Synthetic a priori judgments
Synthetic a priori judgments
David Hume thought there are two categories of knowledge; knowledge that is independent of experience which tell us nothing about the world, and knowledge that is derived from experience. Immanuel Kant came to the conclusion there is another kind of knowledge independent of experience that can tell us something about the world. This kind of knowledge falls under what he calls synthetic a priori. To understand synthetic a priori, some distinction must be made.
The first distinction is between a priori and a posteriori. Knowledge that is independent of experience is a priori, universal, and is a necessary truth. They are universal by being true everywhere and at the same time, and necessary true by being logically impossible in being false. A posteriori knowledge is gained from experience, and is always open to revision; such knowledge would be, “all dogs have two eyes.” This is revisable since we don’t have omniscient knowledge of the world; it is possible a dog is discovered (experienced) that has three eyes. The next distinction is between different thought processes; that is, analytic and synthetic judgments. Analytic judgments which the subject contains the predicate; the definition of the subject is defined in the sentence. Such as, “all bachelors are unmarried.” The subject “bachelor” contains the predicate, “are unmarried”. Analytic judgments are necessary truths, but they tell us nothing about things independent of them, they tell us nothing about the world. Judgments that tell us something independent of the subject are synthetic; such as, “all bachelors are bald,” here the statement gives information that is not contained in the idea of a bachelor. “All bachelors are bald” can also be said negatively as “no bachelors are bald,” without a self-contradiction. This can’t be done with “all bachelors are unmarried,” as “no bachelors are unmarried,” which is a self-contradiction. Hume considered a priori and analytic statements as inseparatable, as well as a posteriori and synthetic statements. That is, they were considered so closely linked that the idea of one of them would include the idea of the other. The idea of an analytic judgment must be a priori because the truth of it does not depend on experience. Similarly, a posteriori and synthetic statements seemed inseparatable since useful information is only provided by experience. But Kant argued for the category of synthetic a priori judgments.
Kant gives the example of, “12 = 5 + 7,” as “12” does not contain the predicate of “five plus seven.” This is an example of synthetic a priori judgment since it is necessary, universal, independent of experience, and gives information that is not defined in the subject “12”. Drawing from this point, Kant says we can derive necessary, and universal truths about the world from certain concepts. “Every event has a cause” is synthetic as the negation, “no event has a cause” is not self-contradictory; it is also universal and necessary and so falls under a priori. If Kant is correct, he has discovered a new way to gain information about the world.
Although Kant’s argument is persuasive, I am not convince of the example, “12=5+7” as a synthetic a priori judgment. It seems to me this is an analytic judgment; if “12” is broken down as twelve “1’s”, and same is done for “5” and “7”, there is basically twelve 1’s equaling twelve 1’s (12=12). So it seems, “5 +7” does contain the idea of 12, which makes it analytic.
David Hume thought there are two categories of knowledge; knowledge that is independent of experience which tell us nothing about the world, and knowledge that is derived from experience. Immanuel Kant came to the conclusion there is another kind of knowledge independent of experience that can tell us something about the world. This kind of knowledge falls under what he calls synthetic a priori. To understand synthetic a priori, some distinction must be made.
The first distinction is between a priori and a posteriori. Knowledge that is independent of experience is a priori, universal, and is a necessary truth. They are universal by being true everywhere and at the same time, and necessary true by being logically impossible in being false. A posteriori knowledge is gained from experience, and is always open to revision; such knowledge would be, “all dogs have two eyes.” This is revisable since we don’t have omniscient knowledge of the world; it is possible a dog is discovered (experienced) that has three eyes. The next distinction is between different thought processes; that is, analytic and synthetic judgments. Analytic judgments which the subject contains the predicate; the definition of the subject is defined in the sentence. Such as, “all bachelors are unmarried.” The subject “bachelor” contains the predicate, “are unmarried”. Analytic judgments are necessary truths, but they tell us nothing about things independent of them, they tell us nothing about the world. Judgments that tell us something independent of the subject are synthetic; such as, “all bachelors are bald,” here the statement gives information that is not contained in the idea of a bachelor. “All bachelors are bald” can also be said negatively as “no bachelors are bald,” without a self-contradiction. This can’t be done with “all bachelors are unmarried,” as “no bachelors are unmarried,” which is a self-contradiction. Hume considered a priori and analytic statements as inseparatable, as well as a posteriori and synthetic statements. That is, they were considered so closely linked that the idea of one of them would include the idea of the other. The idea of an analytic judgment must be a priori because the truth of it does not depend on experience. Similarly, a posteriori and synthetic statements seemed inseparatable since useful information is only provided by experience. But Kant argued for the category of synthetic a priori judgments.
