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Did Kant take Newtonian physics as being synthetic a priori? I get the feeling he did.

If he did, how did he justify this, it seems like a huge blunder for such a careful thinker.

I mean... Kant answered how we get notions of cause and effect... it's a structuring principle of the mind. But that in no way tells us the world will behave according to the connection formed in our minds. Why would Kant even think this way?

Did Kant think he had solved the problem of induction and thereby made science indubitable?

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    There is no way he could have considered the inverse-square law a priori, notions of relative degree are not Categories. And we do not immediately apprehend that gravity should follow such a law, even after we have been exposed to the idea. Mathematics is synthetic apriori because once you have been exposed to the fact, it cannot be imagined to be otherwise without immediately creating contradictions, so you cannot devise a test. But we can imagine a world where gravity dies off linearly, if not in much detail. We have to test it. – user9166 Mar 29 '16 at 19:30
  • @jobermark Kant's a priori do not reduce to "immediate apprehension", he explicitly admits that empirical input (and a lot of it) may be required in practice to discern an a priori. It certainly wasn't lost on him that Newtonian mechanics was a recent discovery. And even in mathematics things can be "imagined otherwise" without creating contradictions "immediately", Euclid does it all the time in proofs by contradiction. So what we can immediately apprehend or imagine has little to offer on Kant's a priori, that's why his laborious transcendental arguments are needed to uncover them. – Conifold Mar 30 '16 at 4:37
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Yes, Kant did consider Newtonian mechanics (or rather his variation on it) to be synthetic a priori in the same way he considered Euclidean geometry so, he gives detailed a priori "derivation" of it in Metaphysical Foundations of Natural Science (1786), see summary by SEP. The derivation of the third law for example goes something like this: changes of matter are changes of motion, changes of motion are reciprocal and equal by geometry and kinematics, every change has an external cause (the law of causality), so the cause of the change of motion of one body entails an equal and opposite cause of a change of motion of the other. "Newtonian mechanics" however only covered Newton's three structural laws, not the inverse square law for gravity, which was typed as empirical. Kant came close to declaring it a priori however, the only empirical input he thought it needed was the dimension of space, he gives an a priori derivation of it assuming that dimension is 3, which is similar to the usual modern explanation for matter fields with a point source and goes back to before Newton, see Who was first to explain intuitively the inverse square law of gravity? For detailed analysis of Kant's arguments see Friedman's Kant and Exact Sciences.

A blunder it was not, at least no more so than the whole idea of synthetic a priori as absolutes. Taking them as evolutionary and early developmental instead we can say that he most likely was right on geometry, and close to right on mechanics. Our sensory-motor stereotypes acquired in early childhood most likely hard wire something close to (at least locally) Euclidean notion of space, and some cross between Aristotelian and Newtonian notions of motion and force. This is why relativistic and especially quantum notions are so hard to process for most people, they require complete re-wiring of ingrained mental templates. See Brook's Kant and the Mind for modern perspective.

Kant certainly did not think that "the world" behaves according to connections in our minds. In fact, he thought that we can never know how it behaves or what it is, nor does science have anything to do with that. It is instead the study of appearances, of how things appear to us, not how they are in themselves, and it makes perfect sense that how they appear to us depends among other things on our mental constitution, including framing intuitions of space and time, and a priori categories of understanding that serve as templates for forming empirical categories. And to the extent that science relies on those bits it is indeed indubitable according to Kant. But that indubitability is very narrow and extends to mathematics and mathematical physics only, he explicitly excluded "purely" empirical disciplines, e.g. he classified chemistry as "systematic art or experimental doctrine but not a proper science", and declared that empirical psychology can never become even that.

Kant got some of the specifics wrong, mostly due to limitations of science of his time, and to the idea that the a priori are absolute, i.e. universal and unchangeable, was an even bigger misjudgement, but it is easy to say so only in hindsight. For his time he was a prophet, in big picture the modern understanding of our mental faculties and their influence on the formation and structure of science largely developed from the Kantian scheme, see What is Kant's influence on philosophy of science and the demarcation problem?

For post-Kantian notion of synthetic a priori see What are the more complex/interesting examples of synthetic a priori statements?

  • How does Kant explain alternative non-Newtonian physics theories? In a similar way as he would explain non-Euclidean geometries? – Geremia Apr 1 '17 at 2:31
  • @Geremia In his time physical theories either were Newtonian or strived to be Newtonian. But the buy-in was never as strong with a priori physics as with a priori geometry, so once the latter went Kantians saw no point in defending the former. Neo-Kantians stipulated that the transcendental method of philosophizing about science is all they retain, Cassirer applies this motto to relativity and quantum theories. He explicitly ejects the schematism, space and time become first conceptualizations, not forms of intuition, hence mutable, see Pringe – Conifold Apr 3 '17 at 23:29
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Kant elaborates his metaphysics of natural science in

Kant, Immanuel: Metaphysical Foundations of Natural Science (German: Metaphysische Anfangsgründe der Naturwissenschaft) (1786)

He writes:

A rational doctrine of nature deserves the name of natural science only when the natural laws at its foundation are cognised à priori, and are not mere laws of experience. A natural cognition of the first kind is called pure, that of the second applied, rational cognition. (A6)

The third part of this work, named Metaphysical Foundations of Mechanics, contains the following propositions:

  • The only way of comparing the amounts q of any two portions of matter is by comparing their amounts q of motion at a single speed. (A108)

  • First law of mechanics. Through all changes of corporeal Nature, the overall amount q of matter remains the same — neither increased nor lessened. (A116)

  • Second law of mechanics. Every change in matter has an external cause. (Every motionless body remains at rest, and every moving body continues to move in the same direction at the same speed, unless an external cause compels it to change.) (A119)

  • Third mechanical law. In all communication of motion, action and reaction are always equal to one another. (A121)

For each of these propositions Kant gives a "proof".

In the second part of this work Kant deals with dynamics. But he does not give a proof of the inverse square law.

Kant does not consider synthetical knowledge a priori the principle of induction. It was just the aim of Metaphysical Foundations of Natural Science to show which insights can be derived without using induction.

Added. One can freely download Kant's work as http://www.earlymoderntexts.com/assets/pdfs/kant1786.pdf

  • But Kant was wrong that these 3 laws can be derived without induction. What kind of proofs did he give? – Ameet Sharma Mar 29 '16 at 20:16
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    @Ameet Sharma I added a link to Kant's work, in order that everybody can check Kant's argumentation. - I agree with you that these propositions should not be considered synthetical a priori knowledge. Instead, they are successful hypotheses. Therefore I put "proof" in quotation marks. – Jo Wehler Mar 29 '16 at 20:21

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