It’s only been four days since.......

The thing-in-itself is a real, physical, space/time thing,
— Mww — Mww

Thanks for reconfirmation. It sounds new and fresh concepts no matter how many times I go over them :D

Just so, and how I "appreciate" the selbst and its translation. — tim wood

Just to be clear, Kant understands us to be organisms with sensory organs and nervous systems which interact with the environment, and evolved from common ancestors, as entirely empirical. The reality of the world beyond the empirical appearance is something we can't know. Thus Meillassoux critique that correlationism means the fossils of our ancestors only tell us what's empirically the case, not what actually happened, since we can't know whether we evolved or there was a big bang. We can only know what appears to us as structured by our reason.

Being a biological organism, there being a time before humans and a cosmos billions of light years beyond humans are all structured knowledge of the space and time categories of thought.

Kant seems consistent with the Copenhagen Interpretation. The quantum world is the thing in itself and consciousness through the categories makes it what it is.

Chapter 6: The Intellectual Conditions of Human Knowledge

This chapter was short but dense. I understand the overall argument, but I'm not sure if I understand a few of the details. I have included a few questions afterwards.

Also, I'm glad to see this thread has started getting more traction. Good discussions!

Summary:

The sensible conditions of human knowledge (the a priori intuitions of space and time) were covered in the previous chapter; this chapter focuses on the intellectual conditions of human knowledge, otherwise called the pure concepts of the understanding, or categories. Kant claims to have made a major advance over Aristotle, because he thinks that his catalog is not only complete, but that it can be demonstrated as being so. Kant goes about deriving the catalog from his analysis of the nature of judgement. His argument moves from the forms of general logic to the pure concepts of understanding.

Somewhat confusingly, “pure” does not indicate a priority with concepts as it does with intuitions. There are in fact a priori concepts which express formal conditions of intuition, which are the concern of mathematics. But a pure concept is really just a shortened version of a pure concept of understanding; “pure” in this case refers to its origin (“seat”) in the nature of human knowledge as that which expresses a fundamental law of the understanding, and which has no reference to the manifold of intuition.

Why pure concepts must be presupposed as necessary intellectual conditions of judgement: without pure concepts, there would not be any concepts at all.

Recall that the essential act of thought is judgement, and the function of judgement is to provide determinate representations (synthesis). The task of judgement is to provide a unification of representations under a concept; every judgement is a conceptualization, and vice versa.

Thus every judgement requires there be some pre-given concepts. So there must be some presupposed concepts that cannot be regarded as products of prior judgements; these are the pure concepts of understanding. These pure concepts are second-order rules for the generation of other rules (concepts). Without these concepts, there would be no concepts at all.

The relationship between the pure concepts and the logical forms

Kant correlates the pure concepts of understanding with the “forms of judgement”, by which he means the various ways in which the representational unity derived from a judgement is possible. Each form is also called a “logical function” or a “moment of thought”, and are grouped under four sets. At least one function from each set must be used in each judgement. Allison does not include an explicit table of the forms of judgement, nor of the pure concepts of understanding, so I have reproduced them below from my copy of the Critique:

Forms of judgement:

• Quantity of judgements:
  - Universal
  - Particular
  - Singular
• Quality:
  - Affirmative
  - Negative
  - Infinite
• Relation:
  - Categorical
  - Hypothetical
  - Disjunctive
• Modality:
  - Problematical
  - Assertorical
  - Apodeictical

Pure concepts of the understanding:

• Of Quantity:
  - Unity
  - Plurality
  - Totality
• Of Quality:
  - Reality
  - Negation
  - Limitation
• Of Relation:
  - Of Inherence and Subsistence (substantia et accidens)
  - Of Causality and Dependence (cause and effect)
  - Of Community (reciprocity between the agent and patient)
• Of Modality:
  - Possibility - Impossibility
  - Existence - Non-existence
  - Necessity - Contingence

The table of logical functions is taken by Kant to yield the table of pure concepts. Since every judgement is a conceptualization, then each of the logical forms of judgement has its own particular way of conceptualizing representations. In order to judge under a logical form, one must already possess a corresponding concept. At least one logical function from each set must be used in every judgement.

Demonstrating the correlation between the tables

Allison continues on to what he considers to be Kant’s explicit argument for the correlation between the table of logical functions of judgement and the table of pure concepts of understanding. Kant says:

“The same function which gives unity to the various representations in a judgement also gives unity to the mere synthesis of various representations in an intuition; and this unity, in its most general expression, we entitle the pure concept of the understanding. The same understanding, through the same operations by which in concepts, by means of analytical unity, it produced the logical form of a judgement, also introduces a transcendental content into its representations, by means of the synthetic unity of the manifold in intuition in general. On this account we call these representations pure concepts of the understanding, which apply a priori to objects - a conclusion which general logic cannot establish.” — Kant

By “transcendental content”, Kant means the form of the thought of an object in general. To introduce transcendental content into representations is to relate them to an object. A pure concept is that under which the objective validity of the synthesis of a judgement is thought; in other words, it is a rule that dictates how an object can be thought if it is to be determined by a judgement of a logical form.

For instance, the pure concept of substance (the conceptual correlate of the categorical logical form) dictates that the subject of a categorical judgement be conceived as a bearer of properties, and not a predicate of something else; that is to say, the subject is necessarily considered as if it were a substance (the ontological status of the pure concept of substance arises from its hypostatization; it need not be the case that this hypostatization is actually real for the concept to perform its function).

Both general and transcendental logic involve this same function of judgement, but at different “levels”; this is what allows Kant to derive the pure concepts (used at the transcendental level) from the logical functions (used at the general level). It is not the case of there being two distinct activities (analysis:general logic, synthesis: transcendental logic) of two separate faculties (the understanding and the imagination); it is rather a single activity (synthesis) of a single faculty (the understanding), operating at two distinct levels (general and transcendental).

