Yes thank you for clarifying my point. In the transcendental aesthetic Kant speaks of space not as an objective absolute background like Newton, nor as a system of relations like Leibnitz but as an integral part of our perceptive apparatus. If Euclidean geometry is meant to be a necessary and timeless truth constrained by the nature of our perceptions then any deviation from this in nature would seem to prove Kant wrong. However, later on in the critique he does seem to talk about space as a coordinate measurement system so this is rather confusing and I'm not sure if he was consistent.

I'm not sure we can rely on geometry remaining Euclidean at human scales because if one takes general relativity into account then masses are warping spaces and causing gravitational geodesics that support our entire existence.

I wasn't trying to pit science against metaphysics, I was making the point that its a worthwhile endeavour to asses the foundations of any system as well as its connection to other fields, rather than just saying shut up and calculate. Why engage in philosophy at all if science seems to work and one can just get busy with that?

I think I will take your advice and look at the literature since I am rather new to all this. However, if you can elaborate some of the conceptual issues with regard to determinism that might be helpful.

I don't think non-Euclidean geometries would be considered intuitive or come under the transcendental aesthetic because they are concepts of the understanding and have to be described mathematically or modelled within Euclidean space. So they would be in the transcendental analytic.

A quote from the essay that summarises the problem:

"Impressed by the beauty and success of Euclidean geometry, philosophers -- most notably Immanuel Kant -- tried to elevate its assumptions to the status of metaphysical Truths. Geometry that fails to follow Euclid's assumptions is, according to Kant, literally inconceivable."

Frank Wilczek

The problem is that for Kant space is not merely a three dimensional framework but the very basis of any possible intuition whatever.

Many thanks for this, ill take a read.

Could this method not lead to avoidance of difficult situations? If one changes their course each time there is turbulence are they not just victims of circumstance?

I suppose one would need to get to the bottom of the source of their feeling in order to understand the connection it has to the direction they have chosen in their life. This is a very personal kind of truth though which could lead to relativism. Is the truth different for everyone?

SophistiCat, just to let you know that I haven't been notified for the past two replies that you have sent me.

Well, the very fact that science gets along quite well with little or no metaphysics - and in particular, without ever needing to resolve the question of metaphysical determinism - is suggestive. Are such questions really meaningful, or are they spurious pseudo-questions that a conceptual analysis can dissolve? — SophistiCat

One could imagine any number of self contained systems that can articulate itself without the need for external verification but sooner or later its relationship to other fields of endeavour must come into question. Can you give any further details of such a conceptual analysis? Perhaps this would extend beyond the boundaries of science.

We know that further details cease to matter because they cease to make a difference. How we understand things to be has become sufficiently invariant. — apokrisis

Can we be sure that this hasn't happened simply because we've traversed a significant course in one particular direction and thus obscured the other possible paths?

It seems you are conflating truth with knowledge. The knowledge we have of how to do things is not "arbitrary"; it is based on workability. The knowledge-for-its-own-sake we have of how the world is is not arbitrary either: it is based on observation, conjecture, experiment and intersubjective corroboration. — Janus

In this definition, knowledge-for-own-sake would correspond to truth. However, this too seems to be based on workability. i.e. the way we chose to observe, conjecture, experiment and the method of interpretation of intersubjectve corroboration.

But how can tell you're not just seeking whatever path happens to be favourable to you. i.e.. because it confirms your biases rather than has genuine merit.

So yes, this is not the good old fashioned truth of the transcendental kind - that which is true even despite there being no one around doing the knowing. — apokrisis

Was Kant's transcendentalism not rationally derived from the foundation of all possible forms of intuition? "Empirically real but transcendentally ideal"

It is truth defined in terms of the concerns of a knower. It is a search for justified answers to the point of exhaustion - which itself is in turn a search to the point that further details cease to matter. — apokrisis

Do we have to assume here that the concerns of the knower are paramount? How can we be justified in stating that further details cease to matter?

