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Kant and Synthetic a Priori

socialpinko
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10/28/2012 5:05:49 AM
Posted: 4 years ago
Kant argued that we could have knowledge of synthetic a priori propositions, meaning that they are known prior to experience (a priori), but the antecedent contains more information than is simply contained in the predicate (synthetic). His example for this started in mathematics, wherein, he argued, that in a mathematical proposition, say 1+2=3, the antecedent (3) isn't contained in the predicate (1+2). When we strictly analyze the predicate we supposedly can't extrapolate 3 as the answer. But I don't think I quite understand how he can say 3 isn't contained in the proposition 1+2. I looked over the part of Prolegonema where he argued for it but it looks like he just took it to be self evident (or maybe I just didn't read far enough). Does anyone know how he concluded this?
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phantom
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10/28/2012 1:48:40 PM
Posted: 4 years ago
He calls it "uncontestably true" but I don't think he just left it as "self-evident".

"We might, indeed, at first suppose that the proposition 7+5=12 is a merely analytical proposition, following (according to the principle of contradiction) from the concept of a sum of seven and five. But if we regard it more narrowly, we find that our concept of the sum of seven and five contains nothing more than the uniting of both sums into one, whereby it cannot at all be bought what this single number in which embraces both. The concept of twelve is by no means obtained by merely thinking the union of seven and five; and we may analyze our concept of such a possible sum as long as we will, till we shall never discover in it the notion of twelve. We must go beyond these concepts, and have recourse to an intuition which corresponds to one of the two - our five fingers, for example, or like Segner in his Arithmetic five points - and so by degrees, add the units contained in the five given in the intuition, to the concept of seven. For I first take the number 7, and, for the concept of 5 calling in the aid of the fingers of my hand as objects of intuition, I add the units, which I before took together to make up the number 5, gradually now by means of the material image my hand, to the number 7, and by this process, I at length see the number 12 arise. That 7 should be added to 7, I have certainly thought in my concept of a sum = 7+5 but not that this sum was equal to 12. Arithmetical proposition are therefore always synthetical, of which we may become more clearly convinced by trying large numbers. For it will thus become quite evident, that turn and twist our concepts as we may, it is impossible, without having recourse to intuition, to arrive at the sum total or produce by means of the mere analysis of our concepts."
-The Critique, P.37/38
"Music is a zen-like ecstatic state where you become the new man of the future, the Nietzschean merger of Apollo and Dionysus." Ray Manzarek (The Doors)
phantom
Posts: 6,774
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10/28/2012 1:49:56 PM
Posted: 4 years ago
At 10/28/2012 1:48:40 PM, phantom wrote:
He calls it "uncontestably true" but I don't think he just left it as "self-evident".

"We might, indeed, at first suppose that the proposition 7+5=12 is a merely analytical proposition, following (according to the principle of contradiction) from the concept of a sum of seven and five. But if we regard it more narrowly, we find that our concept of the sum of seven and five contains nothing more than the uniting of both sums into one, whereby it cannot at all be bought what this single number in which embraces both. The concept of twelve is by no means obtained by merely thinking the union of seven and five; and we may analyze our concept of such a possible sum as long as we will, till we shall never discover in it the notion of twelve. We must go beyond these concepts, and have recourse to an intuition which corresponds to one of the two - our five fingers, for example, or like Segner in his Arithmetic five points - and so by degrees, add the units contained in the five given in the intuition, to the concept of seven. For I first take the number 7, and, for the concept of 5 calling in the aid of the fingers of my hand as objects of intuition, I add the units, which I before took together to make up the number 5, gradually now by means of the material image my hand, to the number 7, and by this process, I at length see the number 12 arise. That 7 should be added to 5, I have certainly thought in my concept of a sum = 7+5 but not that this sum was equal to 12. Arithmetical proposition are therefore always synthetical, of which we may become more clearly convinced by trying large numbers. For it will thus become quite evident, that turn and twist our concepts as we may, it is impossible, without having recourse to intuition, to arrive at the sum total or produce by means of the mere analysis of our concepts."
-The Critique, P.37/38

Fixed
"Music is a zen-like ecstatic state where you become the new man of the future, the Nietzschean merger of Apollo and Dionysus." Ray Manzarek (The Doors)
philochristos
Posts: 2,614
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10/28/2012 2:21:29 PM
Posted: 4 years ago
I don't know what I think about whether 7 +5 = 12 is synthetic or analytic. I think Kant makes a good point that when we think of 12, we don't necessarily think of it in terms of the sum of 7 and 5, so while 12 may be contained in the notion of 7 and 5, 7 and 5 are not contained in the notion of 12. And that makes 7 + 5 = 12 appear to be synthetic.

On the other hand, 7 + 5 = 12 is a necessary truth, which makes me suspect it IS analytic. You might say that not only 7 and 5, but every other combination of numbers between 0 and 12 are contained in 12, including 12 and 0, 11 and 1, 10 and 2, etc. But it being necessary seems to suggest it's analytic.