Therefore, if we assume that the understanding has such a transcendental function (which has not been established yet), and that it uses this function in the same way in which it judges, then the logical functions that it uses when it unites concepts in a judgement are also the forms it uses to unite the intuitive manifold when determining an object for judgement. The pure concepts of understanding are nothing more than the logical functions of judgement, when applied to the manifold of intuition.

Shortcomings of Kant’s argument

Despite his defense of it in general, Allison does not forget aspects of Kant’s argument that are weak. He believes that Kant’s defense of the correlation of the disjunctive function with the pure concept of community is a failure. The disjunctive function is only understood in the sense of an exclusive disjunction, but the pure concept of community is understood as reciprocal connection; there is some degree of similarity in the sense that they both involve the coordination of elements in some way or another, but it’s not enough to actually show that the concept of community is derived from the disjunctive function.

The other shortcoming Allison notes is Kant’s claim that he has supplied a complete table of categories by deriving it from the logical functions of judgement. Even if we ignore the preceding issue of the disjunctive:community correlation, there still stands the issue of whether the table of logical functions of judgement is complete itself. Kant never supplies any argument demonstrating that this is the case. Why indeed are these forms of judgement the only ones? And if there are more logical functions, then there would also be more pure concepts, in which case Kant would be incorrect to state that his table of categories is complete.

Regardless of these two failings, Allison believes that the key takeaway is that Kant demonstrates that judgement requires a set of categorial a priori concepts, which he calls the pure concepts of understanding.

Questions:

• What exactly is "the understanding"? Kant calls it the "faculty of judgement"; so is the understanding just some "thing" that does all the judging?
• What exactly is a "representation"? This term has been used to describe multiple different things but I don't know what it actually means.
• Allison says that at least one logical function from each set (of the table of forms of judgement) must be used in every judgement; why is this the case?
• Allison notes that there is only one faculty (the understanding) operating at two different levels (the general and the transcendental). Am I correct to say that general logic applies to analytic judgements, and transcendental logic applies to synthetic judgements? If so, then why are all actions of the understanding called synthesis?

Let me try:

1) understanding is the categories in the mind while reason-intellect-judgment is the higher free human function that operates to connect all the "given" forms it finds in itself

2) representation is either imagination (pictures in the head) or the phenomena of the world

3) this is because the categories are said to be complete and humanity is made for activity

4) this question throws me but judgment synthesizes all of the work of understanding into free thought and action

Questions..... — darthbarracuda

......are given their ground beginning with A50/B74, in which are found definitions, systemic conditions, and constituent relations. A few pages that set the stage for the morass that follows.

I realized I am not getting the most out of Allison's book if I don't read Kant's Critique alongside with. My own progress is going to be a bit slower on account of balancing two technical books at the same time.

Kant has a wonderful note in the preface to the first edition of the Critique:

We very often hear complaints of the shallowness of the present age, and of the decay of profound science. But I do not think that those which rest upon a secure foundation, such as mathematics, physical science, etc., in the least deserve this reproach, but that they rather maintain their ancient fame, and in the latter case, indeed, far surpass it. The same would be the case with the other kinds of cognition, if their principles were but firmly established. In the absence of this security, indifference, doubt, and finally, severe criticism are rather signs of a profound habit of thought. Our age is the age of criticism, to which everything must be subjected. The sacredness of religion, and the authority of legislation, are by many regarded as grounds of exemption from the examination of this tribunal. But, if they are exempted, they become the subjects of just suspicion, and cannot lay claim to sincere respect, which reason accords only to that which has stood the test of a free and public examination. — Kant

Reading Kant himself will increase your knowledge

“....Thus the person who has learned a system of philosophy—say the Wolfian—although he has a perfect knowledge of all the principles, definitions, and arguments in that philosophy, as well as of the divisions that have been made of the system, possesses really no more than an historical knowledge of the Wolfian system; he knows only what has been told him, his judgements are only those which he has received from his teachers. He has formed his mind on another's; but the imitative faculty is not the productive. His knowledge has not been drawn from reason; and although, objectively considered, it is rational knowledge, subjectively, it is merely historical. He has learned this or that philosophy and is merely a plaster cast of a living man. (...)

All rational cognition is, again, based either on conceptions, or on the construction of conceptions. The former is termed philosophical, the latter mathematical. A cognition may be objectively philosophical and subjectively historical—as is the case with the majority of scholars and those who cannot look beyond the limits of their system, and who remain in a state of pupilage all their lives. (...)

Of all the a priori sciences of reason, therefore, mathematics alone can be learned. Philosophy—unless it be in an historical manner—cannot be learned; we can at most learn to philosophize....”
(A836-7/B864-5)

Just as a note, I think Schopenhauer did a great job dismantling Kant's 12 categories. He was inspired by the transcendental idealism but did not buy all aspects.

Here's only SOME of the many critiques Schop had of Kant (as sourced from Wikipedia). I bolded the m most relevant to this particular discussion. You can do whole threads on each critique alone!

According to Schopenhauer, there is a difference between an object-in-itself and a thing-in-itself. There is no object-in-itself. An object is always an object for a subject. An object is really a representation of an object. On the other hand, a thing-in-itself, for Kant, is completely unknown. It cannot be spoken of at all without employing categories (pure concepts of the understanding). A thing-in-itself is that which appears to an observer when the observer experiences a representation .

Kant altered his first edition to: claim that the spatially external thing-in-itself causes sensations in the sense organs of the knowing subject.

Kant tried to explain how: a perceived object, not mere raw sensation, is given to the mind by sensibility (sensation, space, and time), and how the human understanding produces an experienced object by thinking twelve categories.

Kant doesn't explain how something external causes sensation in a sense organ.

He didn't explain whether the object of experience (the object of knowledge which is the result of the application of the categories) is a perceptual representation or an abstract concept.

He mixed up the perceptible and the abstract so that an absurd hybrid of the two resulted.

There is a contradiction between the object experienced by the senses and the object experienced by the understanding.

Kant claims that representation of an object occurs both through reception of one or more of the five senses, and through the activity of the understanding's twelve categories.

