Cito di Pense wrote: Sweenith wrote:
examples of a priori knowledge: "2+2=4" "no bachelors are married" "all squares have four sides of equal length" those are knowable a priori, because they can be grasped via reason alone.
Incredible. What is prior to making those statements is knowing (or agreeing to) the defintions of 'addition', 'equality', 'bachelor', 'married', 'square', 'side' and 'length'. Having a definition of a geometric square is contingent on having seen or made an approximation of it on the ground. You can go with Kant, and say that space and time are prior to reason, but that's an observation, since humans evolved from bacteria.
Again you're confusing terms with what they stand for. A person can know and understand the truths that 2+2=4
, that no bachelors are married
, that all squares have four sides of equal length
, and so on, without ever actually giving those statements expression in language. And one doesn't
have to have a definition of something in order to know and understand it (I can't define or describe what the color green looks like, but I know it when I see it).
You're talking about innate knowledge
anyways, not a priori knowledge. If knowledge is a priori that just means it can be arrived at through reason alone, and doesn't require recourse to empirical evidence. It's innate
knowledge, on the other hand, which is supposed to be known entirely from birth, non-inferential etc.
In addition, geometrical and mathematical truths aren't contingent upon the existence of space and time (rather, it's our ability to define them that depends on it). That a triangle has three sides
, for instance, would still have been true even if this whole physical universe had never existed and there wasn't any space or time - that's because mathematical truths are abstract and don't depend on there being particular instantiations of them in the real world.
Yes, you're coming at this from a philosophical POV, and like the notion that philosophers work things out from first principles. My view is that all those first principles come by way of the empirical. The best you can do is to suggest that it is reason that imposes order on the empirical, but that is an axiom, and not an a priori. Is the order there first? Can you say that evolution (of reasoning) is possible without some sort of prior order? Is that an observation or a deduction? If the latter, it is perhaps the self-evident axiom you are looking for, and it is not the foundation for philosophy, but for science.
I think Kant's view (the anti-realist bit) is a little crazy myself, and I can't see why anybody would adopt it (as I see it, a consistent Kantian ought to be a solipsist)
I see no guarantee that the exercise of pure reason gives you anything but that, and you have to stop there, because you can't make your definitions do anything much by invention of definitions. If modus ponens works consistently, it is because there is consistency. It's not saying much.
That sounds right to me. I'm not much into system-building. historically, looks to be a fruitless effort (whether it's Spinoza, Hegel, or even a more modern like Carnap)
Cito di Pense wrote:
Well, that's bad for you, since the existing order in the universe will break down, according to the laws of entropy and high energy physics.
That's assuming the universe is a closed system (i.e. it presupposes materialism)
Meh. There is not anything necessarily true, since no truth is not a statement. That's only a definition.
I'm not sure I understand you - are you saying that there are no necessary truths
? If that's so, then what you're saying isn't necessarily true. And that would mean that there's a possible world in which "there are necessary truths" is true. But if something is necessary in one possible world, then it's true in all possible worlds, including the actual one. Therefore, if "there are no necessary truths" is true, then it follows that there is
(at least one) necessary truth. That shows that "there are no necessary truths" is self-defeating.
Cito di Pense wrote:
No I think God has created every existing thing about from himself, but I don't think he created the rules of logic (that seems to be an incoherent idea).
That's nice, Sweenith, but it is a nonsense statement about a nonsense entity. Kronecker's statement is ironic. Even if Kronecker actually believed in God, he only could use it as an axiom, and ironically so. IOW, if you want to talk about authentic a priori knowledge, you will need to talk about God, but that is nonsense. All you will have is connection between necessary truth and the word 'God'. Done with you.
(typo - it was supposed to read "every existing thing apart
from himself" - no doubt that was the source of the alleged "nonsense"
Huh? What does God have to do with a priori knowledge? And who said anything about me being concerned about whether there's a ground for a priori knowledge? I'm inclined to think there is (as I would define it that is), but that's more or less inconsequential relative to the issues that do concern me.
Why is my statement nonsensical? Maybe you can do a better job justifying that sort of claim than has been done in the past (the positivists never did get a successful statement of their verification principle)
Yep. God has ordained it. If you find yourself having to talk about what is prior to everything else, you're doing theology, and not philosophy. Go to the Theism forum, or find somebody else to do it with, here. Theology does not involve the exercise of reason, but the construction of a lot of very trivial tautologies. Not interesting to me.
For a person who finds theology uninteresting, you seem surprisingly eager to turn this into a discussion about God rather than epistemology. I'm not sure I said anything related to theism until you brought up that mathematician actually, and even then I was merely stating my position.
I'd love to go without having to define the same old terms over and over, but then people just talk past one another.
Well, you won't find me trying to talk past you. I'm very plain spoken, am I not? Why did it take us so long to bring God into this? To say that such conversations are about God? You and I can have a conversation about something I will say is nonsense. Speculating about necessary truths is a preamble to discoursing about God. It's just that once we start talking about God, it is plain that we are talking about bullshit. Are we not plain-spoken?
I'm still confused as to where God comes into play here. Just so we're on the same page - when I say "God" I mean something very particular—a morally perfect, personal being that knows all and can do all, insofar as is possible—I'm not
using it in some vague apophatic way as some mysterious X, or as a sort of Hegelian Absolute, or anything like that (those do
seem to me incoherent concepts).
If mine is the very same definition of God you had in mind when you said my statement was non-sensical, maybe you can pin-point exactly what it is that makes it so? (though from past experience I expect a retort to the effect of "cause it's — a fantasy/a delusion/made-up gibberish/etc." , I would be very interested in a more serious answer. From your phrasing it sounds like you're saying the defect in the statement—I think God has created every existing thing apart from himself
—is that it's semantically meaningless, but more often than not I find that what people are really trying to object to is that it's unscientific or incompatible with empiricism or some such thing.