Dr. Bob Zunjic
Prolegomena To Any Future Metaphysics
VII FEATURES OF METAPHYSICS
|In the Preamble Kant undertakes a methodological
examination of the new science by comparing it with other sciences.
"If it becomes desirable to organize any knowledge as science,
it will be necessary first to determine accurately those particular
features which no other science has in common with it, constituting
its peculiarity." Every science (discipline) could be considered
in three regards:
(a) difference of the object of
(b) difference of the source of
(c) difference of the kind of knowledge
(type of judgments).
These three aspects produce distinctive characteristics ("peculiar
features") sufficient to delineate the scope and define the nature
of any particular science. If we do not apply these criteria of demarcation
"the boundaries of all science become confused." Of course,
we do not always need all three of them to establish the "peculiarity"
of the respective science, but ideally they should be applied conjointly.
Application on Metaphysics:
Kant does not
explicitly discuss the first difference (the one
of the subject-matter = object), probably because at this stage he still does not
want to discriminate between
General Metaphysics in the traditional sense and Critical Metaphysics
in the sense of his renovation project. The former, divided into
Ontology, Rational Cosmology, Psychology and Theology, deals with
transcendent objects, which Kant has never entirely renounced but
now regards as a heavy baggage, while the latter investigates the
boundaries of knowledge from principles and represents the knowledge
Kant is presently seeking. The point is that in this latter sense, Metaphysics
does not have any special subject-matter apart from abstract concepts.
Therefore Kant starts his demarcation with the second regard: the
sources of metaphysical knowledge. "Its very concept implies
that they cannot be empirical." Its notions
"must never be derived from experience". In other words,
metaphysical knowledge is not "physical",
regardless whether the physical refers to the external reality (natural science)
or internal reality (empirical psychology). As the very name "Metaphysics"
suggests, its knowledge is "meta-physical" (after/above the physical), that is to say it is non-empirical. Kant explicates
the meaning of the word "metaphysical" as a unique determination,
but at a closer scrutiny what he
says comes down to two different ideas that reveal the above ambiguity:
"the knowledge lying beyond experience", that is to say,
its principles and concepts surpass experience both by their source
and by their scope.
||Metaphysics is the realm of "a
priori knowledge coming form pure reason", to wit, its principles
and concepts precede experience logically if not temporally.
The first connotation is not identical
with the second. Both metaphysics are non-empirical,
but they entail two very different positions with regard to experience.
The first speaks about the knowledge "lying beyond experience"
whereas the second indicates that metaphysical knowledge is to be
understood as an a priori knowledge "underlying experience".
It is not the same to acquire knowledge
"after experience" (hereafter, afterlife) and to gain
knowledge about the forms coming "before experience" (forms
of intuitions and categories).
Although Kant does not denounce this ambiguity here (he speaks rather
as if there is a continuum between the traditional, popular and
scientific connotations) it is clear that his formulations point
to two different and perhaps
opposed ideas of Metaphysics.
Transcendent vs. Transcendental:
|Metaphysics in the traditional sense
has failed to become a science precisely because of its striving to
provide an overarching transcendent knowledge surpassing the objects
of possible experience. Kant, however,
believes that Metaphysics
can become a respected science by focusing not on the objects "lying
beyond experience" (transcendent) but on the conditions
"underlying" our knowledge of possible objects, that is
to say by becoming fundamental (transcendental).
Thus he is with Aristotle in looking for non-empirical principles
as the ultimate objective of First Philosophy, but he is with Descartes
in looking for the principles of knowledge rather than for the transcendent
principles of reality. However, neither Aristotelian natural theology
nor Cartesian empirical psychology show the right way of recovery
from the longstanding metaphysical illnesses. Kant takes a distance
toward both and conceives Metaphysics as transcendental Theory of
Both the traditional and the Kantian Metaphysics are non-empirical,
but only the first goes beyond possible experience. The gulf between
these two gets only strengthened by equating the popular notion
of Metaphysics with the realm of the supernatural. In
contrast, Kant's metaphysics is laid on the firm ground of legislative principles.
The internal tension between the two senses of "non-empirical"
('after' and 'before experience', 'lying beyond' and 'underlying', transcendent
and transcendental) leads to the following division within the concept
In the first part of his discussion about the "sources
of Metaphysics" Kant still preserves the continuity with the
traditional (transcendent) nature of metaphysical knowledge. Later
on he even recognizes that transcendent metaphysical objects represent
"the noblest" objects of human concerns ("the
knowledge of a highest being and of a future existence" corresponds
to the two main objectives of Cartesian Metaphysics: "the existence of God and the immortality
of the soul"). But in the second part of the same paragraph
Kant obviously refers only to the transcendental concept of Metaphysics,
which is evident from the way how he delineates Metaphysics from
two other theoretical sciences: Physics and Mathematics (demarcation
between these three disciplines is an old Aristotelian problem).
By comparatively applying all three Kantian criteria of knowledge
one gets the following diagram:
A priori in abstracto
A priori in concreto
We should be able now to understandable why Kant could not have
drawn a clear cut demarcation line between Metaphysics and other
theoretical sciences by simply defining their specific objects.
Since Mathematics is also a non-empirical science and since its
subject-matter is also abstract and a priori (concepts of
reason), a further differentiation between it and metaphysical concepts
is needed to distinguish between the two. This differentiation is
carried out in the Critique of Pure Reason to which Kant
here refers. The distinction addresses the nature of metaphysical
concepts as opposed to mathematical.
In a nutshell, metaphysical concepts are universal concepts in
abstracto, whereas mathematical concepts require intuition which
considers them in concreto. Metaphysics has to expose its
concepts as adequate to the objects, whereas mathematical
concepts are exempt from that obligation because they stem "from
the construction of concepts". This means that Metaphysics
must conform to the rules of concept synthesis if it is ever to
attain the truth (its knowledge being gained not from axioms but
from concepts by means of reason). Conversely, Mathematics strives
only for validity of theorems derived from whatever axioms
we may choose (mathematical definitions can never be faulty or wrong).
Since the validity of Mathematics does not depend on the veracity
of its axioms, its superb exactness goes hand in hand with
the utmost arbitrariness (at the beginning). By contrast, in philosophy definitions come only at the end, after we ascertain the true nature of the object, not at the beginning
of the process.
from the Latin transcendere
= climb across, go beyond; something superior
or surpassing (for instance, God), something that goes beyond that
what is given to our experience
(metaphysical knowledge in the traditional sense). According
to Kant, however, there can be no knowledge of anything transcendent.
Search for it is a "transcendental illusion".
