Philosphy help: Analytical/Synthetical and a priori/a posteriori

[Ichneumon]

Alright, I need some help. These definitions confuse me a lot.

So, first there's analytical and synthetical.

Analytical: A proposition of which the predicate is already conceptually captured within its subject. (e.g. a square is a rectangle)
Synthetical: A proposition of which the predicate is not already conceptually captured within its subject. (e.g. My curtains are red.)

Then, there's a priori and a posteriori, which as I understand, Kant defines as:
A priori: Something that does not require experience.
A posteriori: Something that does require experience.

WHen you combine these, there are 3 possible combinations (analytical a posteriori is ignored).

Analytical a priori
Synthetical a priori
Synthetical a posteriori.

Now, the trouble is that I can't think of good clear examples of these 3 types, without getting very confused. Could someone help?

Synthetical a posteriori: My p&p RPG collection contains 5 different rollplaying games.

Analytical a priori: Two and two makes four.

I have trouble finding something that is synthetical a priori...

[Chambers]

Analytic-synthetic distinction (http://en.wikipedia.org/wiki/Analytic-synthetic_distinction)

[Telonius]

Oddly enough, math equations are synthetic, not analytic. The concept of "2" is separate from the concept of "4." Analytic a priori are generally only definitional things.

Analytic a priori: All squares have four sides.
Synthetic a priori: 2+2=4
Synthetic a posteriori: My curtains are red.

[mrpitchfork]

Man I need to start reading philosophy books. I'm already a decent philosopher but I don't know about the more super complex stuff.

Are there good books to read (besides the writings of the actually good philosophers), or should I just take a class?

[Chambers]

Man I need to start reading philosophy books. I'm already a decent philosopher but I don't know about the more super complex stuff.

Are there good books to read (besides the writings of the actually good philosophers), or should I just take a class?

Books used in my Analytic Philosophy class.

Language, Truth, & Logic (Ayer) http://www.amazon.com/Language-Truth-Logic-Alfred-Ayer/dp/0486200108
How to do things with word (Austin) http://www.amazon.com/How-Do-Things-Words-Lectures/dp/0674411528
Analysis and Metaphysics (Strawson) http://www.amazon.com/Analysis-Metaphysics-Introduction-Philosophy-Strawson/dp/0198751184
The Philosophy of Logical Atomism (Russel) http://www.amazon.com/Philosophy-Logical-Atomism-Court-Classics/dp/0875484433

[Ichneumon]

Analytic-synthetic distinction (http://en.wikipedia.org/wiki/Analytic-synthetic_distinction)

I checked it before posting this threae, but it didn't really help.


Oddly enough, math equations are synthetic, not analytic. The concept of "2" is separate from the concept of "4." Analytic a priori are generally only definitional things.

Analytic a priori: All squares have four sides.
Synthetic a priori: 2+2=4
Synthetic a posteriori: My curtains are red.

Thanks. That's actually quite odd. Can you give another example? of synthetic a priori?

[Telonius]

I checked it before posting this threae, but it didn't really help.



Thanks. That's actually quite odd. Can you give another example? of synthetic a priori?

"In a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides." True statement, not dependent on personal or external experience, but the concept of "c^2" is not contained in either the concepts of "right triangle," "b^2," or "a^2."

[Ichneumon]

Right, I think I understand. Thanks! :smallbiggrin:

[Weezer]

Man I need to start reading philosophy books. I'm already a decent philosopher but I don't know about the more super complex stuff.

Are there good books to read (besides the writings of the actually good philosophers), or should I just take a class?

I've had some good luck just reading the works of good philosophers. It helps to have someone who knows the material or is just a good thinker to talk them over with. I both taken a few philosophy classes and read a bunch on my own and for me at least the primary reason to take a class is the discussion, professors that just lecture are pointless.

Also I would reccomend not reading books that are just summaries or explanations of other writers, it is always better to read the primary source yourself and try to understand it in your own way.

[Tirian]

Oddly enough, math equations are synthetic, not analytic. The concept of "2" is separate from the concept of "4." Analytic a priori are generally only definitional things.

As a mathematician, I have to say that this is a hundred and twenty years out of date. "4" is defined as the number after the number after "2", and "2+2=4" expresses that definition as much as saying that Buffalo is two stops after Syracuse on the Lake Shore Limited.

I don't want to blame Kant for not knowing this when he originally set out the concept, because arithmetic wasn't formalized until decades after his death, but still.

[Semidi]

Alright, I need some help. These definitions confuse me a lot.

So, first there's analytical and synthetical.

Analytical: A proposition of which the predicate is already conceptually captured within its subject. (e.g. a square is a rectangle)
Synthetical: A proposition of which the predicate is not already conceptually captured within its subject. (e.g. My curtains are red.)

Then, there's a priori and a posteriori, which as I understand, Kant defines as:
A priori: Something that does not require experience.
A posteriori: Something that does require experience.

WHen you combine these, there are 3 possible combinations (analytical a posteriori is ignored).