Sensation and understanding are separate and distinct abilities. Yet, for Kant, an object is known through each of them. This contradiction is the source of the obscurity of the Transcendental

Logic.
Kant's incorrect triple distinction:
Representation (given to one or more of the 5 senses, and to the sensibilities of space and time)
Object that is represented (thought through the 12 categories)
Thing-in-itself (cannot be known).

Schopenhauer claimed that Kant's represented object is false. The true distinction is only between the representation and the thing-in-itself. For Schopenhauer, the law of causality, which relates only to the representation and not to the thing-in-itself, is the real and only form of the understanding. The other 11 categories are therefore unnecessary because there is no represented object to be thought through them.

Kant sometimes spoke of the thing-in-itself as though it was an object that caused changes in a subject's senses. Schopenhauer affirmed that the thing-in-itself was totally different from phenomena and therefore had nothing to do with causality or being an object for a subject.

Excessive fondness for symmetry:
Origin of Kant's Transcendental Logic:
As pure intuitions (in the Transcendental Aesthetic) were the basis of empirical intuitions,
pure concepts (in the Transcendental Logic) were made the basis of empirical concepts.
As the Transcendental Aesthetic was the a priori basis of mathematics,
the Transcendental Logic was made the a priori basis of logic.
After discovering empirical perception is based on two forms of a priori perception (space and time), Kant tried to demonstrate that empirical knowledge is based on an analogous a priori knowledge (categories).

Schemata
He went too far when he claimed that the schemata of the pure concepts of the understanding (the categories) are analogous to a schema of empirically acquired concepts.
A schema of empirical perception is a sketchy, imagined perception. Thus, a schema is the mere imagined form or outline, so to speak, of a real perception. It is related to an empirical abstract concept to show that the concept is not mere word-play but has indeed been based on real perceptions. These perceptions are the actual, material content of the empirical abstract concept.

A schema of pure concepts is supposed to be a pure perception. There is supposed to be a schema for each of the pure concepts (categories). Kant overlooked the fact that these pure concepts, being pure, have no perceptual content. They gain this content from empirical perception. Kant's schemata of pure concepts are entirely undemonstrable and are a merely arbitrary assumption. This demonstrates Kant's purposeful intention to find a pure, a priori analogical basis for every empirical, a posteriori mental activity.

Judgments/categories
Derived all philosophical knowledge from the table of judgments.
Made the table of categories the basis for every assertion about the physical and the metaphysical.

Derived pure concepts of the understanding (categories) from reason. But the Transcendental Analytic was supposed to reference only the sensibility of the sense organs and also the mind's way of understanding objects. It was not supposed to be concerned with reason.

Categories of quantity were based on judgments of quantity. But these judgments relate to reason, not understanding. They involve logical inclusion or exclusion of concepts with each other, as follows:

Universal judgment: All A are x; Particular judgment: Some A are x; Singular judgment: This one A is x.

Note: The word "quantity" was poorly chosen to designate mutual relations between abstract concepts.

Categories of quality were based on judgments of quality. But these judgments also are related only to reason, not to understanding. Affirmation and denial are relations between concepts in a verbal judgment. They have nothing to do with perceptual reality for the understanding. Kant also included infinite judgments, but only for the sake of architectonic symmetry. They have no meaning in Kant's context.

The term "quality" was chosen because it has usually been opposed to "quantity." But here it means only affirmation and denial in a judgment.

The categorical relation (A is x) is simply the general connection of a subject concept with a predicate concept in a statement. It includes the hypothetical and disjunctive sub-relations. It also includes the judgments of quality (affirmation, negation) and judgments of quantity (inclusional relationships between concepts). Kant made separate categories from these sub-relations. He used indirect, abstract knowledge to analyze direct, perceptual knowledge.

Our certain knowledge of the physical persistence of substance, or the conservation of matter, is derived, by Kant, from the category of subsistence and inherence. But this is merely based on the connection of a linguistic subject with its predicate.
With judgments of relation, the hypothetical judgment (if A, then B) does not correspond only to the law of causality. This judgment is also associated with three other roots of the principle of sufficient reason. Abstract reasoning does not disclose the distinction between these four kinds of ground. Knowledge from perception is required.
reason of knowing (logical inference);
reason of acting (law of motivation);
reason of being (spatial and temporal relations, including the arithmetical sequences of numbers and the geometrical positions of points, lines, and surfaces).

Disjunctive judgments derive from the logical law of thought of the excluded middle (A is either A or not-A). This relates to reason, not to the understanding. For the purpose of symmetry, Kant asserted that the physical analog of this logical law was the category of community or reciprocal effect. However, it is the opposite, since the logical law refers to mutually exclusive predicates, not inclusive.

Schopenhauer asserted that there is no reciprocal effect. It is only a superfluous synonym for causality. For architectonic symmetry, Kant created a separate a priori function in the understanding for reciprocal effect. Actually, there is only an alternating succession of states, a chain of causes and effects.

Modal categories of possible, actual, and necessary are not special, original cognized forms. They are derived from the principle of sufficient reason (ground).
Possibility is a general, mental abstraction. It refers to abstract concepts, which are solely related to the ability to reason or logically infer.

There is no difference between actuality (existence) and necessity.
Necessity is a consequence from a given ground (reason).[2] — Critique of Kantian Philosophy Wikipedia Article

Why would Schopenhauer say only causality is a category of the mind. Kant admitted that the self is will ("free will) and since such is apart from space and time the relationship to the world from it is paradoxical

Thanks, I plan on reading Schopenhauer after Kant.