Latin transcendere = climb across, go beyond;
originally, that which surpasses
the most general categories (transcendentalia); according
to Kant, that which precedes experience and determines its content
beforehand (a priori); also the a priori analysis
of pure reason which elucidates the conditions of possibility of
any experience; the transcendental investigative procedure is "occupied
not so much with objects as with the mode of our knowledge of objects
in so far as this mode of knowledge is to be possible a priori".
Waldo Emerson's "Transcendentalism"
and the so called "Transcendental Meditation" of Macharishi
Macheshi do not have anything in common with the transcendental
in this sense apart from the sheer homonymy (the similarity of sound);
their real connotation is rather "transcendent"; indeed
in non-terminological parlance these two words are very often used
interchangeably - a remnant of the medieval equation between transcendentalia
VIII THE UNOBSERVED
|Kind of Knowledge:
both the object and the faculty of metaphysical knowledge Kant moves
on to the question what "kind of knowledge…can alone be called
metaphysical" (§ 2 of the Preamble). His answer is that Metaphysics
must consist of "a priori judgments".
The word "judgment" does not have here the popular meaning
of an evaluative statement. Kant uses it in the manner of the traditional
theory of logic according to which judging relates a predicate term
to a subject term within an assertion. The underlying thought of
every proposition is "I judge that S is P". So conceived,
every judgment is a function of unity of our representations expressed
in different conjunctions of the subject and the predicate
term (general form: 'S is P'). From this point of view all judgments
are synthetical in the sense of connecting a subject with a predicate
by means of a copula ('is' or 'is not'). However, with regard to
"their content" ("relations of ideas" or empirical
connections) and the ground of their veracity (a concept of a
subject or an empirical object) the status of various judgments
could be very different and this difference is what Kant now addresses.
Explicative vs. Expansive:
If the predicate
only explicates the subject "adding nothing to the content"
of the proposition the resulting judgment is explicative or
analytic. If, on the other hand, it adds something to the
subject (expands on it) the judgment is expansive or synthetic
(in the specific sense of putting together different representations).
In the first case, the constitutive terms of the judgment (S and
P) fully coincide ("stand in the relation of logical identity"),
which secures upfront the analytic status of the judgment,
whereas, in the second, the connection between the terms remains
synthetic and the veracity of the judgment cannot be determined
logically, but needs to be tested empirically.
||This Kantian division
between analytic (explicative) and synthetic (expansive)
judgments squares well with the traditional division between a
priori and necessary truths of reason, on the one hand, and a
posteriori contingent truths of fact, on the other (Leibniz).
Stating pretty much the same, Hume spoke about the "relations
of ideas" as opposed to the "matters of fact". The
former are true although repetitive and tautological, the latter can
be only contingent and uncertain.
Truths of reason
Truths of fact
Relations of ideas
Matters of fact
Although these distinctions largely coincide with each other their
respective principles are not identical. The a priori - a posteriori
division is centered around the epistemic source of our propositions,
while the analytic - synthetic distinction points to the
semantic reference of respective propositions. The designations
necessary or contingent are supposed to reveal the
logical status of propositions under scrutiny.
Note 2: All
these distinctions have been challenged by W.V. O. Quine who has shown
that the so called necessary truths (= a priori, analytic)
presuppose the equality of meaning among synonyms no matter whether
their basis is logical, conventional or practical. This presupposition
is so problematic that it negates the special status of analytic
vis-a-vis a posteriori propositions and renders redundant
the very distinction. The distinction between a priori and
a posteriori rests on an ambiguous notion of meaning - it
is just a convention without real ground. According to Quine, there
are no distinct types of reality in the world that would require
different types of judgments.
Analytic judgments with empirical
Kant agrees with
his predecessors that analytic judgments are a priori ("are
in their nature a priori cognitions"). They objectively
precede and ground our knowledge even when they come later in the
temporal acquisition of knowledge. But they perform that role simply
by making more "distinctly"
or fully "conscious" what has been "already
actually thought in the concept of the subject". Thus, strictly
speaking, they are only clarifying judgments. The predicate does
not enlarge the scope of our knowledge of the concept, but only
analyzes it (this is the reason why Kant aptly chooses the
label "analytic" as their designation). For instance,
the analytic judgment "All bodies are extended" does not
amplify the concept of body. It only states what is already included
in it: "extension was
really thought to belong to (the) concept of body before the judgment
was made, though it was not expressed". In other words, the
analytic judgment takes the object (= body) according to its concept
(the subject) and does nothing else but asserts its self-sameness.
This is the reason, on the other hand, why an analytic judgment
must be necessarily and
a priori true, true by virtue of the formal identity
between the subject and the
Kant claims that the connection of the subject and the predicate
could be analytical even when both concepts are empirical provided
that it is a priori, but his example "Gold is a yellow
metal" can hardly convince anybody. In § 3 he refers to Locke's
Essay Concerning Human Understanding (Bk., 4, Ch. III, §
9) as an anticipation and corroboration of his view, but in the
very same paragraph Locke explicitly treats the gold-predications
like having certain weight, being yellow, being malleable and fusible
as non-analytic. By all standards, Kant's example should be regarded
rather as a synthetic proposition based on experience. The assertion
of gold's yellowness is not any different from the statement "gold
melts at 1,064.4C°". Moreover, it could be false - when beaten
into thin foils gold appears green. Kant must have known this but
he obviously did not envision gold as an element in the sense of
the periodic table of elements. He spoke about gold only as "a
yellow metal" in the sense of ordinary language, which usage,
once accepted as the common concept, by definition entails yellowness
as an essential characteristics of gold.
The Law of (Non) Contradiction:
Kant's predecessors have applied the law of (non) contradiction
to all judgments indiscriminately simply as the negative criterion
of their viability. He, however, thought that one had to distinguish
between a negative and a positive application of the law. In the
first case we simply establish formal conditions for a judgment
to be viable, in the latter the principle itself secures the validity
of the judgment. Kant contends that "all analytic judgments depend
wholly on the law of contradiction" in the latter sense. Of course, all
judgments should be free of self-contradiction no matter whether
they are true or not, but analytic judgments are true simply by
virtue of being non-contradictory. And the other way round, if there is a real possibility that they contradict themselves in terms of accepting the subject and denying the predicate they cannot be analytic. But if an "affirmative analytical"
judgment is true based on this law, then its predicate "cannot be
denied (of the subject) without contradiction" because the negation
would then violate the self-identity of the concept (the predicated
connotation being part of the concept). To use the same example
as Kant, if we said "All bodies are unextended" we would contradict the
subject concept by claiming basically that "No body is extended".
