How are à priori synthetic judgements possible?

If I remember this position correctly, the assertion is that pure math and mathematical physics are really the study of the organizing principles by which the intellect interprets and makes sense of the world. Rather than being properties of an exterior phenomenal world, these disciplines describe the rules of the mind itself.

The phenomenal world necessarily appears to conform to these principles because these principles dictate the terms of perception itself. Much as we can’t imagine a sense other than those we’re given, it’s impossible for us to perceive a reality that doesn’t meet the terms imposed by the intellect.

We can look at these principles apart from empirical data because they are, in effect, our own intellect.

Such conclusions are possible because they are axiomatic; they can be considered absolutely true so long as we assume the truth of certain axioms which, in essence, define a complete world. These statements must define a complete system of rules, and if they are true in our world, then all conclusions reached by them apply to our world. Or, they may define a completely non-existent, but internally consistent world. We have no way of knowing for sure, of course, whether the axioms of conventional math and logic are true for our world. I must differ with Harp’s assertion that our perceptions are governed by the products of our intellect, however, as many conclusions guaranteed by our intellectual axioms- ones that were discovered by a logical sequence that, while itself axiomatic, was operating without anticipating the results and without regard for instinct- are still consistent with prior observations. It seems to me that this implies (although of course it does not prove) not only the existence of an absolute truth, but also that our axioms are consistent with that truth, although they may not be entirely complete. Granted, it is possible that the mind to which the perception belongs had worked out the implications of its axioms long before on a subconscious level, but this seems implausible.

Thank you for your responses. Since it seems that those willing to engage this question are willing to do so at this level, I think I can narrow my question a bit.

I agree with the notion of self-consistent axioms Jayne has put forth, however, according to Kant, as Harp I think correctly relates, these axioms somehow arise from the structure of the subjective self-constitution of the mind. I am wondering about the structure of this subjective self-constitution. What is the fundamental structure of our experience of being one and conscious? How do Space and Time factor into it, as Kant suggests?

I believe that there is no fundamental meaning to a discrete self or mind, because the reductionist standpoint, that a person can be described entirely in terms of their physical constituents, does not demand a division between, for instance, the electrical impulses in the brain, the photons that provoke them, the body off of which they reflect, and the electrical impulses in the brain of that body; there is no fundamental cutoff point between self and other. One could, perhaps, take the view that the brain is thereby interwoven with everything else and thus governs it, but this abstraction conflicts with the original reductionist premise. Instead, I conclude that since there is nothing to set the mind apart as unique, it has no role in the shaping of reality. Of course, this is in no way a proof that perception does not control reality, as it assumes that the laws of physics do so; instead, it is simply a demonstration that the philosophy is self consistent, and the existence of the mind does not conflict with the existence of an independent truth.

Assuming that the mind is the arbitrarily defined sum of its physical components, reacting to the universe and affecting it only by direct physical action, there is no reason to presume that its perception of that universe is accurate; in fact, it would be rather surprising if the mind was somehow perfectly attuned to reality. However, it operates on the large scale in roughly the same manner as it does on a small scale- cause and effect, input and output, build logic just as they build nature. If A and B and C, then D; if hydrogen and oxygen and heat, then water (Of course, the cause and effect is much more complicated here, and I am ignoring quantum uncertainty, because I see no reason to believe that it has any real relevance to my argument, which depends ultimately on reductionism; determinism is only relevant for the creation of logic insofar as the brain observes it; that is, on a macroscopic level). So the brain, through observation, has learned a system of thought which mirrors the world as it sees it, and the extension of this logic beyond observation has proved reliable to a point that, as I argued above, goes beyond the simple matching of perception to the brain’s conclusions. So the brain, while a fundamentally flawed and subjective observer, seems to have created an axiomatic system that is a good if not a perfect reflection of an existing reality, without creating any of that reality itself. Again, I am assuming the existence of a reductionist truth, and am simply demonstrating consistency, but see little reason to assume another philosophy. I’m not sure I properly understood what it is you are getting at, however.

I don’t recall where Kant went with this, but an interesting outgrowth of that line of reasoning is to regard self-perception, along with space and time, as also being organizational templates intrinsic to the mind.

The intellect predicates the division of experience into a subject/object dichotomy, a perceiver and the perceived. Self-awareness is the product of that division. But this subject/object opposition is only a reflection of the way the intellect organizes information and gives it meaning. Both the internal self and the external phenomenal world have their origins in the structure of the mind.

The same can be said of time and space; they are the warp and woof of the fabric of consciousness or, to mix metaphors, the stage on which the mind produces the drama of reality.

In short, mind can’t be equated with the little perceiving self that the intellect postulates. That self is only an artifact of the mind’s organization. Mind itself is not an object in the universe, but is inseparable from it and coextensive with it.

I don’t know if Kant would agree.

I think Kant based his argument on his belief in a supreme reality that pervades time and space. This supreme reality is manifest in various universal laws that exist within nature and are recognized and carried within the mind at a deep level.

This scientific study shows how Man has replicated those things in nature which he has recognized as being “perfect” in some way. This recognized perfection of the divine ratio, golden rectangle, etc. was inherent in nature and was recognized because of its adherence to the universal law. Thus no empirical evidence was needed because the universal law was already recognized within the mind.

But I do think that they depend on experience with the real world to validate the laws and help codify them so that others can make use of them.

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Loving the family resemblance up there : )

Can someone get a graduate degree from Fluther U?

I’m just at the beginning of my own philosophical age of studying so I can’t answer your question…but…GQ will be following in the wings

I knew that Kant spoke of a priori knowledge of math, but I was not aware he spoke of physics that way. If he did, he was flat out wrong. Modern physics, especially quantum mechanics, is highly non-intuitive.

There are people on boths sides of the issue regarding whether math is a priori. Some regard mathematics as something like Plato’s Forms. There are others who take the position that mathematics is a social construct. I lean toward the Platonic view. I would like to believe that in any possible Universe there would be numbers and set theory. Is it possible to conceive of a Universe that did not have these ideas?

Some physicists have thrown out the idea that our minds may be interacting with multiple realities (dimensions, the metaverse, etc.) and may also be quantum entangled with other minds. Either of these ideas, if true, would blow the lid off most concepts of thought and reason. And, imagine if time, or cause and effect, are just mental constructs. How do you begin to build a logic?

@steelmarket I luuuuuuurve your answer!!! And i think it’s highly possible that they are just constructs of our mind but what do in know!lol