Analytical a priori
Synthetical a priori
Synthetical a posteriori.

Now, the trouble is that I can't think of good clear examples of these 3 types, without getting very confused. Could someone help?

Synthetical a posteriori: My p&p RPG collection contains 5 different rollplaying games.

Analytical a priori: Two and two makes four.

I have trouble finding something that is synthetical a priori...


OK, this gets complicated because twentieth century philosophy has been all over this and people, to this day, will disagree with each other.

I personally agree with Quine that there really isn't an analytic/synthetic distinction (Two Dogmas of Empiricism for more information)

Anyway,

2 + 2 = 4 is an example of synthetic a priori. Kant actually argued for this. However, as it has been stated, it's bogus. Frege and Russell dealing with this problem actually led to analytic philosophy as we know and love it today.


Man I need to start reading philosophy books. I'm already a decent philosopher but I don't know about the more super complex stuff.

Are there good books to read (besides the writings of the actually good philosophers), or should I just take a class?

Here are some of my favorites:

(Note, these range from awesome and easy to read to awesome and like hitting your head against a brick wall. Also, this is just Analytic Philosophy. I'm actually not too smart on Continental Philosophy.)

Foundation of Arithmetic - Frege
The Tractatus - Wittgenstein
Philosophic Investigations - Wittgenstein
From a Logical Point of View - Quine
Problems of Philosophy - Russell
Language, Truth, and Logic - A.J. Ayer
Principia Ethica - G.E. Moore

Yeah, I'm going to stop here. The easiest here are Problems fo Philosophy and Language, Truth, and Logic. To really understand what they're dealing with you should probably read some Kant and some Bradley.

[Pyrian]

"4" is defined as the number after the number after "2", and "2+2=4" expresses that definition...

I don't want to blame Kant for not knowing this when he originally set out the concept, because arithmetic wasn't formalized until decades after his death, but still.Does that really change the notion or just push it back a few steps into set theory? The synthesis of underlying postulates occurs at a much lower level, sure, such that by the time you've got a number you've already assumed enough that other mathematical operations naturally follow. But any time you combine postulates, wouldn't that be a synthesis?

[Tirian]

Does that really change the notion or just push it back a few steps into set theory? The synthesis of underlying postulates occurs at a much lower level, sure, such that by the time you've got a number you've already assumed enough that other mathematical operations naturally follow. But any time you combine postulates, wouldn't that be a synthesis?

I just don't know; I only took one semester of philosophy in college and Kant wasn't part of it. I'd appreciate it if the OP brought the issue to class and got the professor's opinion on it. Because, to me, the "two less than two-ness" is implicit in the definition of "four" as defined by Cantor and Frege and Peano and all that lot. Again, to me, "4 x 5 = 20" makes a much clearer case of being a synthetical proposition as the definition of multiplication is a heavy abstraction compared with addition.

Having said that, there is an addition problem given as an example of a synthetical proposition on Wikipedia, which clearly has had the opportunity to correct the advances in the field since Kant's death, so this may be a debatable point. If it were me, I'd feel safer coming up with a non-mathematical example for homework and seeing if addition is a can of worms by opening it in class.

[Virgo]

The lynchipin to understanding Kant's claim that synthetic a priori knowledge is possible (or one of the major steps, anyway) is his ideas of time and space as transcendentally ideal. Put another way, time and space are "conditions for the possibility of our experience." One of my philosophy professors memorably likened the entire situation to seeing the world through rose-colored glasses, where everything that we see it tinted red. When we're born, we're born with "space- and time-colored glasses;" space and time don't exist in things as they truly are, but are artifacts of our perceptions, and are necessarily presupposed in order to even imagine any experience at all like our own.

Kant claimed that arithmetic was synthetic because, although the value of "2" is indeed an analytic concept, the idea of adding 2 to 2 requires that we hold the idea of 2 in our minds while we add another 2. Counting was synthetic by the same token; it requires that we remember, to some degree, the value that we had a moment before, meaning that it's a process subject to time and therefore synthetic. However, it was a priori in the sense that we don't require any concrete experience to allow us to perform the mental operations.

[Dancing_Zephyr]

I add my support for math being analytical. I was almost sure thats why mathematicians do proofs, to show that one term is equal (or greater or lesser than) another term. If this is true then one side of an equation is actually a definition of the other.

Its also hard to think of a non trivial analytical claim.

My prof said that anything you have to sit and think about whether its true or not is a posteriori, but he said so in a fairly casual discussion, so don't take that too seriously.

[Zen Monkey]

Man I need to start reading philosophy books. I'm already a decent philosopher but I don't know about the more super complex stuff.


I wouldn't say that epistemology is necessarily more difficult than other fields, but it certainly has an awkward vocabulary and strays into some 'philosophy of language' territory at times. Philosophy is such a big field that people in very different specializations can sometimes have trouble communicating effectively when discussing each other's fields. I taught philosophy of religion, ethics, and political philosophy but didn't have a lot of meaningful common ground with the epistemologists or metaphysics folk.