To avoid it we have only two choices: either to drop the negation
of the predicate (which, by reverting to the complementary class, restitutes the initial judgment: "All bodies
are extended") or to change the subject term into its compliment ("No bodies
are un-extended."). As we glean from the second case, the "opposite
is necessarily denied of the subject in an analytic but negative
judgment". This corroborates the claim that in analytic judgments
both the subject and the predicate are locked up in the relation
of identity whose subsistence is sanctioned by the "law of contradiction".
||Note: Kant obviously uses the term 'contradiction' in a non-technical sense of self-refutation not in the sense of the specific opposition as it is stated in the so called 'square of opposition'. The two judgments "All bodies are extended" and "No body is unextended" are not strictly speaking contradictory but contrary.
|All bodies are extended.
||All bodies are unextended.
|No bodies are unextended.
||No bodies are extended.
1: Kant's definition of analyticity is based
on two criteria, (1) semantical: the predicate of a judgment
is already contained in the concept of the subject, and (2) logical:
the connection of the predicate with the subject is secured negatively
by the principle of contradiction. As far as the latter is concerned,
classical logic does not regard A and E propositions as contradictions
but as contraries. Therefore, "All bodies are extended"
and "No bodies are extended" are not contradictory, because
they can be both false. Second, the proposition "No bodies are
un-extended." is a correct obversion of the A proposition, and
if the original proposition is analytic it must be also analytic.
The moment of contradiction that Kant ascribes to the proposition
"All bodies are not extended" pertains therefore only to
the relation between the subject and the predicate term; Kant obviously
meant that the subject-term "body" was in a semantic contradiction
with the predicate "un-extended".
Note 2: W.V.O.
Quine suspects that this linkage between analyticity and non-contradictoriness
is not explanatory at all because the notion of self-contradictoriness
"is just another unclarified aspect of analyticity". Thus
the burden of proof falls again on the latter. However the above definition
of analyticity has two shortcomings: (a) it is bound to the statements
of S-P form, and (b) the notion of containment is left unclarified.
Quine objects that Kant failed to explain what does it mean for a
subject to "contain" a predicate. In order to avoid these
defects Quine restates Kant's definition in the following way: "a
statement is analytic when it is true by virtue of meanings and independently
of facts". Even if we grant that this rendering is correct (which
is problematic) the burden simply shifts to the notion of meaning
(synonymy) which, according to Quine himself, remains vague.
Synthetic judgments are products of the synthetical work of our
cognitive faculties insofar as they deal with experience. However,
experience is not a mere bundle of representations, but "a continued
synthesis of perceptions". We know something only if we can represent
it in its connections with other representations. These connections
are not self-evident and therefore require stepping out of the subject
concept toward the "testimony of experience" ("passing beyond the
concept of the subject"). The knowledge of facts is in this sense
based on the synthesis of the object in its manifold relations. In other words, we need to
represent the object itself by means of an additional synthesis
which goes beyond the (minimal) concept of the subject. Expansive predication
has the function of establishing this linkage of additional representations:
it supplies the predicates that are not already included in the subject.
Thus "judgments of experience are always synthetic." Unlike analytic
judgments, which are by the rule universal or general (focusing
on the core concept), synthetic judgments are typically particular (speaking
about some instances or some features). Surprisingly, Kant gives
as example a judgment which is universal: "All bodies have weight."
The German original, printed by J.F. Hartknoch in Riga (1783), reads
here "Some bodies are heavy." At first glance, this is in conformity
with the (commonsense?) idea that not all bodies have weight. This
assumption receives experimental corroboration through the fact
that bodies in outer space become weightless. But Kant could not
have known this. It is not an outright implication of the gravity
theory either. Therefore, from the point of view of the eighteenth
century knowledge it is an understatement and does not put into
a sharp contrast the difference with analytic judgments. The statement
"All bodies have weight" offers in that respect a much better
reading. It is formulated as a universal judgment stating something
which is seemingly very difficult to distinguish from the concept
of body. As a matter of fact, this proposition was traditionally regarded as
analytic, but Kant agrees with Hume that it, on the contrary, represents
a piece of synthetic knowledge a posteriori. The point is
that weight is not contained in the concept of body the way extension
is. We need to add it to the idea of body as "something not actually
thought in the universal concept of body". Its negation does not
produce a contradiction, even if it is associated with body "insofar
we can think of". All this suggests syntheticity which Kant explicitly
attests ("must therefore be called synthetic").
Ground of Truth:
||The truth of synthetic propositions is based
on factual conditions. Kant defines syntheticity by means of reversed
criteria for analyticity: (1) Semantically, the predicate of a synthetic
judgment is not contained in the subject but amplifies it, and (2)
there is no strict logical connection with the principle of contradiction.
Kant accepts the view that synthetic judgments are expansive in the
sense that they, the connection of their concepts being true, enlarge
our knowledge of the subject. Because of that informative force they
cannot enjoy the protection of the law of (non) contradiction and
a denial of their predicates does not result in a contradiction. Thus
true synthetic judgments could become false if the facts turn differently.
It goes without saying that they too can be absolutely free from any
inner contradictions but even when this is the case, this fact would not guarantee
that they are true or even meaningful. The basis of the veracity for
synthetic judgments is not in the concept of their subject but in
the object itself as captured in the synthetic subject - object
||Note: Kant asserts that synthetic judgments "cannot possibly spring from the principle of analysis, namely the law of contradiction". The law of contradiction is equated with the principle of analysis because taking apart a judgment demonstrates how its subject and predicate relate in terms of possible contradiction. Since synthetic judgments allow an almost unlimited number of possible combinations between S and P the analysis needs to exclude only those that violate the law of contradiction without determining whic one is right.
Kant disagrees that all synthetic judgments are empirical (although
synthesis is a suitable designation for all judgments of this kind,
it is not tantamount to empirical linkage of a predicate to the
subject). To be sure, synthetic judgments could be derived from
experience tout court ("of empirical origin"), that is to
say, they could be simply a posteriori judgments, as, for
example, the following observations: "This piece of gold is 1 inch
long" or "Kant was a bachelor."
Thus, in contrast to analytic judgments, which are always non-empirical
even when they operate with empirical concepts ("it would be absurd to base an analytic judgment on experience"),
empirical judgments "are always synthetic" although not all synthetic judgments are empirical.
Kant believes that there exists yet another class or sub-class of synthetic judgments which are "certain a priori and which spring from pure understanding and reason".
(a) a posteriori, or (b) a priori.
This means that synthetic judgments could be either
The very idea of a priori synthetic judgments appears as
something self-contradictory, particularly if we equate syntheticity
with the notion of a posteriori (like A. Ayer). But this
identification would be, for Kant, entirely unwarranted. If I affirm
a predicate B as necessarily and universally (though not logically)
linked to the subject A, then B is an a priori synthetic
representation of A, regardless whether the concept of A is a
priori or not. A priori synthesis attributes a necessary
property to the subject which is not contained in it.