Finished the Introduction and Transcendental Aesthetic. Some questions:

• Kant says that knowledge a priori is that which is absolutely independent of all experience. He contrasts this with a posteriori knowledge which is possible only through experience; he uses the analogy of a man knowing that an object will fall because of prior experiences of them doing so. Yet it seems to me that we can conceive of having empirical knowledge about something without every actually experiencing it ourselves. Kant surely doesn't mean that we actually have to experience something in order for it to count as empirical knowledge, is it more like it having the possibility of being experienced which makes it empirical knowledge?
• If I understand correctly, intuitions immediately relate to objects, which are given to us as representations through sensation, which is the mode of sensibility. In other words: sensibility is the capacity to receive representations from objects which affect us; it does this through sensation; sensation is the way in which (empirical) intuitions relate to an object. Here is what I do not get: what is the difference between a sensation and an intuition (what more is there to an intuition other than sensation?), what is meant by "affect" if not simply interacting with us in some way, and what is the difference between the term representation of an object and the term object?
• In what way is a priori knowledge apodictic that makes it impossible for empirical knowledge to provide the same universality and necessity? That 7 + 5 = 12 is a synthetic a priori true proposition is certainly plausible to me, but that it is necessarily and universally true that 7 + 5 = 12 is not. Do I have anything but my current and previous cogitations of this to justify my belief? For what reason do I have to believe that it may not be different in the future?

Kant says that knowledge a priori is that which is absolutely independent of all experience...... — darthbarracuda

From B3:

“....whether there exists a knowledge altogether independent of experience, and even of all sensuous impressions? But the expression, "a priori," is not as yet definite enough adequately to indicate the whole meaning of the question above started. For, in speaking of knowledge which has its sources in experience, we are wont to say, that this or that may be known a priori, because we do not derive this knowledge immediately from experience, but from a general rule, which, however, we have itself borrowed from experience**. (...) By the term "knowledge a priori," therefore, we shall in the sequel understand, not such as is independent of this or that kind of experience, but such as is absolutely so of all experience. (...) Knowledge a priori is either pure or impure**. Pure knowledge a priori is that with which no empirical element is mixed up....”
**impure a priori knowledge, also considered as either intuition, metaphysically, or memory, psychologically.
** in Guyer and Meiklejohn, omitted in Kemp Smith.

Kant is merely distancing the knowledge we’ve already acquired through experience, from knowledge not given from any experience whatsoever. Impure a priori knowledge is like....seen one fireworks display, seen ‘em all kinda thing. Regardless of relative degree, all are still just fireworks displays. Pure a priori knowledge, because it is being herein defined as absent any experience, must then be determined by something other than sensibility. And the only thing remaining after eliminating sensibility, is thought. Therefore, the theoretical ground is laid for deriving the possibility of pure a priori knowledge from understanding alone, which is the faculty of thought.

......is it more like it having the possibility of being experienced which makes it empirical knowledge? — darthbarracuda

Two counter arguments:
First, If possible experience was sufficient for empirical knowledge, how would we tell the difference between what we might know, and what we do know? It is, at the end, contradictory to ascribe certainty on the one hand, and ascribe the same certainty to a mere possibility on the other.

Second, If it is true the only means for empirical knowledge is from experience, then the negation of it must also be true, insofar as without experience there is no empirical knowledge. The proposition is true, therefore the negation is also true.

Best to remember.....the entire treatise is concerned with the question stated above, proving the possibility, validity and the source of the principles which determine the legitimate boundaries of human reason.

what is the difference between a sensation and an intuition (what more is there to an intuition other than sensation?), — darthbarracuda

Sensation arises from the matter of objects and is the initiation of the process by which the system is going to determine how the object is to be known; intuitions are the forms to which the matter attains, whatever that objects may be. Thus it is, sensation is given from physicality, intuition is given from rationality, and therein is the preliminary theoretical ground for the Kantian transcendental idealist science of combining the empiricism of Hume, et al with the rationalism of Descartes et al. Which, from his earliest critical career, was to be his primary philosophical mandate. “Dogmatic slumbers” and all that.

What more is there to intuition than sensation, depends on one’s understanding of the matter/form duality. If one doesn’t grant such a thing, there is no more, at least in the Kantian sense; if one does grant the duality, what more is there, is already given, from the Kantian sense.

The matter of objects can only affect the human system five ways, for there are, of course, only five modes of perception. But any mode of perception gives a representation, which are themselves only distinguishable by the mode in which they are received into the system. Representation of sound from the auditory apparatus is different from the representation of touch from the tactile apparatus, but to the system, all are merely representative of an object’s particular affect, and something more is absolutely required before any determination is possible as to what the object is.

“....Without the sensuous faculty no object would be given to us, and without the understanding no object would be thought. Thoughts without content are void; intuitions without conceptions, blind. Hence it is as necessary for the mind to make its conceptions sensuous (that is, to join to them the object in intuition), as to make its intuitions intelligible (that is, to bring them under conceptions). Neither of these faculties can exchange its proper function. Understanding cannot intuite, and the sensuous faculty cannot think. In no other way than from the united operation of both, can knowledge arise. But no one ought, on this account, to overlook the difference of the elements contributed by each; we have rather great reason carefully to separate and distinguish them. We therefore distinguish the science of the laws of sensibility, that is, aesthetic, from the science of the laws of the understanding, that is, logic....”
(A51/B75)

And here it is that Kant exhibits his admitted dualist metaphysical nature, and the ground for a completely dualistic methodology for human knowledge in general. No escape from it, and those making the attempt otherwise only “...have recourse to pitiful sophisms or confess their ignorance...”

In what way is a priori knowledge apodictic that makes it impossible for empirical knowledge to provide the same universality and necessity? — darthbarracuda

The way in which pure a priori knowledge is apodeitic is becaiuse it arises from the understanding alone, an internal cognitive faculty, thereby granting sufficient causality for certainty, in that there is no other influence on it. That which arises from itself, cannot be other than it is, which holds the same value as truth, but truth restricted to the very domain from which it is given. Now “not other than it is” may eventually be shown to be false, but at the originating time of it, the certainty is not questionable, and if eventually shown to be false, it cannot be of the same domain from which it originated, for in such case, there is an outside influence. It is clear from this stipulation, the only possible pure a priori knowledge is in the form of principles, or the laws derivable from them, either with respect to the physical domain, which is properly science, “...the science of what is...”, or with respect to the metaphysical domain, which is properly morality, “...the science of what ought to be...”. Again, a furtherance of the intrinsic Kantian epistemological dualism.

