Critique of Pure Reason: Introduction B
For Kant, the first question Reason must ask itself is "Is Metaphysics Possible?"
And for Kant, metaphysics consists entirely of "a priori synthetic propositions" (B18)
Hence the fundamental problem of Pure Reason is "How are a priori synthetic judgments possible?"
Our task: What are a priori synthetic judgments?
Kant "introduces" us to the Critique by describing the nature of a priori synthetic judgments
We could say, in the broadest sense terms, that a judgment is "a priori" "synthetic", when it is a judgment that has its seat in Pure Reason (i.e. it is "in" us, and yet it somehow manages to apply to "objects" outside of us).
It is a truth which applies to objects without our having to have any experience of those "objects" (i.e. without our having received anything.)
An example of this would be the proposition or judgment: "God exists."
It is posited as a truth (a Metaphysical truth) and yet it is not something we have any experience of...i.e. The judgment applies to an object (God)without having had any experience of that object (God). It is a proposition or a judgment that is a priori synthetic. (It has its seat in Pure Reason and yet it applies to an object outside of us viz. God.)
Now to anticipate: Kant is going to say that there are such things as a priori synthetic judgments , but that they do not apply to the areas of metaphysica specialis -- rather they apply to the objects of experience (and how they apply to the objects of experience is the first task)...
But what, more precisely, is meant by an a priori synthetic judgment?
What is meant by "a priori"?
What is meant by "synthetic"?
The introduction is concerned precisely with a defining of these terms and a setting of the general problem.
Part I (B1-3) "distinction Between Pure and Empirical Knowledge"
This section defines two kinds of knowledge
(1) Pure Knowledge or knowledge that is a priori
(2) Empirical Knowledge or knowledge that is a posteriori
Re: #1 Definition. A priori knowledge = knowledge that is independent of all experience.
e.g. principle of identity, a=a
Re: #2 Definition. A posteriori knowledge = knowledge that has its source in experience.
e.g. some cats are black.
Part II (B3-6) "We do Possess Certain Modes of A Priori Knowledge."
Kant here gives us the criteria for a priori knowledge and asserts, through several examples, that we do indeed have a priori knowledge.
(1) Criteria (B3-4)
(a) Necessity (notwendigkeit)
(b) Universality (Algemeinheit)
It is to be noted that the marks of strict necessity and strict universality cannot be derived from experience (Kant has Hume in mind here B5) - They must have the source in pure reason.
(2) Examples of this pure knowledge in a priori judgments:
(a) the propositions of mathematics
(b) the proposition "every alteration must have a cause" [here the very concept of cause contains the concept of the necessity of connection with effect and strict universality of the rule (B5)]
Examples of the a priori in concepts (B5-6)
The necessity of the universality of these concepts shows us that they must have their seat in our faculty of knowledge (pure reason)
The preliminary conclusions is that there do exist modes of knowledge that have their origins in us. [This is in reference to B1: "It may well be that our empirical knowledge is made up of (1) what we receive through the senses and (2) what our own faculty of knowledge supplies from itself.]
Part III "There is the Need to Determine the Possibility, the Principles and the Extent of All A Priori Knowledge" (B6-10)
Granting that there are modes of knowledge that have their origins in us, independently of the sense experience - (i.e. there are modes of knowledge that have their seat in Pure Reason.) -
We must determine the principles and the extent of this a priori knowledge - for there is a science (i.e. Metaphysica Specialis) that claims that we can use this knowledge to go beyond the limits of all possible experience.
Metaphysics believes it can arrive at an a priori knowledge of God, freedom, and immortality (B7). And one of the tasks of the Critique of Pure Reason will be to see if this kind of knowledge is possible
But before we investigate the possibility of this a priori knowledge a distinction in the "kinds of knowledge" must be drawn -
Part IV "Distinction Between Analytic and Synthetic Judgments" (B10-14)
Re: Judgments in which the relation of subject (a) to the predicate (b) is thought.
(1) Definition. Analytical Judgment = the predicate (b) belongs to the subject (a) as something which is conceptually contained in the subject (a)
E.g. "All bodies are extended" (the predicate "extension" conceptually belongs to the notion of "body"). Thus in an analytic judgment, the predicate adds nothing to the concept of the subject - it merely provides a conceptual analysis (Kant calls this function explicative)
(2) Definition. Synthetic Judgment = the predicate (b) lies outside the concept i.e., the subject (a).
E.g. "Some bodies are heavy." (The predicate "heaviness" is not conceptually contained in "body", but must be empirically gathered e.g. this body is heavy, that body, is heavy, etc.) [Kant says these judgments are ampliative.]