Note: The logical table
of judgments provides an exhaustive list of all possible judgments
divided into four logical types along with a parallel table of the
concepts of pure understanding "which contain the a priori
conditions of all synthetic and necessary judgments" (§ 23).
|P states S
||P adds to S
||P adds to S
|Causal a priori
||If I say "all effects are caused" I would make an analytic judgment because "uncaused effects" are a logical absurdity. But if I say "all events are caused" I pronounce a genuine synthetic a priori judgment which applies to experience but is not empirical itself. An empirical judgment would be "The event X was caused by Y."
|Every effect is caused
||Analytic a priori
|All events are caused
||Synthetic a priori
|This event is caused by X.
||Synthetic a posteriori
Since they are synthetic synthetic a priori judgments do not "spring from the law
of contradiction". They "must depend upon other principles than
the law of contradiction", which they also, of course, must respect.
But they cannot be deduced from it alone. The law of contradiction
is not the principle of Metaphysics but of pure Logic. The knowledge
of facts, however, is based on the principle of causation rather
than on Logic. As Kant demonstrates in the central part of the Prolegomena,
the general law of all synthetic a priori judgments stems
from the insight that the conditions of the possibility of experience
are the conditions of the possibility of the objects of experience.
Synthetic a priori principles cannot be, therefore, derived
from mere thinking (Logic). But they cannot be deduced from sheer
intuitions (Experience) either. The concept of cause or the principle
of sufficient reason cannot be represented intuitively - precisely
because they are the principles of objects, or better to say, of
the objectivity of objects. They "must express what experience
in general… contains" and they do that by adding some necessary
components "to the sensuous intuition and its logical connection
in a judgment". These conceptual components define the a priori
rules for possible generation of synthetic a priori judgments.
Synthetic judgments a priori are amplifying in the sense
of giving more than mere explication, but necessary in giving more
certainty than regular experiential judgments.
Richard Rorty surmises that the whole "story about synthesis" in terms of our active subjectivity was
invented to explain the possibility of synthetic a priori
judgments. The two doctrines are indeed mutually intertwined, but
the general idea that our cognitive faculties operate synthetically
was for Kant more fundamental even if it was not developed prior
to the discovery of synthetic a priori judgments.
from the Latin jus = law; 1. popular meaning: evaluating
something; 2. in traditional (Aristotelian) logic, asserting or
denying a predicate of some subject; 3. for Kant, who follows this
old usage, any judgment is a relationship of concepts, the subject
and the predicate, within a proposition. This explains why he freely
alternates the term "judgment" with the term "proposition". However,
his theory of judgments includes also a grasp of the object as well
as of the "I" ("the objective unity of apperception") and this moment
moves him away from a purely logical conception of judgments.
Subject, from the
Latin subjectum (i.e., Greek hypokeimenon) =
something underlying, under-carriage, substrate; 1. medieval philosophy,
grammar, logic: the bearer of a property or an attribution (i.e.,
of a predicate), the subject-term, substance; 2. modern philosophy:
the self, the mind, the "I", the consciousness; ordinary language:
(a) object, topic, (b) the subordinate (person). In logic the subject-term
is a singular term which names an entity.
Predicate, from the
Latin praedicatus = proclaimed; something asserted about
something else, that which is affirmed or denied about a subject.
The predicate-term is a general term which is true (or not) of an
Analytic Judgments, from
the Greek analytikos = pertaining to taking apart; the propositions
(judgments) which are necessarily true due to the relation between
their concepts (logically true: "A = A") or true by virtue
of the meanings involved (true by definition): "All bachelors are
unmarried" or "a bicycle has two wheels".
from the Greek synthetikos = put together; the judgments
in which what is asserted by the predicate has not been thought
in the subject; for instance, "all bachelors are happy" or "this
bicycle has an elongated seat". Synthetic judgments are not logically
true nor true by definition.
Principle of (Non) Contradiction,
one of the laws of the traditional Aristotelian logic which
says that an affirmative proposition and its negation cannot be
both true at the same time in the same respect. For instance, "X
is white" and "X is not white" cannot be both true at the same time
(or false). Kant omits the phrase "at the same time" in his phrasing
of the law, because he wants to avoid all temporal (empirical) references
in the formulation of general principles. This principle is for
him a universal although negative condition of admissibility of
all our judgments but specifically the test of veracity for analytical
judgments (if not contradictory they are true).
Principle of Sufficient Reason,
the principle of universal causation ("nothing happens without
a cause"); was introduced by Leibniz as the fourth law of logic
and the governing principle of the truths of fact.
IX THE CASE OF MATHEMATICS
Kant is convinced that precisely the judgments which express a
priori cognitions of synthetical kind make up the body of Metaphysics,
Mathematics and pure (theoretical) Physics. In order to demonstrate
more cogently their existence he first undertakes a careful analysis
of mathematical propositions. The greatest novelty (and at the same
time the most controversial point) of Kantian analysis is the contention
that mathematical propositions are not analytic (as has been always
thought) but synthetic, although synthetic a priori: "mathematical judgments
are all synthetic". Kant acknowledges that this thesis goes directly
against all accepted notions, but he claims that "it is incontestably
certain and most important in its consequences". Unfortunately,
it has been overlooked.
"This fact seems hitherto to have altogether escaped the observation
of those who have analyzed human reason." This oversight was caused
by an incorrect understanding of the role the law of contradiction
plays in Mathematics. Mathematical conclusions all proceed in accord
with the law of contradiction, "as is demanded by apodictic (mathematical)
certainty", but they are not known or derived solely from it. Mathematical
propositions can be established by the law of contradiction indeed,
but never by that law alone. They also need some intuition and synthesis
in time. Of course, they are not derived from experience either.
"All strictly mathematical judgments are a priori, and not
empirical, because they carry with them necessity, which cannot
be obtained from experience." But they are not analytic, for mathematics
would not be able to furnish additional knowledge if its statements
were just a matter of definition or stipulation.
Note: The prevalent
view in the philosophy of mathematics has been and still is that
mathematical knowledge is a priori. Both formalism and conventionalism
seem to agree on this. Only some empiricists contend that mathematical
truths are very general empirical propositions. But a growing number
of philosophers in the aftermath of Goedel's and Quine's insights
challenge the mainstream view thus providing new support for Kant's
theory. Leonard Nelson and Irving Copi assert syntheticity for geometry
and arithmetic respectively.
of Mathematical Judgments:
"The essential and distinguishing feature of pure mathematical
knowledge among all other a priori knowledge is that it cannot
at all proceed from concepts, but only by means of the construction
of concepts." To construct a concept means to represent it in an
intuition a priori. As mathematical necessity is not
purely logical but constructivist, mathematical propositions cannot
be generated only "by dissection of the concept". "Pure mathematics,
and especially pure geometry, can have objective reality only on
condition that they refer merely to objects of sense." This way
of proceeding requires synthetical judgments which go beyond concepts
toward that which is represented in intuition. According to Kant,
this comes down to judgments of the third type, namely to wit, synthetic
a priori judgments. He shows that this holds true both of Arithmetic
and Geometry at least as far as they are branches of pure Mathematics.