Universality and necessity are principles that cannot apply to anything empirical, because they are overturned by, subsumed under, the more powerful Principle of Induction, which makes explicit experience is always contingent: undeniable observational proof that what’s true today may not be true tomorrow, re: determinations of the nature of the observable Universe. What reason seeks, on the other hand, is that which is never contingent, or, which is the same thing, never self-contradictory, itself just conventional speech for seeking the unconditioned, the ideal, the irreducible. The question then becomes....does reason ever reach that state of affairs, and the Kantian speculative metaphysics proves it does not, and it cannot.

Given what reason cannot do, it remains to be determined what reason can do, the controlling condition being the LNC, which immediately suggests the entire human cognitive system is inherently logical. This, in turn, makes it impossible to demonstrate how logic itself comes about, but instead, must simply be granted as being the case. Otherwise, no theoretical sciences of any kind that are predicated on logical propositions can facilitate knowledge, which means we can never claim knowledge of anything at all.

That 7 + 5 = 12 is a synthetic a priori true proposition is certainly plausible to me, but that it is necessarily and universally true that 7 + 5 = 12 is not. — darthbarracuda

Truth here is irrelevant. Synthetical propositions denote nothing but the relation of conceptions to each other, with no judgement as to the truth of the proposition being enabled. Again...dualism, in that synthetical is only to differentiate a kind of relation of conceptions from its complement, the analytical. It is identity, not truth, which makes these relational determinations. Analytical propositions are those in which the conceptions hold similar identities, synthetical propositions are those in which identity does not hold. Identity herein meant to indicate only that the conception in the predicate of a proposition can be found in the subject of that same proposition. In synthetical propositions, then, the conception in the predicate cannot be found in the subject.

From that it follows that while 7 + 5 = 12 is synthetical, in that neither of the numbers to the left, in and of themselves, can give the number on the right.....

“....The conception of twelve is by no means obtained by merely cogitating the union of seven and five; and we may analyse our conception of such a possible sum as long as we will, still we shall never discover in it the notion of twelve. We must go beyond these conceptions, and have recourse to an intuition which corresponds to one of the two—our five fingers, for example, or like Segner in his Arithmetic five points, and so by degrees, add the units contained in the five given in the intuition, to the conception of seven. For I first take the number 7, and, for the conception of 5 calling in the aid of the fingers of my hand as objects of intuition, I add the units, which I before took together to make up the number 5, gradually now by means of the material image my hand, to the number 7, and by this process, I at length see the number 12 arise....”
(Added in B16, not found in A)

.....the fact that the proposition is true only arises from empirical proofs, in which it is found that it is impossible for this particular arithmetic operation to give a different result, and thereby sets the stage for establishing the criteria for any mathematical entailment, and in turn, establishing the possibility and the validity of pure a priori conditions in general. In this way, all logical propositions determined by reason are in logical form only, the content be what it may. From the simplest analytical proposition, A = A, to the most complex abstract synthetical mathematical calculus, the proofs of all logical forms depend on empirical conditions.

For what reason do I have to believe that it may not be different in the future? — darthbarracuda

According to Kantian metaphysics, you don’t. Knowledge destroys belief, so if you know without the possibility of refutation that mathematical propositions are the mark of absolute certainty, because you can prove all of them to yourself, you have no reason whatsoever to doubt them. It behooves one, nonetheless, to keep in mind such certainty is only determinable under the auspices of the very system from which the the ground for it is given. In such case, not only is it impossible to doubt this certainty, but it is just as impossible to think of what form the doubt would have.

The justification of all this, is in the categories, the “...pure conceptions of the understanding...”, from which are given the schema of “quantity”, first in the form of numbers, and thereafter in the form of unity, the manifestations of the permissible connectedness of numbers. Because it is the case, at least in this particular epistemological theory, that the categories are absolutely essential, and given that the schema of the categories are always the same, it becomes impossible to arrive at different conclusions for any one proposition predicated on them, assuming internal logical consistency is met, the primary condition of the system as a whole. Still, justification is not proof, which, as already shown, is entirely dependent on empirical conditions.

Universality and necessity, in fact any terminology of any kind, the categories, even reason itself, if developed by humans, only applies to humans. Mathematical propositions will therefore be true, iff a human is responsible for them. They will be true wherever and whenever there is a human to think them, but not necessarily otherwise. To a rational agent with other than a intuitive/discursive cognitive system, nothing about mathematical truths, or any truths at all, can be said. Does 1 + 1 = 2 to an elephant? Or a resident of a planet we don’t even know about? Not only can we not say, but we don’t even have the means to understand how to ask.

And Nagel thought himself the first to wonder. No reason for it, really, for the answer had already been given, fully 200 years before he even thought about it.

Why would Schopenhauer say only causality is a category of the mind. Kant admitted that the self is will ("free will) and since such is apart from space and time the relationship to the world from it is paradoxical — Gregory

Schopenhauer thought the 12 categories were unnecessary and arbitrary I believe. In Schopenhauer's system, time, space, and causality in the general a priori cognitive limits of how the Will is represented creating the subject-object "illusion" which is the realm of the phenomenal world we "think" is going on (but is only represented or cognized). From there he goes on to explain the fourfold "root" of the Principle of Sufficient Reason. Of course, this itself doesn't necessarily answer the question of how such a perceiver exists in the first place (the first "eye" that sees the world, if you will). Mark Linsenmayer from the podcast The Partially Examined Life has the best critique on this aspect of Schopenhauer, which I will quote below. It is also something I have brought up here in TPF in previous threads. I can give you those links if you want, but I'd have to dig back a little.

