apriori knowledge

[musenji]

But what about the proposition “the sums of the angles of a triangle is 180 degrees”? There is no such thing as a degree in reality;

Let me make sure I understand you. Are you also saying there is no such thing as an angle in reality? A degree is an abstraction, but it is not a priori. The concept "degree" (as used in geometry) is derived from the concept "angle". And angles exist in reality, and in reality, their sizes vary.

The same essentially applies to the form of the triangle itself. If someone were to point out a triangle in reality and say, “this is what I mean, thus it is justified by experience” I would simply ask: how do you know that figure is a triangle?

First off, to be accurate, you would point to several triangles, not just one, and what's more, triangles with different measurements. From this, the person you're talking to could see what is similar about them and what is different. If he couldn't, you could show him that, whatever their specific measurements, each one has three sides. He could infer that what you are calling "triangle" is a figure with three sides.

But strictly speaking, your question is just a question about language, right? Concepts can have a number of names, as is illustrated by the existence of many different languages that have a word for the concept which is designated in english as "triangle".

[DavidOdden]

Well justifying is kind of important, because otherwise how do you know something? I’m sitting in front of my computer right now. How do justify that statement, that is: how do I know it is true?

It's perceptually self-evident, and in need of no justification.

But consider now if I somehow at a later date I happen to forget that I wrote this post, and looking in this tread I see my post again. From that I could conclude that I, at some previous time was sitting in front of my computer and wrote this post. But that proposition would not be true by experience, so I would have to justify it by reason.

You don't have to justify it at all. I'm not saying that justification is never useful -- sometimes it is. For example, suppose a guy breaks in to your house and tries to chop of your head with an axe. You manage to grab a baseball bat and whack him hard, killing him. Then you might have to justify your action in court. Or, you might present a paper where you state that Aristotle believed in abstract forms that projected themselves into our plane of existence -- then you would have to justify that statement. I suppose if you use N computers to post and it's important to establish that you used The Home Computer, you could for example use the IP address stamp as your justification for the claim. The mistake you're making is not distinguishing the creation of knowledge (the original issue) and the justification of a claim (your current interest). The discussion is not about the social matter of persuasion, which is why justification is not relevant.

And in case a priori is limited only to pure a priori justification (a priori without any experience, like an innate idea or some other odd thing I guess) then the concept becomes useless, why define it in such a fashion?

Existents precede terms: why posit a useless term like "a priori" which doesn't actually mean anything? Funny thing about the mind: people can posit "ideas" without there having to be anything that they refer to. I'm certainly not responsible for the useless term "a priori".

[Zip]

So a person who is born blind knowing what the colour 'red' is would be considered as having a priori knowledge of 'red'?

Edited April 6, 2008 by Zip

[DavidOdden]

So a person who is born blind knowing what the colour 'red' is would be considered as having a priori knowledge of 'red'?

Yeah. That's not the most typical example, though. The idea of an "a priori" claim is that there are some things you can know to be true (or false) independent of experience. A less bizarre example would be that ice is frozen. You don't need to scientifically test this, if you know the meaning of "ice" and "frozen". Or, "cubes have 6 sides", "3+2=5", "Dogs are warm-blooded". To take the latter, I assume you are familiar with the fact that "dog" definitionally refers to a particular species of mammal and that one of the defining characteristics of mammal is warm-bloodedness. So just from knowing the definition of "dog" and "warm-blooded", you know dogs are. (More often, people use the relationship between unmarried and bachelor). Whereas you might have to do research to determine if all dogs bark.

[musenji]

In the full sense, he doesn't have knowledge of it. He can't differentiate it from other colors, he can't point to it--he can't even imagine it--and he wouldn't even be able to if he suddenly gained sight. He would have to be told, upon gaining sight, "remember that 'red' we told you about? These things are red."

Someone correct me if I'm wrong...

[Zip]

So a priori knowledge is deductive reasoning.

[DavidOdden]

So a priori knowledge is deductive reasoning.

That seems to be what they're trying to base it on. It's deduction based on the meaning of words, though it's an unformalizable deduction. The classic "all bachelors are unmarried" predominates in the discussion, because it's not an inane tautology like "All pigs are pigs" or "All gleebaxes are gleebaxes" where you don't even have to know the meanings of the words to decide that these are true statements (they don't even have to be real words). There is a very low-key profundity to saying that once you know the meanings of the words "bachelor" and "unmarried" that you can wisely surmise that "all bachelors are unmarried".