Note: Great mathematicians
like Frege and Hilbert admit that at least geometry is founded on
intuition but they stop short of accepting syntheticity as the right
designation for mathematics in general.
Previous analyses of arithmetical propositions were mislead by
the simplicity of their examples (typically, Descartes and Hume
were considering very simple operations like "2 + 2 equal 4" or
"2 + 3 = 5" which create the impression that the result is analytically
deduced from the concepts of additives). To avoid the same delusion
of analyticity these thinkers fell prey to, Kant purposely takes
much less obvious propositions. His formula of choice is: "7 + 5
= 12". He contends that one misunderstands this proposition if it
is viewed as an analytical statement supported by the law of contradiction.
He is aware that people reason like this: to say that the sum of
7 + 5 is anything other than 12 would be contradictory, therefore
this is an analytic proposition. But he insists that the concept
of the sum of 7 and 5 contains "merely their union in a single number",
not the particular number 12. An analytical version of the said
equation would be "7 + 5 = the sum of 7 and 5". But this is not
what the mathematical proposition "7 + 5 = 12" states. It says that
"the sum of 7 and 5" equals the particular number 12. To replace
"the sum of 7 and 5" with the number 12, which is not "thought by
merely thinking of the combination of seven and five", we "must
go beyond these concepts, by calling to aid some intuition", for
instance 5 fingers or five points and to add them "successively".
In other words, we need to get engaged in counting which clearly
indicates that the judgment "7 + 5 = 12" truly amplifies our knowledge
of the subject concept "7 and 5". Since we cannot figure out the
sum of 7 and 5 without resorting to these calculative aids, the
conclusion is inevitable that "arithmetical judgments" are in fact
"synthetic". The synthetic character of arithmetical propositions
becomes even more manifest when we perform mathematical operations
with bigger numbers and magnitudes.
Note: The most questionable
point in Kant's argument is the contention that "the sum of 7 and
5" does not "in any way" already include 12. What about the sum
of "twenty and five"? Can one say that "twenty and five" does not
include "twenty five"? Kant could point out that "twenty and five"
is only a formulation of a task, whereas "twenty five" is the solution
(Max Apel), but the relationship seems to be clearly analytic. However,
the same cannot be asserted for all equations. Kant is certainly
right in claiming that the sum of "twenty and five" does not include
"five times five" analytically. To be sure, the propositions of
arithmetic are rather satisfiable than necessarily valid - some
could be denied without entailing any contradiction.
Kant attests the same a priori syntheticity for geometrical
propositions. This time his example is: "Straight line is the shortest
path between two points." He claims that the concept of straight
line establishes only the quality of the line (being straight
as opposed to being curved or zigzag), not its quantity (distance).
Straight line is the line produced by moving a point into one and
the same direction. The concept of direction contains a priori
the notion of the straight, but not the longitude. Therefore, the
aforementioned proposition is synthetic, though a priori.
The concept of the "shortest" is entirely "additional" and cannot
be "obtained by any analysis of the concept 'straight line'". To
be able to reach the conclusion that the straight line is the "shortest
path" we must resort to intuition (indirect way) and use it as a
representational aid in the matter.
Kant admits that upon reflection one must closely link the "shortest
distance" with the concept of the "straight line", but his point
is that distance was not actually thought in the concept itself.
The reason for fusing these two things into one and for the ensuing
transformation of syntheticity into supposed analyticity is the
ambiguity of the phrase "straight line" (Kant speaks about "the
duplicity of the expression"). It could denote the nature of a line
as well as shortest distance between two points.
Note: By the same token Kant would regard the following statement as
synthetical a priori: Circle is a plane curved figure that encloses
bigger space than any other with the same perimeter.
Note 1: In the original
text the paragraph with this explanatory remark is obviously misplaced
during the printing of the manuscript. It does not make sense immediately
after the passage discussing downright analytic propositions. The original edition apparently suffers from some mix-up that has gone unnoticed either in the manuscript or in the galley proofs.
Note 2: We can grant that 'A straight line
is the shortest distance between two points' is a synthetic proposition
unless we phrase it as a proposition of a Euclidean geometry - there
it is true by implication. As to the assertion of syntheticity for
geometrical propositions in general, one should bear in mind common
intuitive aspects of geometrical demonstrations. At the time of
Kant it was customary to establish theorems by means of the construction
of figures and this fact could have convinced Kant that he was correct
in claiming that geometrical propositions are a priori though
synthetic. Furthemore, Kant did not know for the possibility of
non-Euclidean Geometry. On the contrary, he was convinced that Euclidean
Geometry was the only possible Geometry, and consequently the true
Geometry of space. Obviously, if Kant thought that the only possible
geometry was Euclidean (three dimensional) he was wrong and this
mistake is often adduced against him. But he was right in implying
that the space of human experience is Euclidean. Our intuition of
space conforms to the space of Eucliedan geometry. In fact, the
very possibility of non-Euclidean geometries could be interpreted
as an indication that geometry is not analytic.
Analyticity in Mathematics:
| The axioms of geometry are not analytic
in the sense of logical truths, meaning they are not necessarily valid
for all systems. But it does not follow that they are synthetic unless
we define syntheticity simply as not being analytic. Kant does not
deny that at least in geometry we also make use of analytic propositions
in the proper sense. These propositions are, of course, directly dependent
on the law of contradiction. He cites the following examples: "a =
a", "the whole is equal to itself" and "a + b > b". But these are
sheer tautologies ("identical propositions") which serve only as a
means of concatenation to formulate true geometrical judgments. Moreover
Kant even contends that these analytic propositions ("valid from concepts")
are accepted by geometers only because they can be intuitively represented.
Note: Definitory propositions like "triangle
is a plane figure with three sides" are analytic in this sense.
The same holds true of geometrical demonstrations which are based
on intuitive axioms. The problem, however, is that this type of
proof is not entirely adequate because it grounds mathematical demonstration
on spatial perceptions. Anyway, the fact is that a proposition is
analytic with regard or within one language. The problem is how
to make it analytic for all languages. This was Kant's dream, but
Quine has shown that to gauge analyticity or syntheticity of isolated
propositions without placing them in a particular system or language
must be always misleading.
||Strictly speaking, Hume has allowed
only analytic (a priori) and synthetic (empirical) judgments.
He has ascribed the former to Mathematics ("abstract reasoning concerning
quantity or number") and the latter to the descriptive sciences ("experimental
reasoning concerning matter of fact and existence"). But Kant discovers
more in Hume than Hume was himself aware: "Although he did not divide
judgments in this manner formally and universally as I have done here,
what he said was equivalent to this: that mathematics contains only
analytic, but metaphysics synthetic, a priori propositions."