You may recall that for Kant, whether or not time has a beginning or not is an antinomy: There are equally good reasons on both sides, and so the correct answer it to say that we just can't know and/or that the question somehow doesn't make sense. Temporal sequence only applies to phenomena, which depend on minds, so asking whether things in themselves are in an infinite or finite temporal series is attempting to use the concept of time outside of the realm in which it was developed, which is the realm of our experience. It does not follow from this that the Thing-In-Itself is atemporal, but simply that the Thing-In-Itself is not something we're in any position to make a judgment either way about. Compare to the question "Is God green?" You might say qua Maimonides that no, of course God is not green; colors apply to finite things. But neither can we positively say that God has the positive property of not being green, or not having color. Maybe He does have color, but in some higher way that we can't understand. We are in the same position regarding the Thing-In-Itself: by definition it's something we can't perceive or even really conceive of in its wholeness, in its essence, in its positive aspects.

Schopenhauer thinks that Kant is in no position to decide this issue "by definition," and thinks he has other reasons (mystical and artistic experience, i.e. the verdict of genius, plus the philosophy of science considerations surrounding "force" belabored in our discussion) for thinking we can know some positive things about the Thing-In-Itself, but he still fundamentally doesn't give us a reason for insisting on its lack of plurality and hence its non-temporal, non-spatial status. So why does he insist on this? I think he's just adhering to the heuristic (Kant might call it a regulative principle of Reason) to seek simplicity/unity. Saying that ultimately existence is One is supposed to be more satisfying somehow than saying that it's irreducibly Many. It's somewhat ironic that Schopenhauer dismisses this principle when it comes to science (in his rejection of reductionism) only to assert such unity at the metaphysical level.

Setting that aside, and granting Schopenhauer the point about the Thing-In-Itself's unified, atemporal character, and granting him the (contentious) proposition that differentiation within the Thing-In-Itself (the Will) only happens because perceivers pop up to perceive some part of the Will, haven't we just pushed the antinomy back one level? Schopenhauer is able to answer the question "does time have a beginning of not" by saying "no, not on the level of representation, but yes, before the first perceiver, there was no time," but he is then faced with a similarly insoluble question: "How could the first perceiver perceive something unless there was something already there to perceive?" This is to ask "why the principium individuationis?" which is in Schopenhauer's system the tragic question of Being. — Mark Linsenmayer

I plan on rereading a few books of Schopenhauer's in the future, having finished some books by Hegel recently. There is this element in psychology where we know there are other people and we know we are dependent but there is then are element in logic that makes the world dependent on us. The scientific mind tries to understand these together by analyzing the mind-object relation

Thanks for the detailed responses, I appreciate it :up:

Pure knowledge a priori is that with which no empirical element is mixed up....”
**impure a priori knowledge, also considered as either intuition, metaphysically, or memory, psychologically. — Mww

Okay, memory (or imagination) was the thing I had in mind when I wondered about Kant's definition of the a priori. I can taste a strawberry, but I can also remember or imagine the taste of a strawberry. But the pure a priori is that which is absolutely independent of all experience (=sensibility?).

That does not mean that I can have pure a priori thoughts, though:

Pure a priori knowledge, because it is being herein defined as absent any experience, must then be determined by something other than sensibility. And the only thing remaining after eliminating sensibility, is thought. Therefore, the theoretical ground is laid for deriving the possibility of pure a priori knowledge from understanding alone, which is the faculty of thought. — Mww

Without the sensuous faculty no object would be given to us, and without the understanding no object would be thought. — Mww

From the simplest analytical proposition, A = A, to the most complex abstract synthetical mathematical calculus, the proofs of all logical forms depend on empirical conditions. — Mww

Kant starts the Critique by claiming all knowledge begins with experience. Within the context of the above quotes, does this basically mean that thought is always tied to sensibility, but is nevertheless different from it?

The way in which pure a priori knowledge is apodeitic is becaiuse it arises from the understanding alone, an internal cognitive faculty, thereby granting sufficient causality for certainty, in that there is no other influence on it. That which arises from itself, cannot be other than it is, which holds the same value as truth, but truth restricted to the very domain from which it is given. — Mww

That makes sense. Apodeiticity comes from the closed nature of the understanding, it is complete and unalterable. Truth is restricted to the domain in which it is conditioned, the thing-in-itself is literally outside of truth (for humans). Correct?

The question then becomes....does reason ever reach that state of affairs, and the Kantian speculative metaphysics proves it does not, and it cannot. — Mww

Do you mean that reason cannot ever reach absolute proof for empirical propositions, or that reason cannot ever reach absolute proof (within the domain of the human mind) for any proposition whatsoever?

Sensation arises from the matter of objects and is the initiation of the process by which the system is going to determine how the object is to be known; intuitions are the forms to which the matter attains, whatever that objects may be. — Mww

Hence it is as necessary for the mind to make its conceptions sensuous (that is, to join to them the object in intuition), as to make its intuitions intelligible (that is, to bring them under conceptions) — Mww

What I don't understand is how "form" is different from "concept"; sensations (matter) are given form (intuitions), but intuitions themselves are unintelligible without being brought under a concept by the understanding through an act of synthesis involving the pure concepts.

My biggest source of confusion while reading Kant has been with the meaning of these words: intuition, object, and representation. They seem to often be used in different ways and it's difficult for me to keep track of what they mean in each context.

what is the difference between a sensation and an intuition (what more is there to an intuition other than sensation?), — darthbarracuda

Can intuition have contents? I often hear about thoughts and sensations have contents, but never came across contents of intuition. Things are supposed to be given to intuition from the external world in CPR, which sounds like intuition is also type of mental process, but could it be storage like memory or a mental faculty of its own?

does this basically mean that thought is always tied to sensibility, but is nevertheless different from it? — darthbarracuda

Not quite. Thought is different from sensibility, but thought is always and only tied to understanding.

“....For it** is, according to what has been said above, a faculty of thought....”
“....understanding cannot intuit, and the sensuous faculty cannot think...”
(** “it”, in context, is understanding; “what has been said above” doesn’t paraphrase properly. See A69/B94)

Empirical intuition is tied to sensibility. We don’t think about our sensations; we only realize there has been one.

