In one of the letters written to the Infeld group in Warsaw Einstein wrote:
"A new manner of thinking is essential if humankind is to survive."

  

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Kant and Einstein (answer)
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KANT
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We have allocated in this site considerable 
space to Einstein's Relativity and it seems only 
fair to recall the pertinent ideas of Kant prior
to comparing the two.

Talking about Kant has to follow one of two
ways:

1.Learn to use his terminology inside of the
  Universe of discourse of his time. Only after
  having accomplished that would we be able to
  talk reasonably about "synthetic judgements
  a priori" and their role in "transcendental
  logic, or aestetic".
2.Express his Weltanschaung in contemporary
  terms.
 
We shall stick subsequently to 2. 

Any theory is for us, today, axiomatic. What
would we see as definitions, axioms and
theorems of Kant's Epistemology?
We shall list them first and comment afterwards.

Axiom A1: necessary and universal science exists.
 
Definition D1: Science is created by inductive
inference.
 
Definition D2: Only a priori inference is
necessary and universal.
 
Definition D3: Induction a priori requires
subjective representations a priori (categories)
encompassing space and time.
 
Axiom 2: Space is a subjective representation
a priori. We can imagine "empty space" without
any "objects"(1) but we can only represent
objects in space.
The same holds for time.
 
Theorem T1: Induction a priori exists.
Proof: A1+D1+D2+D3+A2.   

COMMENTS
 
A1: Newton's Theory cnsidered (by anticipation) 
Kant's time and space as necessary and universal. 
Even the 19th century mechanistic Physics claimed 
these qualities. Only post Einstanian Physics 
considers science as fuzzy and restricted.
 
D1: We still agree with it.
 
D2,D3,T1: We accept now only induction a
posteriori.
 
A2: Kant's main objective was to create the
"Transcendental Logic" with induction a priori
in its center. For this purpose A2 was a
necessary addition to A1. "Empty space" and
"objects in space" correspond to our "common
sense" intuition. Only Einstein, as we can
see in chapters on Relativity, abolished the 
concept of "empty space" and replaced it with 
#space created by field.
 
Transcendental Logic: Kant tried to create
some "prototype" of Propositional Calculus.
He failed due to missing mathematical and
logical tools developed only at the end of 19th
century. He considered only statements, but
not operators on statements. His classification
of statements encompasses:
-Statement analytical a priori which we would
 call deductive,
-Statement synthetical a posteriori which we
 would call inductive,
-Statement synthetical a priori which supports
 the induction a priori non acceptable for us. 
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COMPARISON
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They are both right, talking however about two
different things: Kant about PS and Einstein
about MS.
We defined PS (Glossary) as "unique per observer 
and Theory independent". Now, a single subject
perceives indeed phenomena of his PS exactly
as described by Kant: ordered by unique values
of space and time. Mapping this PS directly
into a naive MS we obtain a 4 dimensional 
#space whose time component is affine with 
respect to the 3D space sub-#space. Time and
space sub-#spaces have no common measure, thus
the space-time #space is affine. Consequently, 
scalar product, angle and rotation in planes x,t 
are undefined. Transformations are thus limited 
to translations, i.e. to Galilean Transformations.
This direct PS to MS mapping may be naive, but
it supported the Newton's Model, the greatest
intellectual achievement of all times which 
stays till now as a rigorous approximation
sufficient for most of applied dynamics including
space travel.
This Kant-Newton affine space-time #space could
accommodate low speed dynamics, but not invariability 
of C nor phenomena involving speeds comparable with C.
The involved MS required metric 4D #space.
Now, a participant (Moss) rigtly said:
"Time and space are ... so qualitatively different 
that they are  not the kind of things which can 
be combined into one", which is another way to
say that space-time #space is necessarily affine
and cannot be made metric.
Einstein's genial idea was to create a 4D #space
whose all 4 components have a common space or
distance measure: 3 space dimensions and one
LIGHTTIME (not time!!!), Ct dimension having
distance measure. Now, all these distance 
dimensions can perfectly be structured into
metrics: Minkowski metric for SR and Riemann
metric for GR.
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(1) The term "object" does not exist in Physics.
In the metalanguage it is multivalued and
charged with noxious metaphysical connotations.
We use it here as synonym of "observation" in
order not to diverge to far from Kant's
terminology.   
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