2.3. the Disaster : Kant Wakes

2.3. the Disaster : Kant Wakes

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Bechler/Legitimation

3.1. Actualism and Critical Idealism

3.1.1 How is a prioriinformation possible?

3.1.2 Kant’s three refutations of a prioriinformativity

3.1. 3. Kant’s solution: “synthetic” information and form

3.1. 4. Mathematics as mere form - the first information drainage......

3.1.5. Pure physics as a mere form – the second drainage

3.1.6. The ontological basis of emptiness

3.1.7 From subjectivity to certainty

3.1.8. Summing up: skepticism, completeness and emptiness

3.1.9. What, then, is the syntheticity of the a priori?

3.1.10. Syntheticity and informativity - the great confusion

3.2 A system of non-informativity

3.2.1. Syntheticity of the a priorias a rule of construction

3.2.2. Emptiness and non-Euclidean geometry

3.2.3. Mathematics as construction and definition

3.2.4. Mathematics as an “arbitrary synthesis”

3.2.5. Nature as a story and a unified dream

3.2.6. Man legislates to nature

3.2.7. Internalizing truth - demolishing the bridge to reality

3.2.8. Flight from madness

3.3. Critical Idealism and Actualistic Ethics

3.3.1. Actualistic ethics

3.3.2. Hume’s ethical nihilism

3.3.3. Kant awakens from his ethical slumbers

3.3.4 The pure formality of Kant’s moral principles

3.3.5. The moral law as a law of nature

3.3.6. Moral truth is coherence

3.3.7. Despair: Kant glues content

3.3.8. and conjures an absolute end

3.3.9. and covers up a contradiction

3.3.10. “The objective is the subjective itself” - Hegel’s critique

3.1. Actualism and Critical Idealism

3.1.1 How is a priori information possible?

About Hume’s influence Kant wrote in words that gained fame:

I openly confess, the suggestion of David Hume was the very thing, which many years ago first interrupted my dogmatic slumber, and gave my investigations in the field of speculative philosophy quite a new direction. (Prolegomena:7)

Something is going on. Why “I confess”? Why “openly”? And what is the meaning of “the suggestion of David Hume”? Well, after Kant published his principal book The Critique of Pure Reason (1781), some reviewers pointed out the close kinship between his theory and what was then called “the idealism of Berkeley and Hume”. In order to repel this accusation, Kant wrote his Prolegomena to Any Future Metaphysics (1783) and after he confessed in the introduction that Hume “interrupted my dogmatic slumber”, he followed up with a qualification:

I was far from following him in the conclusions at which he arrived by regarding, not the whole of his problem, but a part, which by itself can give us no information. (Ibid.)

Kant could argue in this manner and could keep on believing in this because he never actually read Hume’s principal work but only some translated passages from it, and so he never became closely acquainted with Hume’s critique of the concepts of substance and the ego as well as his construction theory. As a consequence, he could represent his own uniqueness as the one who first saw that Hume’s problem of causality is merely a special case of a general problem, which Kant formulated first, and whose solution was the philosophy he created. This problem he formulated thus:

How are synthetic propositions a priori possible? (Ibid: §5)

The concept “synthetic propositions” was coined by Kant to mean a proposition which is not “analytic”, and by “analytic” he meant a proposition whose subject is logically non-separable from the predicate, or, “the predicate is contained in the subject”. He now argued that contrary to laws which are logically true, such as “the whole is greater than its part”, “magnitudes which are equal to another magnitude are equal to each other” (laws which are classified in Euclid’s geometry as “general notions” and were also called “axioms”) which are clearly analytic (there is no meaning in the notion of a part except in connection with a whole and so on) none of the propositions of geometry are analytic, and hence they are “synthetic”.

But he argued also that all the theorems of mathematics are certain and necessary, for a simple reason: they are certain and necessary for us. It is a psychological fact undoubted even today, that we are not able to describe to ourselves what the negation of a geometrical theorem could mean. For example, we are unable to imagine how two points in a plane would look, through which more than one straight line passes. It is a fact that in order to imagine such a thing we are forced to “bend” the plane. And since no certainty and necessity cannot be obtained by experience, as Hume’s argument sufficiently showed, Kant argued that it follows that all the theorems of mathematics are independent of experience and are logically “prior” to it: the theorems of mathematics are not only non-analytic, they are also non- empiric: they are synthetic and a priori. This, then, was the full formulation of what he called “Hume’s problem”, i.e., how is it possible to explain such a unique fact?