I think there are better examples. There are some contingent truths that are known a priori. Here are some examples:

1. The uniformity of nature, i.e. the idea that the future will be like the past or that nature behaves the same way when we're not looking as it does when we are looking.

2. That our memories correspond to a past that actually happened.

3. That our senses correspond to an external world that really exists.

4. That there is such a thing as causation that is more than just contiguity in space and time.

5. That there are other minds besides your own.

6. That 'ought' implies 'can.' I.e., that you cannot have an obligation to do something if you are physically incapable of doing it.

7. That your 'self' endures through time and change.

8. That time exists.

9. That there's such a thing as right and wrong that is true independently of a culture or individual's preference or values.

Yeah, I realize some of those are controversial. After all, they are not necessary truths. It's at least possible for each one of them to be false. But if even one of them is true, and if we are justified in believing it, then there is such a thing as synthetic a priori knowledge.
"Not to know of what things one should demand demonstration, and of what one should not, argues want of education." ~Aristotle

"It is the mark of an educated mind to be able to entertain a thought without accepting it." ~Aristotle
socialpinko
Posts: 10,458
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10/29/2012 4:15:53 PM
Posted: 4 years ago
At 10/28/2012 2:21:29 PM, philochristos wrote:
I don't know what I think about whether 7 +5 = 12 is synthetic or analytic. I think Kant makes a good point that when we think of 12, we don't necessarily think of it in terms of the sum of 7 and 5, so while 12 may be contained in the notion of 7 and 5, 7 and 5 are not contained in the notion of 12. And that makes 7 + 5 = 12 appear to be synthetic.

On the other hand, 7 + 5 = 12 is a necessary truth, which makes me suspect it IS analytic. You might say that not only 7 and 5, but every other combination of numbers between 0 and 12 are contained in 12, including 12 and 0, 11 and 1, 10 and 2, etc. But it being necessary seems to suggest it's analytic.

I like Phantom's quote where Kant seeks recourse in larger sums to show that it can't be analytic and that we have to go with intuition to add the sums together. The confusion might rest in the fact that we add 7 and 5 instantly to 12 so it's hard not to think of it in the same sense that one would think of the proposition that all bachelors are married. It's obvious. But what about the proposition 1,234,523,789,999,868,382.56949498488 + 1,283,746,745,784,241.559494. It doesn't look self evident so we're not hangered by habit as we seem to be with more simple mathematical propositions. Look at it all you want but unless you're a savant you'll have to introduce intuition.

I think there are better examples. There are some contingent truths that are known a priori. Here are some examples:

1. The uniformity of nature, i.e. the idea that the future will be like the past or that nature behaves the same way when we're not looking as it does when we are looking.

Oh my God as a lover of Hume that hurt my eyes to read.

........

Yeah, I realize some of those are controversial. After all, they are not necessary truths. It's at least possible for each one of them to be false. But if even one of them is true, and if we are justified in believing it, then there is such a thing as synthetic a priori knowledge.

Most of those I think are false but I understand the sentiment. At the very least the ordering of our experiences in space-time seems a conceptual necessity as well the inner-workings of our thought processes i.e., we can't conceptualize outside of logic lend credence to synthetic a priori and Kant's philosophy of mind (that it orders the world not the other way around).
: At 9/29/2014 10:55:59 AM, imabench wrote:
: : At 9/29/2014 9:43:46 AM, kbub wrote:
: :
: : DDO should discredit support of sexual violence at any time and in every way.
:
: I disagree.
Zaradi
Posts: 14,125
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10/29/2012 4:20:43 PM
Posted: 4 years ago
At 10/28/2012 2:21:29 PM, philochristos wrote:
1. The uniformity of nature, i.e. the idea that the future will be like the past or that nature behaves the same way when we're not looking as it does when we are looking.

Stop

6. That 'ought' implies 'can.' I.e., that you cannot have an obligation to do something if you are physically incapable of doing it.

The

9. That there's such a thing as right and wrong that is true independently of a culture or individual's preference or values.

Madness!
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philochristos
Posts: 2,614
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10/29/2012 6:58:42 PM
Posted: 4 years ago
All Hume showed was that the uniformity of nature can't be proved. It didn't show that it's false or that it's not rational to believe it. To get there, you have to add another premise: If something can't be proved, then it can't be known. But that is a self-refuting premise. Hume himself relied heavily on the uniformity of nature in his argument against miracles, so even though he showed that it couldn't be proved, he obviously thought it was quite rational to believe. And let's be honest with ourselves. We couldn't learn anything from experience if not for the uniformity of nature. Science wouldn't work without this assumption. I think it is one of the clearest examples of synthetic a priori knowledge that we have.
"Not to know of what things one should demand demonstration, and of what one should not, argues want of education." ~Aristotle

"It is the mark of an educated mind to be able to entertain a thought without accepting it." ~Aristotle
Sidewalker
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10/30/2012 8:06:37 AM
Posted: 4 years ago
The axiom of existence is the one undeniable synthetic a priori truth.
"It is one of the commonest of mistakes to consider that the limit of our power of perception is also the limit of all there is to perceive." " C. W. Leadbeater