Kant thus ascribes to Hume an implicit discovery of synthetic a
priori judgments within Metaphysics. Why does he then complain
that Hume has overlooked this third kind of judgments? The answer
is simple: Because he suspects that Hume did not seriously believe
in any combination between the synthetic and the a priori (hence
that what he might have imputed to Metaphysics was tantamount to its
dismissal), and second, because Hume has excluded Mathematics from
that same type of judgments.
||Hume has recognized the
importance of the realm of a priori cognitions but he
"heedlessly severed from it a whole… province of mathematics". How?
By proclaiming it entirely analytic whereas it is only partly analytic.
By overlooking "pure synthetical cognitions a priori"
in Mathematics Hume has in fact reduced the realm of admissible a
priori knowledge to mere "identical propositions". Furthermore,
the neglect of the synthetic a priori character of Mathematics
proved to be very "disadvantageous" for Metaphysics. Though "unique
in its kind", Metaphysics cannot be "wholly isolated" from other sciences
(in this respect we need to correct one previous statement of Kant
which overstresses the separateness of Metaphysics). Hume's conclusion
that Mathematics is analytical was simply unfounded. Kant supposes
that Hume succumbed to the delusion of analyticity in Mathematics
because he thought that mathematical propositions were more intimately
related to the law of contradiction.
So Hume opened up a deep gap between the logical statements of Mathematics
and the "arbitrary" statements pertaining to synthetic knowledge.
To fully justify his conclusions about contingent character of synthetic
cognitions, Hume should have included "the possibility of mathematics
a priori" into his questioning of our synthetic judgments.
He has not done that. This failure "had a decidedly injurious effect
upon his whole conception" for he discarded the most valuable part
of knowledge, although not in the sense of analyticity. The injury
was self-inflicted although not less painful.
Note: Kant's description
of Hume's position ("equivalent to this: that mathematics contains
only analytic, but metaphysics synthetic propositions") is problematic
because (a) Hume did not use this terminology at all, and (b) some
of his formulations indicate that he has not regarded all mathematical
statements as purely analytical. Of course, this does not mean that
he would have accepted the Kantian view that they are synthetic a
priori - the view which many dismiss as the grandiose misunderstanding
of the nature of Mathematics (B. Russell). Hume would have been probably
more receptive to the idea that metaphysical propositions are special
(neither just analytical nor just synthetical), but he would have
denied any real value to that "mixed" category. Synthetical
propositions were him unambigously empirical (a posteriori).
It is interesting to note that Hume claimed analyticity only for Arithmetic,
not for Geometry.
X METAPHYSICAL JUDGMENTS
||Why does Kant insist so much on the scientific
and the synthetic character of mathematical propositions? Because
he bears Metaphysics in mind all the time while he talks about Mathematics.
The strategy is to link closely the fate of Metaphysics to that of
Mathematics. If the same findings could be attested for both Mathematics
and Metaphysics, the latter should be entitled to share the status
of all other respectable sciences: "The good company into which Metaphysics
would thus have been brought would have saved it from the danger of
a contemptuous ill-treatment…" At stake is thus no secondary issue
whether mathematical propositions are really synthetical and in which
sense (if at all), but the final verdict about the standing of Metaphysics.
Either it should be recognized as valid (and exempt from the "ill-treatment")
or Mathematics should be treated the same way because its propositions
are not a priori in the sense of the analytic a priori.
||If Metaphysics is accused of blowing up
sheer experiental observations, then Mathematics should be also put
on trial ("the thrust intended for metaphysics must have reached mathematics").
This would require to subject "the axioms of Mathematics to experience"
the way Hume has "impregnated" the concept of causation with experience.
But an astute philosopher like Hume would have never done this with
Mathematics. This allows Kant to create an unbearable inconsistency
for Hume which undermines Humean effort to put a wedge between Mathematics
and Metaphysics. If what he has presumed for Metaphysics could be
also demonstrated for Mathematics, then he should have either rejected
both or accepted both. Had Hume noticed that Mathematics consists
of synthetic propositions known a priori, he would have treated
Metaphysics differently and would have recognized causality as a valid
although synthetic principle known a priori.
||Kant adumbrates that an unsatisfactory (narrow)
understanding of judgments was responsible for much of the defective
analysis of the concept of cause in Hume and, along with it, for his
unsubstantiated conclusions about the status of Metaphysics. As Kant
puts it, Hume asks "how is it possible… that when a concept is given
me I can go beyond it and connect with it another which is not contained
in it, in such a manner as if the latter necessarily belonged
to the former?" Though not using the Kantian terminology, he was in
this way inquiring about the possibility of synthetic a priori
judgments. However, he has concluded that "nothing but experience
can furnish us with such connections", which means, he thought that
a priori synthetic cognitions in Metaphysics are impossible
(they are only "a long habit of accepting something as true"). Since
causal connection was not clearly observable in experience, he finally
asserted (erroneously) that it was fictitious ("sophistry and illusion")
and consequently treated it like all other metaphysical fantasies
("commit it then to the flames."). Hume's contention that a statement
like 'A causes B' is neither analytic nor synthetic ("the fork")
led to the conclusion that the concept of causation was only the expression
of an expectation, like the concept of God. By following this logic
Hume deprived himself of any prospect to discover a third class of
propositions consisting of synthetic a priori judgments. Instead
he delivered human mind to the wanton influx of impressions without
supplying it with means to organize experience conceptually. This
was intellectually a very difficult position but Hume tried to hold
it in a playful manner.
||The objectivity of causal inferences in
everyday life and in science hinges on the possibility of synthetic
a priori judgments. This does not mean that these judgments
should exist simply because we need them to ensure the objectivity
of our knowledge. The objectivity of our judgments is rooted in the
concepts and the way how human beings comprehend reality (these concepts
"lay at the basis of their observations"). There is already
an existing difference between a mere succession of events A and B
and a causal connection which entails that, without A occurring, B
would not occur. The first can be expressed solely in terms of judgments
of perceptions ("Every time the sun shines, the rock becomes warm."),
the second requires a real cognition of the connection which would
hold true at all times ("Because the sun shines, the rock will therefore
Repeated succession is not sufficient to support the latter judgment
of experience. It is a necessary condition, but without an a priori
concept of causality it will never amount to an objective cognition.
