead.

That's Kripke's necessary aposteriori in a nutshell. — Mongrel

No, it's not. The necessary a posteriori applies to things like identity statements using differing names of the same individual. I.e., there is no world in which Hesperus isn't Phosphorus. There are certainly worlds in which France has a different capital.

For example, the world in which the capital is Cannes instead. — The Great Whatever

That wouldn't be the thing we rigidly designated as France. How do we know that? Per Kripke, apriori. Let's read Naming and Necessity. And... get.... the... low down.

I've read Naming and Necessity. I'm actually pretty familiar with it.

The thing we rigidly designated 'France,' is France, which is depending on how you slice it a geographical area, nation-state, or cultural locus in Western Europe. It's perfectly possible for that very thing to have a capital other than France. It's not like having France as a capital is some essential property of it, or part of the definition of the word. It's kind of bewildering that people are seriously suggesting this tbh.

I'm not sure why taking several primitive deductive steps to get from one thing to another means that the meaning isn't so in virtue of the words. And I've never heard anyone say that the number of 'steps' involved (whatever that might mean) is relevant to the distinction. It's worth noting that a minimum required number of steps is not a semantic notion to begin with: there are no 'steps' to whether one meaning is contained within another, it just is or isn't by some well-defined containment relation (like the extension of one term being a subset of the other in any possible world). Deductive steps are a proof-theoretic notion, which isn't the issue. And in that case, how many steps minimum something requires depends on your proof-theoretic machinery.

Even if it were a modal possibility it certainly doesn't seem to be an empirical possibility that Paris is not the capital of France, and that is why TGW, despite his elaborate argumentation, is wrong.

I suppose it could be possible if you hold a view such that knowledge of the operations of a language is impossible without world-knowledge. — The Great Whatever

Wouldn't the popular view of meaning as use make this a given? You learn how to use a word by growing up around people who use it, so...

There is no elaborate argumentation here. When we say something's an empirical proposition, we mean roughly it pertains to some contingent matter of fact that might have been otherwise. Clearly Paris doesn't have to be the capital of France. It's synthetic a posteriori pretty uncontroversially on anyone's standards.

It may not be an epistemic possibility, in that what we know about France rules out that the actual world is one in which some place other than Paris is the nation's capital. But this is true of all sorts of empirical propositions. It's an empirical proposition that the sun is shining here and now, like you said, but given what I know about today's weather, there is no serious epistemic possibility that it isn't.

Explain, then how that would be empirically, as opposed to merely modally, possible. I 'm not denying that it is a logical possibility that France could have had a capital in a different location, and named differently than Paris; but we are talking here about the empirical world, France and Paris as they now stand.

How can a proposition that is necessary (and known to be necessary) be knowable only aposteriori? Kripke’s answer appeals to our knowledge of which properties are essential. He argues, quite plausibly, that we know apriori that properties like non-identity, being human, being not made out of clay, and being made out of molecules are essential properties of the things that have them. So we know apriori that if things have these properties, then they have them necessarily. — Soames

All you have to do is recognize that having Paris as its capital is essential to the thing we call France. And voila... it's necessary. I'm not sure why that seems bewildering. Kripke's possible worlds are just abstract objects anyway (there are no real grape growing regions in them, for instance.)

but we are talking here about the empirical world, France and Paris as they now stand. — John

Then you're not talking about it being metaphysically possible or impossible, but about it being actual or factual.

To say a proposition is contingent is not to say that we don't know in the actual world whether it's true. I know it's sunny right now; but it could have been otherwise. Just because it actually is sunny doesn't mean the proposition expressing that isn't based on experience, or contingent, or whatever you like.

I feel the same.
But I can see no other distinction between the assertion
'P1: If X is a bachelor then X is not married'
and
'P2: 7+5=12'
Statements such as 'P1 is true by virtue of the definition of bachelor' are meaningless. P2 is also true by virtue of the definitions of '7', '5', '+', and '12'. Given the definitions, one executes a sequence of deductive steps and arrives at the sentence '7+5=12'.

Similarly, given the definition

'D1: X is a bachelor at time T if X is a live, adult, male human at time T that has never been married at any time T2<T'

we can execute a series of deductive steps to arrive at the sentence

'If X is a bachelor then X is not married'

I must own that I cannot see any substantive difference between the two cases other than the length of the deductive sequence.

If Kant's claim was that statement D1 is an analytic proposition because it is identical to the definition of bachelor, then we would have a clear meaning of 'analytic proposition'. An analytic proposition is simply a sentence that is also a definition.

But under that approach, as soon as a deduction is needed to get from the definition to the sentence - even if that deduction is only a single step - the sentence ceases to be analytic.

All you have to do is recognize that having Paris as its capital is essential to the thing we call France. — Mongrel

But it quite clearly isn't. France could change its capital in the future.

I'm not sure why that seems bewildering. — Mongrel

It seems bewildering because it's clearly false, and you're defending it apparently with a misreading of Kripke. I'm not sure of any reasonable way to claim that France's capital being Paris is an essential property of France. In fact it seems insane. Maybe you can explain why you think that?

Even if it were a modal possibility it certainly doesn't seem to be an empirical possibility that Paris is not the capital of France, and that is why TGW, despite his elaborate argumentation, is wrong. — John

What do you mean by "empirical possibility"?

P2 is also true by virtue of the definitions of '7', '5', '+', and '12'. — andrewk

If you think math is learned synthetically, then you're going to deny this. This was more or less the default position in philosophy prior to the rise of logicism, as far as I know. Mathematical equations were not taken to be made true in virtue of definitions, but in virtue of intuitions about space and number.