knowledge

It was a revelation to have read An Introduction To Philosophical Analysis, by John Hospers in two days, all 600 or so pages of it. I recommend the book to all interested in philosophy. The man was a presidential candidate, and a professor of philosophy.

He begins with language, words, definitions, the basic construct of language, then he talks about knowledge, after which he goes on to talk about cause, determinism, God. I find the first 200 pgs or so facinating, and I’ll endavour to provide you with a summary in the next few days, it would enhance our understanding of philosophy for it clarifies all the concepts I have had into a coherent system of thought.

For the mean time, I’d like to explain my understanding of the theory of knowledge.

A priori = necessary truth for all cases. ‘if someone is in New York, we do not need to investigate further to discover whether he is also in California.’
Analytic = tautology. ‘A is A’
A posteriori = contingient truth, ‘any statement that we do have to test to see whether it holds for future cases is a contingent statement.’
Synthetic = not analytic

Analytic statements are necessarily true for all cases, therefore it is a priori. A posteriori statement is ‘the cup is on the table’, it is synthetic because you can not verify the veracity of it on analysis of the statement itself, you have to test it.

The question then raised was whether synthetic a prior statement is possible? it is a statement that is not analytic that is true for all cases. He gave many examples, like

‘2 + 2 = 4’
‘Every event has a cause’
‘Everything that is colored is extended. (Extended = spread out in space.)’

Rationalists believe such statements are synthetic a prior, but empiricists do not. The empiricists say either a statement is a priori, and not synthetic, or synthetic and not a priori.

is ‘2+2=4’ analytic? it would appear so, because 4 is a signifier for 2+2
is ‘every event has a cause’ synthetic? yes, but it is not a priori because what is the cause of the first event?

I wonder if a posteriori analytic statement is possible.

to be continued.

Something which is not an event. God is not an event because he does not “happen”. God is necessary. Everything else happens. This is not necessarily my view, though, but it is a view.

So what do necessary and contingent mean, exactly?

As regards propositions, it depends on whether they can be denied without self-contradiction.

As regards real beings, it depends on how is their relation to existence. Necessary: cannot not exist. Contingent: can not exist.

And please don’t pretend that you don’t understand what I mean on the ground that some contemporary philosophers do not want to apply these concepts to real beings.

not even kant believed that a posteriori analytic statements were possible…

-Imp

A necessarily true proposition is one whose negation is impossible. For instance, “Nothing can be red and green all over” The negation of that, namely, that something can be red and green all over leads to a contradiction, “this is both red and green all over”.

A contingently true proposition is one whose negation is not logically impossible. For instance, “This rose I have in my hand is red”. Suppose that statement is true. It would be possible for it to have been false, if for instance I had been holding a white rose.

A “real being” is contingent just in case the denial that it exists is possible. Which is to say, we are really talking about the proposition that so-and-so-exists. And a “real being” is a necessary being just in case it is true of it that it is impossible that it should not exist, or, to put it into the language of propositions, if it is true of some so-and-so that it is impossible that so-and-so does not exist. So, the concepts of necessity and contingency can be applied to real beings, since we can translate them into talk about necessary and contingent propositions.

The question now is whether the proposition that so-and-so exists can ever be a necessary truth. As Hume pointed out, whatever can be conceived as existing can be conceived as not existing. It that is true, then there are no necessary truths of the form, so-and-so exists. And, so, there are no necesssary beings.

If you are asking whether a statement like “things equal to the same thing are equal to each other” (which some have said is analytic) could be known by sense-experience (which is what many would say is meant by “known a posteriori”) then I don’t see why not. Someone could, for instance, take two small sticks, A and B, and then see whether both of them are equal (in length) to another small stick, C, find out that they are, and then determine whether A and B are equal in length to one another. And the person could repeat this experiment with other sticks as often as he pleased, and after he had achieved the same result, announce that he had come to know that whenever two sticks are equal to a third stick in length, they are equal to one another in length. He came to know this by observation.

I don’t see how your example of an a priori truth is in fact a “necessary truth for all cases.” If someone is in New York, we do need to investigate further to determine for sure whether he is not also in California. Practically, you may be quite confident that he is not in California, but there’s no logical self-contradiction in him being in both places at once. It may contradict some other axiom you hold, like “a being can only be in one place at a given time” – but the proposition “a man is in New York and the same man is in California” does not contain a self-contradiction.

‘2 + 2 = 4’ is an analytic statement; it can be proven from a set of axioms.