What other possible criteria for judgements of objectivity could we employ, other than intersubjective criteria? — Janus

I was not suggesting to look outside of intersubjective criteria, but rather that we may need a better method of assessing those criteria. Otherwise we could be in a position where I can objectify as true anything with which I can obtain consensus.

How would you know they are not "objectively true" though, other than by reliable observation and intersubjective corroboration? — Janus

My point was that those two things alone are not enough to confirm or deny objectivity.

I don't understand this question. Humans desire knowledge in order to accomplish practical ends, and they also desire knowledge just for its own sake. — Janus

In which case is the truth not an arbitrary product of the particular ends which we select?

Of course one could just get on with the business of science without any need for contemplating its foundations and why it works but this always strikes me as avoiding the most interesting questions.

Perhaps you're right. But it could also be a recipe for mass conformism. How does one tell the difference?

This still does not sound like enough to qualify as being "objectively invariant". One could imagine many things that are reliably observed and intersubectively corroborated that are not objectively true. Political associations or stock markets maybe?

The thing is, if we concede that knowledge is only practically rational does this not mean that there is truth only with regards to certain ends?

Are you then a dualist in asserting that the mind is something distinct from the brain?

The problem still remains that if the activity of the mind is the source of the creative process we need some way of distinguishing between truths inherent in the world and patterns created by the mind.

This sounds like a psychological process, perhaps similar to what they call "prediction error" in neuroscience and learning theory. How can we tell the extend to which a pattern is created by the brain rather than inherent in world?

It sounds like you are advocating a kind of statistical analysis to find correlations between the patterns in nature. This still doesn't get us over the "correlation is not causation" problem though.

I suppose 18th century science could be said to "assert determinism". The question is, does our modern science allow for non-deterministic events to take place?

logicians agree that deduction offers no new information, only clarify that which is know — charleton

Could clarification not provide new information? After all, if it is already known then why clarify in the first place?

Only if you accept that free will is defined as not compelled to act from external forces — charleton

So do you say that to be free is to act only from internal forces? How does one begin the process of disassociating from external forces in order to follow internal ones? Would this change not violate determinism?

If one were to follow Hume's position that we have no rational basis for believing that induction from experience is a valid form of knowledge, then how can we claim that these invariances are objectively true?

Is it rational to believe there are established invariances if all our experience indicates that there are? — Janus

One would need to determine if we have grounds to believe that our experience is offering us valid insights into the nature of these established invariances.

Thank you for your answer, I will read into Kant to try to get a deeper understanding of these subtleties.

Knowledge might be viewed as a recognition of patterns that are always subject to change — Rich

The question is how do we know when these patterns are inherent in nature as opposed to arbitrary artefacts of our mode of perceiving?

Deduction is basically playing with definitions; nothing more. — charleton

I believe this would depend on your metaphysical assumptions. It sounds like you are taking a nominalist position which would reduce deduction to the abstract rules of description. If one were to take a more "realist" position with regard to concepts then the information derived from deductive analysis could have ontological validity.

Don't buy into this free will clap trap, as this flies in the face of the massive advances in science of the last 250 years which assert determinism. — charleton

Does this mean that you believe free will to be incompatible with determinism? Would you then say that our sense of free will is an illusion?

Undoubtedly it works but as a theory of knowledge it seems to take us into the realm of what I suppose you would call pragmatism or utilitarianism. To say it's true because it works seems unsatisfactory.
Hume new this which is why I wonder if he had a rationalist streak to his epistemology, despite being empirical by method.

Thank you. I have heard of that book. I'll add it to my reading list.

The difficulty is that if inductive knowledge is purely contingent on repetition then it isn't really true knowledge because no matter how many times we do the experiment it could always fail the following time. This seems to make our claims of knowledge groundless and any assertions of probability merely cumulative of previous experiences and hence subjective or psychological.

Thank you both. I am a newbie with an interest in the epistemological development of science. I apologise if this was a bit of a stock question.

So his empiricism rests on his taking experience as the starting point for knowledge instead of basing it on innate ideas or a priori thinking.

If induction is not based on a rational principle then how does one go from a constant conjunction to an assertion of probability?