Philosophers who believe in this distinction often express genuine surprise that a person might not know that a bachelor is by definition unmarried, so if you try to persuade them that there is an experiential component to the proposition, i.e. that you have to research the matter a bit, they say "Well, then that person just doesn't know the meaning of "bachelor". Fair enough, and so similarly, the person who doesn't know that "All dogs are warm-blooded" is a tautology simply doesn't know the meanings of "dog", "mammal" and / or "warm-blooded". They get somewhat irate if you point out to them that the word also refers to a sex- and marriage-neutral academic degree, a member of an Iris band, a young seal and a knight not of an organized order, so that the deductively true sentence is really "All bachelors, in the sense of unmarried males over the age of majority, are unmarried", i.e. the inane tautology.

There is a further hair-splitting into a priori vs. necesssary vs. analytic statements, but I don't see the need to care.

[Zip]

That seems to be what they're trying to base it on. It's deduction based on the meaning of words, though it's an unformalizable deduction. The classic "all bachelors are unmarried" predominates in the discussion, because it's not an inane tautology like "All pigs are pigs" or "All gleebaxes are gleebaxes" where you don't even have to know the meanings of the words to decide that these are true statements (they don't even have to be real words). There is a very low-key profundity to saying that once you know the meanings of the words "bachelor" and "unmarried" that you can wisely surmise that "all bachelors are unmarried".

Philosophers who believe in this distinction often express genuine surprise that a person might not know that a bachelor is by definition unmarried, so if you try to persuade them that there is an experiential component to the proposition, i.e. that you have to research the matter a bit, they say "Well, then that person just doesn't know the meaning of "bachelor". Fair enough, and so similarly, the person who doesn't know that "All dogs are warm-blooded" is a tautology simply doesn't know the meanings of "dog", "mammal" and / or "warm-blooded". They get somewhat irate if you point out to them that the word also refers to a sex- and marriage-neutral academic degree, a member of an Iris band, a young seal and a knight not of an organized order, so that the deductively true sentence is really "All bachelors, in the sense of unmarried males over the age of majority, are unmarried", i.e. the inane tautology.

There is a further hair-splitting into a priori vs. necesssary vs. analytic statements, but I don't see the need to care.

Okay, I think I've got it. the idea is that some things are just 'known'. But anyone who has watched a child discover it's world can tell you that it just isn’t so.

For example, even the most basic knowledge like "fire burns" is unknown to an infant and it will stick its tiny fist into the fire to learn the truth of that statement.

Seems to me that everything that is not a natural function of the human body (circulation, respiration etc) is learned.

[Animae]

Let me make sure I understand you. Are you also saying there is no such thing as an angle in reality? A degree is an abstraction, but it is not a priori. The concept "degree" (as used in geometry) is derived from the concept "angle". And angles exist in reality, and in reality, their sizes vary.

I’m not denying that we experience angles in reality, what I’m saying that there is no such standard as a “degree” in reality, just like a unit of length—or any other unit—it’s reference is a matter of choice. The reason there is 360 degrees in a circle is because we define it as such.

First off, to be accurate, you would point to several triangles, not just one, and what's more, triangles with different measurements. From this, the person you're talking to could see what is similar about them and what is different. If he couldn't, you could show him that, whatever their specific measurements, each one has three sides. He could infer that what you are calling "triangle" is a figure with three sides.

But strictly speaking, your question is just a question about language, right? Concepts can have a number of names, as is illustrated by the existence of many different languages that have a word for the concept which is designated in english as "triangle".

It’s not just a matter of language, but let’s say for the case of the argument that the whole base of math can be derived by induction. Now if a mathematician wanted to justify his one of his theorems—that is, to check if it is true or false—he would not do so by looking at reality. He would validate it a priori, and quite often it is actually impossible to even compare it to something we experience, as many mathematical concepts are beyond human experience.

So whenever at the fundamental level, the mathematician uses concepts derived from experience does not change the fact that he proves his theorem through reason.

A priori and a posteriori does not refer to where the concept comes from, as far as I understand it. It refers only to the method by which we validate knowledge. Otherwise I could say that since I learned about triangles in elementary school (or whenever I now learned about them first) my knowledge of triangles is a posteriori. Where we pick up ideas is not really of interest epistemologically.

It's perceptually self-evident, and in need of no justification.

Yes, I experience it therefore it is true (I don’t think that there is any need to mention that it implies that my brain functions properly, I’m not hallucinating or anything).

Oh and I use the term “justified” as synonym with valid in this context. All knowledge must of course be valid—otherwise it’s not really knowledge but rather belief.

I don’t think that philosophers mean knowing-that-precedes-knowing or anything bizarre like that when they refer to a priori knowledge, at least I don’t think that what most philosophers mean by it.

To me it seems that a priori/a posteriori simply refers to whenever the knowledge is attained by deduction or induction.

And a priori/a posteriori does not refer to the same thing as analytic/synthetic so they should not be confused.