That does not mean that I can have pure a priori thoughts, though — darthbarracuda

Sure you can. Every change has a cause is an impure a priori cognition, insofar as here, something that changes is presupposed. You don’t have to step on the gas to know your car will go faster if you do. You also know it will also go a little faster if you get hit in the back by a little car, as well that it’ll go a lot faster if hit by a big truck.

But every change must have a cause is a pure a priori cognition, for it doesn’t consider any objects, but only the relation between objects in general, and time, which is.....as we all know....a pure intuition. And any proposition containing a pure representation, is pure a priori cognition. All parts of space are themselves space. And so on.

This reflects back to the mention of pure a priori cognitions thought as principles, or the laws derived from them. There is no exception to the principle, “every change must have a cause”, hence it is a pure a priori cognition. “No A can be not-A”, a law; “every existence is necessary”, a law; “existence cannot be a predicate but subject only”, a principle but not a law, for it has to do with the structure of pure reason itself, which is always speculative.
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meaning of these words: intuition, object, and representation. — darthbarracuda

Kant doesn’t say exactly what an intuition is, only what they do or how they come about. Empirically, or that which is an “external intuition” because its source is without us rather than within:

“....If, on the other hand, the object conforms to the nature of our faculty of intuition...”
“....sensible intuition, and hence are only conditions of the existence of things as phenomena...”
“....an intuition can take place only in so far as the object is given to us...”

This is quite difficult, because Kant also talks about “internal intuitions”, which do not arise from sensibility, hence are not susceptible to being phenomena, in other words, where an object is not given to us. As such, and because I can intuit myself as a thinking rational agent, but myself can hardly be considered a phenomenon, so it would seem internal intuitions are necessary. Kant is either not very clear about this, or he is far too clear, to the point of confusing his readers.

“...Now if there did not exist within you a faculty of intuition a priori; if this subjective condition were not in respect to its form also the universal condition a priori under which alone the object of this external intuition is itself possible; if the object (that is, the triangle) were something in itself, without relation to you the subject; how could you affirm that that which lies necessarily in your subjective conditions in order to construct a triangle, must also necessarily belong to the triangle in itself?...”

Good luck with that little tidbit. From that bolded, I just let the faculty of intuition be some contingent state of my subjective condition. I don’t really need to know exactly what it is, or its exact origin. If it ain’t broke, don’t fix it sorta thing.

An object in Kant is either a real physical thing, iff it can be represented as a phenomenon, or a predicate belonging to a copula, iff contained in a logical proposition, re: an object of reason, or an object of experience. The real object and the object of experience are not the same, but relate to each other with sufficient logical justification to say the sensed object is to be known as a certain thing. An object of experience, on the other hand, is nothing but what the cognitive system says it is, after applying itself to the real perceived object, re: cloud formations, mirages, or, what the system conceives on its own accord, without the presence of an object, re: hallucinations.

A representation is just what the cognitive system substitutes for the real thing, the most general word for an object at any stage in its de­termination by the subject, or for the subjective act of forming the object at that level. Intuitions and conceptions are representations, judgement is a representation of a representation. Knowledge is not, insofar as the determination of the object by the subject, is already accomplished.

For what it’s worth.....

“...Now if there did not exist within you a faculty of intuition a priori; if this subjective condition were not in respect to its form also the universal condition a priori under which alone the object of this external intuition is itself possible; if the object (that is, the triangle) were something in itself, without relation to you the subject; how could you affirm that that which lies necessarily in your subjective conditions in order to construct a triangle, must also necessarily belong to the triangle in itself?...” — Mww

It would seem (subject to correction) that while there might be triangular shapes all around all the day long, what it takes to recognize them as triangles is an internal intuition with which those experiences conform. And this seems reasonable. As there is no such thing as a triangle - and if there were, as noumenon how would anyone know it - it must exist as idea.

The question arises if it is always there, or learned? If "universal conditions a priori" can be learned, or must be learned, then it appears that what is truly, and only, universal is the capacity to learn such things. Hmmm.

As there is no such thing as a triangle — tim wood

Just baffles me that people are alive and otherwise well, that reject that truism. Still, check out these rock formations:

https://thedailyplasma.blog/2017/11/03/triangles-in-nature-why/#:~:text=Triangular%20shapes%20are%20everywhere%20in%20Nature.%20They%20show,…%20well%2C%20natural.%20Or%20is%20it%20that%20simple%3F

Kinda hard for the average Smuck On The Street to agree there’s no triangles in Nature, when he can look right at ‘em.
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there might be triangular shapes all around all the day long, what it takes to recognize them as triangles is an internal intuition with which those experiences conform. — tim wood

I think Kant would say those shapes are sensed, become phenomena, so must be empirical intuitions. The shapes may be recognized as triangles merely from being told the object is shaped in that particular way. In this case, the perceiver has no need to think a priori about lines or the arrangement of them, because the lines are there and they’ve already been arranged. Judgement merely says...yep, the spatial extension perceived conforms to the mental form cognized.

I think the key takeaway with respect to that quote, is that not everything of perception is a thing in itself. The first part of it states “object of this external intuition is itself possible”. But we’ve already agree there are no triangles in Nature, so it must be that “the object of this external intuition” is a sensible object we ourselves put in Nature. And because we created it, in accordance with its form residing in reason, It must appear to us as it is in itself. But it bears remembering we don’t need to cognize this appearance, herein the triangle in itself, because we’ve already cognized a priori exactly how the appearance will manifest and it is already known to us accordingly.

The second part asks, even if that which we construct and objectively illustrate then becomes a phenomenon because it affects our faculties of representation, we cannot say we know it as a thing in itself, which is already proven to be impossible, so it must be known in conjunction, not with its appearance from sensibility, but with its form from intuition, which we already have. Which is exactly what we did when we originally cognized it a priori, before the illustration of it.