This fact became even more peculiar when Kant discovered that mathematics is able to link separate concepts only through what he called “intuition” and this, as far as it is possible to extract from his words, is the imagination in which we draw to ourselves pictures and drawings. Since such mathematical “intuition” does not employ our eyes, Kant called it “pure”:

So we find that all mathematical cognition has this peculiarity: it must first exhibit its concept in intuition (Anschauung) and indeed a priori, therefore in a visual form which is not empirical, but pure. Without this, mathematics cannot take a single step; hence its judgments are always visual, viz., “intuitive”; ... this observation on the nature of mathematics gives us a clue to the first and highest condition of its possibility, which is, that some non-sensuous visualization (called pure intuition or reineanschauung) must form its basis, in which all its concepts can be exhibited or constructed, in concreto and yet a priori. (Ibid:§7)

Kant used this discovery in order to explain and sometimes to prove the “synthetic” character of mathematics. Because its meaning was that it is impossible to prove mathematical theorems merely by analyzing their concepts, and therefore that the theorems are not analytical; the subject concept in each such theorem does not contain in its meaning the predicate concept, and so the subject and predicate are separate from each other.

3.1.2 Kant’s three refutations of a priori informativity

Thus was created a paradoxical concept - “a priori intuition”. What does such an intuition mean and how is it possible? If it is an intuition (be it as internal and pure as it may) it is an intuition of something - “of an object”, but since it is a priori as well, it is necessary that this object did not exist prior to the intuition, that is, separately from it. And therefore, it is obvious that the object of an a priori intuition must exist only as an effect of the intuition, for otherwise it would be an a posteriori intuition, an empiric intuition into what already exists. And so a dilemma emerged - either mathematical intuition is indeed an intuition, and then it must have its object existing before it and separately from it, and then it cannot be a priori. Or it is a priori but then it is not intuition, i.e., no intuiting of any object at all. And so Kant formulated it:

The question now is “how is it possible to intuit anything a priori?” An intuition is such a representation as immediately depends upon the presence of the object. Hence it seems impossible to intuit from the outset a priori, because intuition would in that event take place without either a former or a present object to refer to, and by consequence could not be intuition. ...but how can the intuition of the object precede the object itself? (Prolegomena: §8)

This was the first difficulty which Kant had to face as a consequence of viewing mathematics as both a priori and “synthetic”.

The second difficulty was the notion that an a priori knowledge of facts is possible. Kant opposed this vehemently, fully accepting Hume’s empiricist thesis (e.g., Critique A765/ B793) that there is no a priori information. That is to say, there is no description of things which is possibly true in the world and therefore also possibly false in the world - as informative descriptions usually are - and which is nevertheless a priori true, that is, true independently of the state of the world and logically prior to it. And against whoever doubted this, Kant posed the question:

...I should be glad to know how can it be possible to know the constitution of things a priori, i.e., before we have any acquaintance with them and before they are presented to us? (ibid: §11)

similarly, he explained that if we assume that that we know the objects of experience by our concepts, then

I am perplexed again as to how we can know anything a priori in regard to the objects ( Critique, second preface : xvi).

And he included the same empiricist demand in one of his formulations of the essence of his idealism :

The principle that throughout dominates and determines my idealism is[..]: “ All cognition of things merely from pure understanding or pure reason is nothing but shere illusion, and only in experience is there truth”. ( Prolegomena: Appendix, 151 in the open court edition)

There can be no doubt , therefore, that Kant denied the possibility of a priori true information[1], and so that he had to face the second difficulty - if mathematics is based on an a priori intuition, how can it possibly be informative as well?

And a third difficulty which now emerged as a consequence of accepting that mathematics is synthetic and a priori was this: even if this pure or a priori intuition provides information, how can it possibly be certain information? How does the fact that this intuition is now internal, (i.e., not by means of our flesh eyes) save it from the well-known fate of all observation as a source of information - lack of certainty and lack of necessity? As Hume taught him, no kind of observation, whether internal or external, can possibly present to us the necessity of an informative link, i.e., the necessary link between two facts or two “ideas” which are separate and mutually independent. And therefore, all that intuition is able to do is only to show us that things are such and such, but never that this is necessarily so. But mathematics deals only with things which are interconnected by necessity. And so, this third difficulty was, if the synthetic of mathematics carries certainty, how can it possibly be based on any intuition at all?

3.1. 3. Kant’s solution: “synthetic” information and form

Kant solved these three difficulties in one spectacular move, and this is the essence of all that will be called in the future his Copernican Revolution:

Hitherto it has been assumed that all our knowledge must conform to objects. But all attempts to extend our knowledge of object by establishing something in regard to them a priori, by means of concepts, have, on this assumption, ended in failure. We must therefore make trial whether we may not have more success in the tasks of metaphysics if we suppose that objects must conform to our knowledge. This would agree better with what is desired, namely, that it should be possible to have knowledge of objects a priori, determining something in regard to them prior to their being given. (Critique, preface to 2nd edition:xvi)