Necessity and universality do not spring from experience although
they are not encapsulated in analytic propositions only. Hume's failure
to recognize the existence of synthetic a priori judgments
was therefore by no means an insignificant deficiency, for such judgments
are necessary principles of human knowledge.
||Descartes' Cogito has already indicated
that Metaphysics might possess some necessary and a priori, although
non-analytic propositions. Unfortunately, later philosophers tended
to press all similar propositions either into the rubric of synthetic
or into the rubric of analytic judgments alone. Kant illustrates this
point in § 3 by adducing the example of Wolff and Baumgartner (the
followers of Leibniz) who were trying to present the principle
of sufficient reason as an analytic proposition by deriving it
from the principle of contradiction. In contrast to
them, he shows that the principle of sufficient reason, according
to which nothing can be so without reason why it is so, clearly represents
a synthetic a priori judgment and consequently cannot be deduced
from any analytic proposition. The fact that Kant criticizes Wolff
and Baumgartner on this point does not mean that he does not accept
the law of sufficient reason. He concedes its truth, but claims that
it should be demonstrated "from pure reason a priori"
and not from the identity of the concepts employed.
||The supplemented division between analytic
a priori and synthetic a priori judgments is absolutely
"indispensable" for the proper critique of our cognitive faculties.
In that sense it could be called "classical". Unfortunately,
it was overlooked both by empiricists and rationalists. Kant does
not want to overstress its importance. He even says that in itself
it does not mean much. Perhaps that was the reason why even those
who were on the verge to recognize it eventually did not pay attention
to it. "Dogmatic philosophers" of all breeds have entirely neglected
it, simply because they have not realized that the source of metaphysical
judgments is not a special "metaphysical activity" ("metaphysics itself")
but reason as such ("pure laws of reason generally"). Only John Locke
might have adumbrated the "classical" difference by placing together
identity or contradiction ("diversity") as analytic
judgments, while putting on the other side "the co-existence of ideas"
("ideas in coexistence") as synthetic judgments with an a priori
status. But he has not determined the latter as such (Locke in
fact says that our knowledge of this kind is very limited). "In his
remarks on this species of knowledge, there is so little of what is
definite and reduced to rules that we cannot wonder if no one, not
even Hume was led to make investigations concerning this sort of propositions."
The truth is, however, that metaphysical judgments are "all synthetic"
a priori. To realize this, we must distinguish "judgments pertaining
to metaphysics from judgments properly called (metaphysical)".
Many judgments that pertain to Metaphysics are in truth analytic (as are those that pertain to Mathematics).
Metaphysics has been always using analytic propositions the way
Mathematics uses them: "We can be shown indeed many propositions,
demonstrably certain and never questioned; but these are all analytic…"
However, they have only a supportive role within Metaphysics. They
"rather concern the material and the scaffolding for metaphysics
than the extension of (metaphysical) knowledge, which is our proper
object in studying it."
The analytic judgments of the aforementioned kind are very instrumental
in explicating certain operative concepts of Metaphysics, but they
do not really belong to its body of knowledge. Only their constitutive
concepts could be regarded as immanent to metaphysical considerations.
||Kant's example of a synthetic a priori judgment in Metaphysics is: "Substance is something permanent". If we say that "substance is that which only exists as subject" then we only explicate the metaphysical term "substance" by dissecting its concept. But the judgment resulting from this dissection (= the bearer of properties is underlying these properties), is not itself a "metaphysical judgment proper". Its analysis is no "different from the dissection of any other, even empirical, concept". In other words, by saying that "substance exists as subject" we perform basically the same operation as when we define air as "an elastic fluid". This kind of analysis ("dissection") of a priori concepts that are being used by metaphysicians could be very valuable. A collection of their definitions would make up a kind of "definitive philosophy" (philosophia definitiva) consisting solely of analytic judgments pertaining to Metaphysics. But they are not the true end of Metaphysics for the sake of which "various dissections" of concepts need to be undertaken.
||Note: The expression philosophia definitiva is a reference to the work of F. Baumeister entitled Philosophia definitiva, h.e. definitiones philosophicae ex systemate celeb. Wolfi in unum collectae, Wittenberg 1733.
If it consists only of analytical judgments it is really completed.
||Metaphysical judgments proper are generated
by means of metaphysical concepts - "previously analyzed". Metaphysics
makes judgment that are non-empirical, which means that they are a
priori. Any attempt to derive them from experience would be a
kind of generatio aequivoca = generation by similarity, not
a logically correct procedure. Kant was convinced that these judgments
make up a special realm, independent of experience but governing it.
According to him, there must be certain a priori rules for
possible experience that are not themselves experiential the way there
are certain principles of logic.
Metaphysics purports to say something substantial about experience
and transcendent object and not only to explicate the meaning of concepts.
To push further the already quoted examples, Metaphysics should be able
to "prove that in all which exists the substance endures", that "every
event has a cause", that "everything which is a square has a
shape", that "no surface, if it is red all over, is at the
same time green all over", or that "every promise gives
rise to obligation". Formulation of such judgments "constitutes"
the real subject and "end" of Metaphysics. Kant claims that metaphysical
propositions by rule belong precisely to this category of synthetic
judgments known a priori.
||Synthetical a priori
||Substance is that which is a subject.
||Substance is that what is permanent.
While the three classical principles of logic (identity,
non-contradiction and excluded middle) are analytical, the fourth,
added by Leibniz, is synthetical a priori.
Depending of their applicability in experience three types of
judgment bear the following truth values:
||Synthetic a priori
||If synthetic a priori judgments are
possible, Metaphysics is possible as a science. Fortunately, "we have
at least some uncontested synthetic knowledge a priori" pertinent
to the issue whether Metaphysics is possible at all. These already
existing "a priori synthetic cognitions" are to be found in
pure Mathematics and pure Physics. Both Mathematics and Physics "contain
propositions which are unanimously recognized, partly apodictically
certain by mere reason, partly by general consent arising from experience
and yet as independent of experience". This fortunate circumstance
facilitates the resolution of the second question - whether synthetic
a priori knowledge is possible. While we had to ask whether
Metaphysics is possible, it is not necessary to ask whether its type
of knowledge (synthetic a priori) is possible, because it is
already secured through the existence of Mathematics and Physics.
XI THE HOW OF POSSIBILITY
The following chart represents different judgment kinds
as appropriated by different types of sciences:
Pertaining to Metaphysic
|| The assertion that propositions of pure Mathematics
and Physics are not analytic, but synthetic a priori, has a
twofold impact. First, we need to revise some common notions about
the nature of theoretical knowledge and the role of analytic and synthetic
judgments in it.
Second, in accord with the analytic method adopted in the Prolegomena,
one can "start from the fact that such synthetic but purely rational
knowledge actually exists" and then proceed to examine "the ground"
of this possibility "in order that we may deduce from the principle
which makes given knowledge possible the possibility of all the rest".
The "rest" refers clearly to Metaphysics itself. If Metaphysics can
produce the same synthetical a priori judgments that occur
in Mathematics and Physics, then Metaphysics needs only to display
and validate their presence within itself and to explain their role
in cognition. This is precisely what Kant was trying to do by showing
not only that synthetic a priori judgments are possible in
Metaphysics, but also that they represent a priori conditions
of the possibility of objects.