Edit: Wikipedia seems to agree on the a priori/a posteriori distinction as being the distinction between inductive and deductive knowledge.

"The terms "a priori" and "a posteriori" are used in philosophy to distinguish between deductive and inductive reasoning, respectively."

Wikipedia

Edited April 7, 2008 by Animae

[Thomas M. Miovas Jr.]

So whenever at the fundamental level, the mathematician uses concepts derived from experience does not change the fact that he proves his theorem through reason.

A priori and a posteriori does not refer to where the concept comes from, as far as I understand it. It refers only to the method by which we validate knowledge. Otherwise I could say that since I learned about triangles in elementary school (or whenever I now learned about them first) my knowledge of triangles is a posteriori. Where we pick up ideas is not really of interest epistemologically.

Actually, that is the problem with a priori and a posteriori, they are not really based upon how man actually gains knowledge. There is no knowledge apart from the facts of reality (a priori) and experience in and of itself does not comprise knowledge (a posteriori).

Reasoning is not just any ole thing one can do with one's mind. To be rational, one must organize and conceptualize the facts of reality in a non-contradictory manner. Starting with a formula, as you indicate about mathematics, is rationalism, not reasoning. That is, to validate one's knowledge about anything, including theories, one must see if the theory matches some aspect of reality. In other words, there is no process (mathematical or otherwise) divorced from something to process -- i.e. the facts of reality. One cannot say, a priori, that x+y=z; one has to know what addition means and what the symbols represent, which, in this case, means commensurate units of measurement of some quantity, which is gotten from and observation of reality conceptualized by man's mind.

And as to choosing those units of measurement -- i.e. degrees -- they are not arbitrary, even though there can be different systems of units. Yes, it would be possible to come up with a sort of metric measurement of angles, whereby a full circle would be comprised of, say, ten or one hundred of such units. But so long as one is consistent with what those units measure and the quantity of that unit, it is not arbitrary. And since an angle is a real thing in reality, conversion ratios could be used to translate one set of units to another -- i.e. 360 degrees = 100 metric angle units.

Basically, if you read Introduction to Objectivist Epistemology, Miss Rand shows that all knowledge is based upon the facts of reality as grasped by a conceptual mind; and so Objectivism dispenses with a priori and a posteriori. The fundamental means of being rational is to organize the facts of reality according to similarities and then omit the measurements. One cannot do that before the facts and the facts by themselves is not knowledge. As with everything else in Objectivism, reasoning is a specific relationship between man's mind and existence, and that fundamental relationship is to organize facts according to similarities and omit the measurements to arrive at an abstraction that can then be made into a concept.

[cmdownes]

"So a priori knowledge is deductive reasoning."

It's very important - especially in the context of Kant, which the OP is referring to - to keep the differences between the a priori, the analytic, the necessary and the deductive clear.

The a priori/a posteriori distinction is an epistemic one. A priori knowledge is knowledge which can be gained independently of experience. A posteriori knowledge is gained through experience.

The deductive/inductive distinction is a distinction between types of arguments. A deductive argument is an argument such that neccessarily if the premises are true, then the conclusion is true. An inductive argument is one such that if the premises are true, than the conclusion is unlikely to be false. Deduction and induction refer to the relations between premises in different types of arguments.

A concrete example of the difference. Bill can have a posteriori knowledge of the fact that it rained April 6th in Seattle, but have it because of a deductive argument. The argument that gives him this knowledge might look like:

P1: It has rained every Sunday in Seattle for the last 10 years.

P2: April 6th was a Sunday.

C: Therefore, it rained in Seattle on April 6th.

That's a deductive argument. If the premises are true, the conclusion is necessarily true. But because Bill's knowledge of the premises relied on experience (He's been looking out his window every Sunday for 10 years, he looked at a calendar, etc), the knowledge that he derives deductively from those premises is a posteriori knowledge.

These two should further be distinguished from the analytic/synthetic distinction, which is a semantic distinction between different sorts of propositions.

[y_feldblum]

The sum of angles in a plane triangle (any plane triangel) is 180 degrees (a straight angle). That is a concept and is derived a priori from the postulates of Euclid. One need not measure the angle sum. One can deduce it. A Priori is Latin for "from what is before or prior". In this case a proposition is deduced from logically prior propositions.

All mathematical theorems are examples of a priori propositions.

Bob Kolker

It seems you are confusing knowledge of a fact without prior experience of that particular fact with knowledge of a fact without prior experience of any facts at all.

We can deduce, from Euclid's axioms, that the sum of the angles of a triangle form 180 degrees. But we have knowledge of Euclid's axioms. And that knowledge of Euclid's axioms comes from experience.

But we cannot somehow just know about triangles before opening our eyes for the very first time.