The model of this new strategy, Kant explained, is the first Copernican revolution, in which change of reference system led to success. Similarly in this case of explaining the fact that there exists synthetic yet a priori kind of knowledge such as mathematics:

A similar experiment can be tried in metaphysics as regards the intuition of objects. If intuition must conform to the constitution of the objects, I do not see how we could know anything of the latter a priori; but if the object (as object of our senses) must conform to the constitution of our faculty of intuition, I have no difficulty in conceiving such a possibility. (ibid.:xvii)

Accordingly he concluded from his difficulties that even though mathematics is “synthetic” it cannot contain any information about the world. His hypothesis was that the “syntheticity” of mathematics expresses merely that mathematics deals strictly with the “form of phenomena” and with nothing concerning their contents. This hypothesis was, therefore, the essence of his solution to the first difficulty - the paradoxicality of a priori intuition.

His considerations on his way to this hypothesis were based on the accepted principles of empiricism concerning informative knowledge of the world and mainly on the principle that every information which we attribute to the separate world is doubtful and by its nature lacks necessity. He explained that even if we could intuit directly the world, even then it would be incomprehensible how intuiting an object present to us can produce in us knowing this object in itself, “since its properties cannot migrate into my faculty of representation” (Prolegomena§9). That is, even in the case of such direct intuition, there would be some doubt about the correspondence or conformity of the image within me and the object out there. And therefore, any information we attribute to the world is necessarily doubtful, even when the evidence reaches us by some super-empirical ways. Afortiori, when the evidence exists in us a priori, independently of any possible experience. That is to say, if I have no direct intuition of the world as it is in itself,

there is no reason that can be imagined of a relation between my representation and the object, unless it depends upon a direct inspiration (Prolegomena§9)

and if there is no reason to assume such a mystical relation, there is also no reason to assume the certainty and necessity of the image within me. And therefore, if this intuition, on which mathematics is based, contains some content, i.e., information about the world, then mathematics could not be certain and necessary, and therefore it would not be a priori. But since there is certainty and necessity in any theorem of mathematics, i.e., since it is a priori, it can not possibly contain information about the world. Now, on the one side, as Kant concluded, this means that this pure intuition deals merely with the form of perceptual experience and not with its contents:

Therefore in one way only can my intuition (Anschauung) anticipate the actuality of the object, and be a cognition a priori, i.e., if my intuition contains nothing but the form of sensibility, antedating in my subjectivity all the actual impressions through which I am affected by objects. (Ibid.: §9)

Mathematics contains, therefore, only the form of phenomena but nothing of their contents. This is the straightforward voiding mathematics of information about the world and this voiding was Kant’s explanation of the fact that mathematics, even though it is based on intuition, is certain and necessary, i.e., is a science a priori.

But now it became urgent to explain something new and no less peculiar - how is it possible that even such a form, (i.e., the theorems of mathematics) applies necessarily to the objects of our experience? To meet this, Kant created the second component of his hypothesis: the form of mathematics describes not the form of things in themselves. This at once neutralizes the informativity of mathematics, and so answrs the puzzle from the impossibility of a priori information. Moreover, Kant added the further component of Copernican strategy, this form is only of our sensuous faculty - it is the form of human sensibility. And so,

we shall easily comprehend, and at the same time indisputably prove, that all external objects of our world of sense must necessarily coincide in the most rigorous way with the propositions of geometry; because sensibility by means of its form of external intuition, i.e., by space, the space with which the geometer is occupied, makes those objects at all possible as mere appearances. (Ibid.: §13 Remark I)

3.1. 4. Mathematics as mere form - the first information drainage

Mathematics reflects, therefore, the form of one of our faculties - our sensibility - and not the form of the separate world. And this explains also the fact that it applies necessarily to the phenomena : first, this faculty does not contain information about the phenomena at all, and second, it is the form of the faculty which makes the phenomena possible for us. The only information which mathematics contains, maybe, is not about triangles and circles etc., but strictly about ourselves, about the form of the faculty which makes the phenomena possible at all. In other words, the form of phenomena originates in and is the form of the faculty which makes them possible, our sensibility. In what sense is this sensibility the necessary condition of the phenomena, that which makes them possible? In the sense that sensibility determines the form of the stream of sensations which it receives.

Contrary to the world in itself, the phenomena are inseparable from our faculties and our sensibility, for the simple reason that only our sensibility makes it possible, i.e., creates the world of phenomena in an important sense: by being a precondition (i.e., a priori) for the perceivablity of anything as experience and phenomena, and therefore our sensibility does not at all determine any content. Sensibility is not any content (information) but merely form (formation). Hence the a priori in mathematics:

As soon as space and time count for nothing more than formal conditions of our sensibility, while the objects count merely as phenomena, then the form of the phenomenon, i.e., pure intuition, can by all means be represented as proceeding from themselves, that is, a priori. (Prolegomena §11)