In raising the question of synthetic a priori judgments
we should resist the temptation to conceive them simply as a
priori products of "metaphysical imagination". Metaphysics,
as envisioned by Kant, is not a self-generated art or discipline,
but the science of how we conceive objects a priori. The
source of metaphysical judgments is not metaphysical imagination,
but "the laws of pure reason". Although not necessary in themselves
(logically), they are necessary for experience which is organized
through intuition and concepts. "But the generation of a priori
knowledge by intuition as well as by concepts, in fine, of synthetic
propositions priori, especially in philosophical knowledge,
constitutes the essential subject of metaphysics."
Kantian pair of intuitions and concepts obviously corresponds to
the Humean pair of impressions and ideas. The duality of intuitions
and concepts encompasses both types of representations and both
sides of our subjectivity, the receptive and the active one. Intuitions
are immediate representations of immediately present and particular
objects whereas thinking provides mediate representations of something
in general. Through intuition our organs are "approached" by appearances,
through thought we bestow a priori forms of intuition to
perceptions. Real knowledge is unification of intuitions and concepts.
A merely intuited or conceived object is not an object at all; the
latter is just a thought, the former just an incomprehensible perception.
|Ground of Possibility:
||It is not, however, sufficient to state that we have
a priori representations - we must explain how they
can exist and how they are applicable to experience. In other
words, we must inquire into the ground of their possibility in order
that we may "be enabled to determine" the conditions, the sphere and
the limits of a priori knowledge. Thus the question "How is
Metaphysics possible as a science" turns into the question "How are
synthetic a priori judgments possible?" This is the "problem
upon which all depends": "Metaphysics stands or falls with the solution
of this problem." This question includes two sides: (1) How is a necessary
synthesis of two concepts possible, and (2) How does reality correspond
to these combinations, i.e., how these connections are objectively
||No matter how plausible, a priori cognitions
which assert non-logical and non-empirical connections need to be
explained and finally justified before the tribunal of reason. Without
the question of possibility fully answered everything we say as a
piece of synthetic a priori knowledge could be regarded
as a "vain, baseless philosophy and false wisdom". This is the reason
why Kant proclaims a temporary suspension of metaphysical constructions
until the foundation of synthesis a priori cognition is adequately
answered. From this suspension he exempts only those who want to pursue
Metaphysics as "an art of wholesome persuasion" and "not as a science".
These persons act in the realm of "rational belief" where one formulates
the most probable trans-empirical guidelines "for the understanding
and the will in life". Although based on assumptions and conjectures,
this is a permissible practical skill of self-guidance equaling to
what is nowadays called "self-help" literature. But it does not have
anything in common with the speculative Metaphysics which formulates
necessary judgments about the world.
from the Greek apodeixis = pointing out, proof, demonstration;
an apodictic proposition states what must be the case, in contrast
to an assertoric one, which states what is the case, and
a problematic one, which states what can be the case.
from the Latin experientia = trial, experience; 1. that what
is happening to the subject, events, feelings, states of consciousness;
2. that what stems from the acts of the subject; for Aristotle,
a general knowledge derived from many memories of the same thing;
for Kant, the realm of possible knowledge, practically identical
with nature in the sense of the Newtonian physics: "Experience consists
in the synthetic connection of phenomena (perceptions) in consciousness,
so far as this connection is necessary."
The English rendition of the German Anschauung = mode of
visual perception (comes from the Latin in + tueor
= to see, look, gaze); in Kant, the faculty of apprehending the
concrete singularity of things as they are given in space and time
but not yet subsumed under abstract concepts; it is both something
conditioned (receptive aspect of experience with regards to objects)
and conditioning (pure forms of sensible intuition, space and time,
precede and determine all actual impressions of objects).
In accord with the general idea of transcendental approach, transcendental
philosophy purports to provide "the complete solution of the problem"
how synthetic a priori judgments are possible. The metaphysical
a priori becomes the transcendental with a synthetic power.
The elaboration of this position is an inquiry "into purely rational
knowledge". It explains in which sense the cognition a priori
"lies at the basis" of Metaphysics. As theory of knowledge, transcendental
philosophy secures the foundations of theoretical sciences along
with Metaphysics. Consequently, "transcendental philosophy" is the
investigation of those conditions that are necessary conditions
of all cognitions a priori. Therefore, "transcendental philosophy"
must precede all Metaphysics (including the "scientific" one) by
securing its possibility.
These formulations suggest that transcendental philosophy coincides
with the critique of pure reason. It is certainly not psychology
of knowledge. But the whole tenor of the Prolegomena as well
as particular passages favor a clear separation between the two,
while equating the system of transcendental philosophy with Metaphysics
as a science (=system of a priori principles). The Critique
retains a preparatory function with regard to that objective. Even
though Kant likes to call the preliminary part of his project "the
Metaphysics of Critical Idealism", it should not be confused with
the Metaphysics as a science about those "noble objects". Metaphysics
as theory of knowledge (transcendental) is different from the dogmatic
(transcendent) Metaphysics which goes beyond experience.
In keeping with the adopted analytical method, Kant first scrutinizes
two sciences of "theoretical knowledge", pure Mathematic and pure
Physics, which "exhibit to us objects in intuition". Having demonstrated
that these theoretical sciences possess cognitions from pure reason,
he then shows how they achieve the conformity of their a priori
cognitions with concrete objects (this approach in concreto is
opposed to the procedure of the Critique of Pure Reason that
starts from concepts in abstracto). The explanation
how the a priori judgments of Mathematics and Physics are
valid is at the same time a proof of their validity. Finally, he
turns to the metaphysical science of a priori principles
in general (metaphysica generalis) and explains how Metaphysics
as science is possible. Thus the transcendental examination of the
conditions of such science advances through four stages:
1. How is pure mathematics
possible? (§§ 6-13)
2. How is pure natural
science possible? (§§ 14-39)
3. How is metaphysics
in general possible? (§§ 40-60)
4. How is metaphysics
possible as science?
Mathematics, Physics and Metaphysics all make universal
claims as exemplified in synthetic a priori judgments ("Straight
line is always the shortest distance between two points.", "All
bodies attract each other with gravitational force.", "All events
have cause."). Truly, the possibility of equally valid metaphysical
judgments is still not recognized, but the very existence of Mathematics
and Physics provides the required proof. From the possibility of
the given knowledge a priori in Mathematics and Physics follows
the possibility of metaphysical a priori knowledge.
However, the possibility of scientific Metaphysics must be prepared
by an appropriate discussion of Metaphysics as a "natural disposition",
which explains the necessity of the fourfold (instead of threefold)
articulation of the problem.