‘Every event has a cause’ is analytic if you define “event” as “something which has a cause”; but synthetic a posteriori if you do not make that definition. It’s not a tautology without the definition (therefore synthetic), and there is no self-contradiction in denying it – I can easily conceive of an event without a cause, for example an object popping into existence for no reason whatsoever. Therefore it is also a posteriori.

‘Everything that is colored is extended’ is also synthetic a posteriori. It’s not a tautology, and I can easily imagine a colored point (even though I’ve never seen one).

In fact, I would go so far as to say that

  • A proposition is analytic if and only if it is a priori
  • A proposition is synthetic if and only if it is a posteriori

therefore the concepts are merely redundant and confusing.

I’m not sure I can offer a proof, but I challenge anyone to offer an example of synthetic a priori or analytic a posteriori.

The red/green object thing fails for the same reason as the man in new york/california. There’s no logical contradiction in an object being both red and green all over, even though you’ve never seen it. So “no object red and green all over” is a synthetic a posteriori statement (unless you have an axiom like “colors may not overlap” which would itself be a synthetic a posteriori axiom).

Last night i had the idea that a true proposition has to be analytic, because the truth of a proposition is always contained in the proposition itself. The empiricsts are right.

Snow is white was often considered synthetic LINGUISTICALLY. But conceptually (Snow is white) is white is a conceptual tautology.

aporia:

The logical positivists thought so too.

I don’t think so. Even if the above is correct, the concepts are still different. A priori/a posteriori has to do with the nature of justifications of the truths of statements, analytic/synthetic has to do with the nature of the truth of statements. They may, perhaps, be co-extensional, but they’re not the same thing.

That’s not Empiricism. That’s Rationalism. Leibniz, the last of the three great Rationalists proposed the "in est " principle which held that every predicate is contained in the subject (except for the predicate of existence which is contained in the subject only of God) except that no human mind is able to “see” that except in definitional contexts like “all fathers are males”. God, however, who has an infinite mind, can “see” how whiteness is contained in the subject of snow.

I think to figure this out we first have to clarify what “A priori” means. Necessary truth for all cases could simply mean something is never false, but I don’t think this is what you have in mind. It could also mean that you cannot imagine it being another way, but is this simply for lack of imagination? Finally, it could mean that it is contingent from the laws of logic. I think this definition makes the most sense given what you are trying to convey. For example, if a law of logic states that something cannot have a property and not have that property at the same time, then a contingent statement is that a statement cannot be true and false (untrue) at the same time.

So to more clearly ask your questions, more clearly, we could ask if a synthetic statement can be directly derived from the laws of logic.

‘2 + 2 = 4’
‘Every event has a cause’
‘Everything that is colored is extended. (Extended = spread out in space.)’

I think the latter two are obviously not directly derived from the laws of logic, but the first one is not as clear. I still don’t think it is derived from the laws of logic, however, because it refers to specific things, such as objects and ideas. If you have two objects, or ideas, and you get two more, you will end up having four. You cannot know what will happen with things such as objects or ideas unless you actually have some experience of objects or ideas.

A priori is Latin for “comes before”. To say that a proposition is known a priori means that the proposition is known before sense experience, or, more accurately, is known independently of sense-experience. Thus, to take a simple (and trivial) example, the proposition, “All dog are dogs” is known a priori, because it is consistent with all sense-experience. No sense-experience could refute it. There have been, however, less trivial cases of a priori propositions proposed. For instance, that all things equal to the same thing are equal to one another. Or even that every event must have a cause. It is also often held that all propositions that are known a priori are also necessary truths.
A necesssary truth is a truth whose negation is impossible, or implies a contradiction. For instance, the negation of “all dogs are dogs” would be “Some dogs are not dogs” and that would be a contradiction, or a proposition which would state an impossibility.But “a priori” does not equal “necessary truth” since the former refers to how the proposition is known, and the latter to the kind of proposition it is. So, although it might be true that all a priori propositions are necessary truths, and all necessary truths are a priori propositions, even if that were the case, “a priori” and “necessary truth” would not mean the same thing.

“Contingent” is the contrary of “necessary”. If a necessary truth is a truth whose negation is impossible, a contingent truth is a truth whose negation is possible. For example, that all dogs bark might be true, but it is a contingent truth, since it would be possible for there to be a non-barking dog even if, in fact, there are no non-barking dog.

dogs with relish seldom bark…

-Imp

dogs with relish seldom bark…

But you must admit that dogs often piss on bark with relish.

Dunamis

How clever!

please don’t confuse linguistic a priori with conceptual a priori. when you speak of a dog, are you speaking of it in the conceptual or linguistic sense?