Non-Euclidean Geometry vs Kantian Space

[Veritas Aequitas]

I often come across the invocation of non-euclidean geometry to object against Kant's space.
As usual it is the realists who made the objections from their rigid realist paradigm, i.e. reality is independent of the human conditions.

Historically, this [objection] was initiated by Helmholtz who argued that Kant’s theory of space is untenable in the light of the discovery of the non-Euclidean geometries3.
His line was later forcefully supported by Paton, Russel, Carnap, Schlick and probably at most Reichenbach, who famously criticized Kant’s conception of space on the basis of a complex analysis of the visual a priori which he took to underlie Kant’s doctrine of geometry4.
Wes Alwan
https://partiallyexaminedlife.com/2013/ ... intuition/

Here are some defenses on the issue;

1. Kant on Euclid: Geometry in perspective, Stephen Palmquist
In short, I will argue that, far from assuming a kind of absolute validity for the classical theories of Euclid, Aristotle, and Newton, Kant ties their views to a well-defined perspective in such a way that their validity is actually limited, and that in so doing he actually prepared the way (sometimes with surprising foresight) for modern developments in geometry, logic, and physics.
https://repository.hkbu.edu.hk/cgi/view ... ext=rel_ja

2. Why Non-Euclidean Geometry Does Not Invalidate Kant’s Conception of Spatial Intuition
Everyone once in a while I run across the opinion that non-Euclidean presents a serious problem for Kantian epistemology. While I've rebutted this notion before, it's common enough that I thought I'd have another go at explaining why it's a misconception.
Wes Alwan
https://partiallyexaminedlife.com/2013/ ... intuition/

3. KANT’S THEORY OF SPACE AND THE NON-EUCLIDEAN GEOMETRIES
Boris_Grozdanoff
Recently, Parsons refers to this line as “the most common objections to Kant’s theory of space”5 and concedes that Kantian could still accept some more primitive geometrical properties (than those provided by the 5th postulate of Euclid’s Elements, for example) to be known a priori even if he abandons the claim that in specific propositions of the Euclidean geometry can be known a priori.
Though this is an attempt to salvage some part of the geometry doctrine I do not think that this is in the spirit of the Transcendental Aesthetic and also, I believe that it would be insufficient for Kant’s purposes.

My aim in this paper will be defend the view that Kant’s doctrine of geometry can survive criticism based on appeal to the non-Euclidean geometries.
http://www.personal.ceu.hu/students/03/ ... etries.PDF

...................

There are loads of more articles out there defending Kant against any critical impact from non-euclidean geometry.

One hint is,
Non-euclidean Geometry does not have any critical nor significant impact on Kant's concept of space or else Kant would not have polled regularly as one the Greatest Western Philosophers of all Times within the modern philosophical community.

[uwot]

I often come across the invocation of non-euclidean geometry to object against Kant's space.

What a path you must travel. You can read the whole of the Critique of Pure Reason and gradually and painfully have it dawn on you that Kant summed it all up quite nicely in his Inaugural Dissertation:
Space is not something objective and real, nor a substance, nor an accident, nor a relation; instead, it is subjective and ideal, and originates from the mind’s nature in accord with a stable law as a scheme, as it were, for coordinating everything sensed externally.
There's nothing inherent in non-euclidean geometry to contradict that, it is really Einstein's ontological claim that space is a substance that is at odds with Kant's epistemological insistence that it isn't.

One hint is,
Non-euclidean Geometry does not have any critical nor significant impact on Kant's concept of space or else Kant would not have polled regularly as one the Greatest Western Philosophers of all Times within the modern philosophical community.

The point about a hint is that it is not a reliable guide; nor is an argumentum ad populum. Even being right has little to do with philosophical greatness; that Aristotle wrote some right royal bollocks - he's still one of the biggies. Non-euclidean Geometry does not have any critical nor significant impact on Kant's concept of space because one is mathematical and one epistemological

[Veritas Aequitas]

I often come across the invocation of non-euclidean geometry to object against Kant's space.

What a path you must travel. You can read the whole of the Critique of Pure Reason and gradually and painfully have it dawn on you that Kant summed it all up quite nicely in his Inaugural Dissertation:
Space is not something objective and real, nor a substance, nor an accident, nor a relation; instead, it is subjective and ideal, and originates from the mind’s nature in accord with a stable law as a scheme, as it were, for coordinating everything sensed externally.
There's nothing inherent in non-euclidean geometry to contradict that, it is really Einstein's ontological claim that space is a substance that is at odds with Kant's epistemological insistence that it isn't.

One hint is,
Non-euclidean Geometry does not have any critical nor significant impact on Kant's concept of space or else Kant would not have polled regularly as one the Greatest Western Philosophers of all Times within the modern philosophical community.

The point about a hint is that it is not a reliable guide; nor is an argumentum ad populum. Even being right has little to do with philosophical greatness; that Aristotle wrote some right royal bollocks - he's still one of the biggies. Non-euclidean Geometry does not have any critical nor significant impact on Kant's concept of space because one is mathematical and one epistemological

Noted.
Point is I don't have everything on my finger tips.

I understand 'a hint' is not reliable, but it is a strong hint given that claim is acceptable by the majority of philosophers. If it it accepted by the general public then that would be questionable.
Nevertheless I would expect that 'hint' to be further substantiated by justified evidence.

[uwot]

Hang on a mo:

Non-euclidean Geometry does not have any critical nor significant impact on Kant's concept of space

and

...that claim is acceptable by the majority of philosophers

And yet:

I often come across the invocation of non-euclidean geometry to object against Kant's space.

So who are these minority of philosophers or others that you "often come across"?

[Veritas Aequitas]

Hang on a mo:

Non-euclidean Geometry does not have any critical nor significant impact on Kant's concept of space

and

...that claim is acceptable by the majority of philosophers

And yet:

I often come across the invocation of non-euclidean geometry to object against Kant's space.

So who are these minority of philosophers or others that you "often come across"?

This OP was triggered upon this claim by Conde Lucanor in this forum;

Non-Euclidean geometry. It's a well known instance in which Kant was proven to be dead wrong.
viewtopic.php?p=508219#p508219

Atla made a similar claim but he deleted his post.

As for philosophers, note in the OP

Historically, this [objection] was initiated by Helmholtz who argued that Kant’s theory of space is untenable in the light of the discovery of the non-Euclidean geometries3.
His line was later forcefully supported by Paton, Russel, Carnap, Schlick and probably at most Reichenbach, who famously criticized Kant’s conception of space on the basis of a complex analysis of the visual a priori which he took to underlie Kant’s doctrine of geometry4.
-Wes Alwan
https://partiallyexaminedlife.com/2013/ ... intuition/

From my survey there are various articles that made the same claim.

[Atla]

Atla made a similar claim but he deleted his post.

I realized it's pointless to argue. You mean well, but you simply lack the intelligence for philosophy, you should look for another hobby.