Kant gives the example of, “12 = 5 + 7,” as “12” does not contain the predicate of “five plus seven.” This is an example of synthetic a priori judgment since it is necessary, universal, independent of experience, and gives information that is not defined in the subject “12”. Drawing from this point, Kant says we can derive necessary, and universal truths about the world from certain concepts. “Every event has a cause” is synthetic as the negation, “no event has a cause” is not self-contradictory; it is also universal and necessary and so falls under a priori. If Kant is correct, he has discovered a new way to gain information about the world.
Although Kant’s argument is persuasive, I am not convince of the example, “12=5+7” as a synthetic a priori judgment. It seems to me this is an analytic judgment; if “12” is broken down as twelve “1’s”, and same is done for “5” and “7”, there is basically twelve 1’s equaling twelve 1’s (12=12). So it seems, “5 +7” does contain the idea of 12, which makes it analytic.
I would agree, when I read this in the "Critique of Pure Reason", his argument for 7+5=12 being synthetic did not seem convincing. Analytic can be said to be "A is A", "7+5 is 12". It seems quite clear it is analytic.
ReplyDeleteNow I think this shows Hume was wrong as well, math is very vital to natural science, so analytic truths are indeed non-trivial. I think the solution to Hume's skepticism is to find fault with his premises, not accept them and find an obscure third path.
Your judgment about 12=5+7 of not being synthetic but analytic is difficult to analyse because there are infinite possibilities for 12 to be arrived although it contains 5 & 7 which can be excluded in analysis of infinite possibilities.
Deletethanks for the comment; I didn't think people actually read this.
ReplyDeleteI only read Kant's Prolegomena, I was hoping for a better explanation in his CPR but haven't had the chance to look, but I since read a convincing argument of why 5+7=12 is considered synthetic (Frege talks about it), pathetically, I can't remember the argument now!
I hope to look back into it when I find time.
Your judgment about 12=5+7 of not being synthetic but analytic is difficult to analyse because there are infinite possibilities for 12 to be arrived although it contains 5 & 7 which can be excluded in analysis of infinite possibilities.
Deletethanks so much for the break down it helped a lot
ReplyDelete'It seems to me this is an analytic judgment; if “12” is broken down as twelve “1’s”, and same is done for “5” and “7”, there is basically twelve 1’s equaling twelve 1’s (12=12). So it seems, “5 +7” does contain the idea of 12, which makes it analytic.'
ReplyDeleteNo.
Perhaps, meditate on this: if 5+7=12 was an analytic judgement, then it would not be knowledge, it would be meaningless.
This is only an attempt to rephrase what you offered: 'Judgments that tell us something independent of the subject are synthetic;..'
Shall we say, that it would not be important to take math in school, there is no 'science' here, if these were not synthetic judgments.
If they are not synthetic judgments then it's 'meaningless'? It's 'not knowledge'?
What about analytic judgments, then?
Such as, as you give for an example, all bachelors are unmarried. I call this meaningless and not knowledge. What I'm trying to say is like this, suppose we have a dialogue:
me: "You know, all bachelors are unmarried"
you: "You're shitting me no duh this does not change my opinion of you that you know nothing, but what somebody who knows nothing, nevertheless (scare quotes) 'knows'".
Similarly, you do not learn in science class at school, that a bachelor is unmarried. If you suppose yourself to have learned in school that a bachelor is unmarried, then you perhaps were taking English as a second language?
I'll take a page from Wittgentstein, and offer that all analytic judgments say the same thing.
Nothing.
Does math say nothing? Then there's no need to learn it there is no such activity as math either.
Something's got to give, here? This is something to practice with, point is you're going to need to come around to the view that math is synthetic.
If you write 5 ones and 7 ones next to each other, you still have 5 ones and 7 ones. In order to get 12, a person needs to utilize the intuitive senses. All Math (applied or pure) is , at very least, a short hand for the creation of synthetic products, if not, a direct exercise in synthetic thought.
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