@Corvus @Wayfarer
The term "Transcendental Idealism" is central to the Critique of Pure Reason
In the
Conceptual Map of the Critique of Pure Reason, the first item is Transcendental Idealism, establishing the importance of the term.
Kant defines "Transcendental Idealism" in the Fourth Paralogism"
A 369 I understand by the transcendental idealism of all appearances the doctrine that they are all together to be regarded as mere representations and not as things in themselves, and accordingly that space and time are only sensible forms of our intuition, but not determinations given for themselves or conditions of objects as things in themselves.
In today's terms, Indirect Realism, aka Representative Realism.
Kant did propose that the term could be improved
However, Kant did propose that the phrase "Transcendental Idealism" could be improved.
In the Introduction to the CPR:
Specifically, he differentiated his position from Berkeleian idealism by arguing that he denied the real existence of space and time and the spatio-temporal properties of objects, but not the real existence of objects themselves distinct from our representations, and for this reason he proposed renaming his transcendental idealism with the more informative name of "formal" or "critical idealism," making it clear that his idealism concerned the form but not the existence of external objects.
Therefore, the term Transcendental Idealism should be treated more as a figure of speech than literally.
It is a transcendental idealism not a transcendent idealism
Note that it is
Transcendental Idealism not Transcendent Idealism, meaning that it is about the limits of what we can cognize about our experiences having been determined a priori before having such experiences. It is not about being able to cognize about our experiences beyond limits predetermined a priori .
Kant is putting a limit on our cognitive abilities.
A priori pure intuition of space and time and a priori pure concepts of the understanding (the Categories)
Space and time are the Categories are both a priori, however, space and time is the necessary foundation for the categories. For example, we have the concept of space and we have the concept of a number such as two, though it is a fact that although we can imagine empty space empty of numbers, we cannot imagine numbers outside of space. Consequently, first is the pure intuition of space and time within which are the pure concepts of the understanding (the categories).
We can use our cognitive facilities on our sensibilities about external objects affecting our sensibilities, but what we are able to cognize is limited by our a priori pure intuition of space and time and the a priori pure concepts of the understanding (the Categories).
What for Kant is the source of the a priori?
Kant says we have no innate knowledge of any particular proposition, ie, "postboxes are red", but he does say that it is not the case that our sensibilities are the cause of what we cognize about them but rather an priori cognitive ability makes sense of these sensibilities, ie, I perceive the colour red rather than the colour green when looking at a wavelength of 700nm
Introduction: Kant agrees with Locke that we have no innate knowledge, that is, no knowledge of any particular propositions implanted in us by God or nature prior to the commencement of our individual experience. But experience is the product both of external objects affecting our sensibility and of the operation of our cognitive faculties in response to this effect (A I, B I), and Kant's claim is that we can have "pure" or a priori cognition of the contributions to experience made by the operation of these faculties themselves, rather than of the effect of external objects on us in experience.
IE, Kant's position is that of Chomsky's Innatism rather than Skinner's Behaviourism.
Understanding Transcendental Idealism using the analogy of colour
When a wavelength of 700nm enters my eye, I see the colour red because I have the innate ability to see the colour red when looking at a wavelength of 700nm. When a wavelength of 300nm enters my eye, I don't see the colour ultra-violet, because I don't have the innate ability to see the colour ultra-violet when looking at a wavelength of 300nm.
This is the meaning of transcendental in "Transcendental Idealism", in that the colours I can see when looking at different wavelengths has been limited by a priori conditions of perception. and has the consequence that because I can see a colour such as red, this doesn't of necessity mean that the colour red exists in the world.
The fact that I cannot see the colour ultra-violet when looking at a wavelength of 300nm is why the term isn't "transcendent idealism".
"Idealism" because the colour red exists in my mind not the world.
Kant is a Realist because, for him, the cause of our seeing the colour red originated outside our mind rather than within our mind.
The relationship between objects and their properties
Kant does not directly deal with objects of empirical cognition, but investigates the conditions of the possibility of our experience of them by examining the mental capacities that are required for us to have any cognition of objects at all. (Introduction page 6)
As regards properties, suppose I see a red postbox. The postbox is an object and redness is a property. But what are objects? An object is no more than a set of properties, in that if all the properties of an object were removed, no object would remain, in that is it impossible to imagine an object if it has no properties.
So a postbox is the set of properties such as redness, rectangular, extended in space, etc, but as the property redness only exists in the mind of the perceiver and not the world, one can conclude that the object, which is no more than a set of properties, where properties exist in the mind of the perceiver and not the world, also only exists in the mind of the perceiver and not the world.
Therefore, not only do properties such as redness only exist in the mind, but also objects such as postboxes only exist in the mind as concepts.
Interpreting A369
I understand by transcendental idealism that all appearances of objects such as postboxes and properties such as redness are to be regarded as mere representations and not as things in themselves, ie, postboxes and the colour red existing in the world, and accordingly, what we perceive as space and time only exists in the mind as a foundation for being able to perceive objects and their properties as mere representations and not as things-in-themselves.
The space, time, objects and properties we perceive only exist in the mind, although we can reason about their existence in the world using the transcendental category of causation.