The proper conclusion is, then, that there must be a faculty of intuition a priori within us.

Hope that makes sense, cuz it’s the hardest my brain has worked since.....oh, 1984, I think.

we cannot say we know it as a thing in itself, which is already proven to be impossible, so it must be known in conjunction, not with its appearance from sensibility, but with its form from intuition, which we already have.... The proper conclusion is, then, that there must be a faculty of intuition a priori within us. — Mww

And how not? How could anything be understood absent the faculty of understanding however it might work. (And in trust no one of sense by this time denies that animals also possess a faculty of understanding however it might work.)

But whence that which is understood? I am pretty sure it is all taught/learned. Your/Kant's "which we already have," then, something of a problem. Beyond capacity, what is there? What would that even be? Even space and time taught/leaned. In trust it's clear I do not mean taught/learned in any schoolboy sense. Rather while it seems to me that nothing is known at first, the being learns, puts-it-together, PDQ.

And it makes a priori itself a problem. It would seem the term must be an after-the-fact judgment. Without the judgment, what could it mean?

An implication is that if the CPR is intended to establish a ground for scientific thinking, which I think it is and does, it itself grounded in practical reason. Or at least the connection between pure and practical reason substantial and necessary with much back and forth.

How could anything be understood absent the faculty of understanding — tim wood

Of course nothing can be, but intuition doesn’t have anything to do with understanding.....

“...the understanding cannot intuit and the sensuous faculty cannot think...”

....but we’re still in the sensing stage, not the conceiving stage. We’ve synthesized matter to form, according to appearance, giving phenomena, but haven’t yet synthesized concepts to phenomena, according to judgement, giving cognition.

Besides, all this intuitive synthesis being completely outside our awareness, it must be a priori, or, it isn’t even happening that way at all. Hence....speculative metaphysics. We are aware of sensuous impressions, we are aware of how those impressions are to be known. All in between, is guesswork, albeit necessarily logically consistent.
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if the CPR is intended to establish a ground for scientific thinking, which I think it is and does — tim wood

Nahhhh....scientific thinking had already been established, and it is the ground for the theoretical epistemology of pure reason.

“.....Whether the treatment of that portion of our knowledge which lies within the province of pure reason advances with that undeviating certainty which characterizes the progress of science, we shall be at no loss to determine. If we find those who are engaged in metaphysical pursuits, unable to come to an understanding as to the method which they ought to follow; if we find them, after the most elaborate preparations, invariably brought to a stand before the goal is reached, and compelled to retrace their steps and strike into fresh paths, we may then feel quite sure that they are far from having attained to the certainty of scientific progress and may rather be said to be merely groping about in the dark....”

CPR admits the validity of scientific thinking, that is, logical theory verified by experience, and thereby attempts to ground metaphysical thinking in accordance with the certainty of scientific thinking. It begins by asking, “...how is metaphysics as a science possible...”. (absent in A/ added in B22)

Now, if you’d said, CPR is intended to establish the ground for thinking scientifically......we’d be off to the rodeo.
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if the CPR is intended to establish a ground for scientific thinking (...) it is itself grounded in practical reason. — tim wood

I’ve noticed you speak of this in other places and times. Sooner or later I probably would have asked about it.

Kant must have attributed to reason three fundamental conditions, for there are ....DUH!!!....three critiques, to wit:, theoretical (CPR), judicial (CofJ) and practical (CpR). Everydayman thinks more about his actions than about how he comes up with his actions, which implies practical reason has more importance overall than either of the other two conditional forms of reason. Nevertheless, given the two basic kinds of reason qua reason, pure and practical....

“.....To this question we have given a sufficient answer; for we have shown that, as the former stands in a relation to a different kind of condition from those of the latter, the law of the one does not affect the law of the other and that, consequently, both can exist together in independence of and without interference with each other....”

....I shall await your exposition as to how the one might be grounded in the other.

Kant must have attributed to reason three fundamental conditions, for there are ....DUH!!!....three critiques, to wit:, theoretical (CPR), judicial (CofJ) and practical (CpR). Everydayman thinks more about his actions than about how he comes up with his actions, which implies practical reason has more importance overall than either of the other two conditional forms of reason. Nevertheless, given the two basic kinds of reason qua reason, pure and practical....

“.....To this question we have given a sufficient answer; for we have shown that, as the former stands in a relation to a different kind of condition from those of the latter, the law of the one does not affect the law of the other and that, consequently, both can exist together in independence of and without interference with each other....”

....I shall await your exposition as to how the one might be grounded in the other. — Mww

Hmmmmm, a question: Of course, this division between the practical and rational is subsumed under conditions that make thought even possible at all. One has to think through the categorical imperative and practical matters in general, that is, synthesize representations. to determine what to do, so the Critique of Pure Reason is analytically presupposed by the practical, one could argue. If the matter is "the law" of the one not affecting the other, then the matter rests with what is meant by "affect" which requires contextual clarification.

Hmmmmm, a question: — Constance

Sorry......what?

Maybe I missed the issue coming in as I did. I took it that your question as to how the one might be grounded in the other referred to how an analysis of reason and judgment could be a ground (a general notion) for practical affairs in light of the fact that prior to any formal exposition there is first the "everyman" acting spontaneously, not thinking analytically, and so, any analysis of thinking as such would not come to bear on the practical end of things.
I read through your discussion quickly, so I could have missed the mark.

I took it that your question as to how the one might be grounded in the other — Constance

While I didn’t technically ask a question, I was querying Tim, as to how he thought the one grounded in the other. The quote merely relates to Tim’s assertion, as a preliminary reference.

While I didn’t technically ask a question, I was querying Tim, as to how he thought the one grounded in the other. The quote merely relates to Tim’s assertion, as a preliminary reference. — Mww

Yes, I see. But you did "ask" an implicit question of Time Wood, with "I shall await your exposition as to how the one might be grounded in the other," which is, "How can the one be grounded in the other?" Sounds more like a clear, if impilcit, question.