Kant then joins the previous distinctions (A priori/ a posteriori) to the current distinctions (synthetic/analytic).
Analytic judgments [where the predicate (b) is contained in the subject (a)] are a priori (necessary and universal)
Synthetic judgments are a posteriori.
At B13 he then introduces the notion of the a priori synthetic.
There exist certain judgments (viz. a priori synthetic) which contain a peculiar mode of knowledge.
In these judgments there are the marks of necessity and universality (i.e., the marks of the a priori) - which means that the source of the judgments is to be located in the mind (i.e. Pure Reason) -- And yet, these judgments apply to the objects of experience (i.e. things outside the mind).
This mode of knowledge, while having its source in the mind, pertains to objects outside the mind. [This is to say, in these instances, Subjectivity is structurally related to Objectivity.]
Kants example: "Everything which happens has a cause" (B13) [Kant analyzes this in the Transcendental Deduction under the Second Analogy.]
Summary of the different kinds of knowledge (Parts II and IV)
Analytic A priori
Synthetic A priori
Analytic A posteriori (X)
Synthetic A posteriori
We conclude the following:
(1) Since all a posteriori judgments are synthetic, an analytic a posteriori judgment is not a real possibility.
(2) Analytic a priori judgments are purely formal.
(3) Synthetic a posteriori judgments are empirical and rest upon sense experience.
(4) Synthetic a priori judgments are characterized by (a) an a priori element which is universal and necessary as well as (b) an empirical element which applies to the world. Thus there is in the "synthetic a priori" that which is not derived from experience, but yet applies to experience.
Part V (B14-18) "Synthetic A Priori Judgments are Contained in the Sciences."
There are synthetic a priori judgments (we are in possession of a priori synthetic (i.e. knowledge (see source notes))
(1) We have these in mathematics (e.g. 7+5=12)
(2) We have these in Physics: the concept of Substance (B17), the concept of cause: "Everything which happens has its cause." (B13)
(3) We ought to have these in Metaphysics: "The world must have a first beginning (God)." (B18)
Metaphysics ought to contain nothing but a priori synthetic judgments - Thus the general problem of Metaphysics becomes the general problem of a priori synthetic judgments.
Part VI "The General Problem" (B19-24)
A priori - (1) a mode of knowledge that has its origin in the Mind (Pure Reason)
(2) It exhibits the marks of strict necessity and universality.
Synthetic - (1) it extends our knowledge
(2) it applies to the objects outside the mind.
judgment - A kind of synthesis, A tying of things together
[E.g. I judge that, "the table is brown." (tying together table and brown) or "7+5=12" or "God exists"]
The question, granting that there are a priori synthetic judgments, becomes: "How are a priori synthetic prepositions possible?"
This becomes the general problem of a critique of pure reason -
I.e., How is it possible for us to tie things together in such a way that one element of that tying together has its origin in us while another element at the same time applies to objects outside of us?
(Kants real task is to investigate that element that originates in us. viz, the a priori elements of human knowledge.)
What concerns us here is no longer the "objects of our knowledge", but rather our mode of knowing objects. I.e., we are not concerned with the object, but rather with how we know the object i.e., our mode of knowing the object.
This is a completely different approach than any other heretofore attempted, and it gives us the idea of a critique of pure reason.
Part VII "The Idea of a Critique of Pure Reason" (B24-30)
"Reason (Vernunft )is the faculty that supplies the principles of a priori knowledge" (it is the seat for all the universality and necessity that is found in our a priori synthetic judgments)
A "Critique" of this pure reason would be an examination of its sources and its limits.
In searching out the source and nature of this a priori knowledge, we will be concerned, not with the objects of knowledge, but with our mode of knowing objects.
Kant entitles such a search transcendental.
Thus the "idea" of a Critique of Pure Reason entails the idea of a transcendental critique. (B26, 28). It will seek out the conditions which underlie, and make possible our (a priori) knowledge of objects. It will seek out the principles of Pure Reason i.e. those principles which go to make up the conditions for the possibility of a priori synthetic judgments.
This is how the Critique will answer its general problem viz. "How are a priori synthetic judgments still possible?" (which is at the same time the problem of whether metaphysics is possible.)
It will answer this problem by uncovering the conditions for the possibility of knowledge (of objects), which is at bottom an investigation into the conditions for the possibility of experience.
Kant will find these conditions in certain principles found in the faculty of Pure Reason i.e., Kant will find these conditions for the possibility of experience (and eo ipso knowledge) in certain very formal structures that the mind imposes upon the world.
The Introduction has therefore established that the Critique or Pure Reason is to be a transcendental critique of human knowing.
Robert Cavalier, Carnegie Mellon Univeristy