Hegeler Institute

THE IMPOSSIBILITY OF TRANSCENDENTAL DEDUCTIONSAuthor(s): S. KörnerReviewed work(s):Source: The Monist, Vol. 51, No. 3, Kant Today: Part I (JULY, 1967), pp. 317-331Published by: Hegeler InstituteStable URL: http://www.jstor.org/stable/27902036 .Accessed: 26/03/2012 18:38

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THE IMPOSSIBILITY OF TRANSCENDENTAL DEDUCTIONS

The purpose of this paper is first to explain a general notion ot transcendental deductions, of which the Kantian are special cases; next to show, and to illustrate by examples from Kant's work, that no transcendental deduction can be successful; and thirdly to put one of Kant's achievements in its proper light by substituting for his spurious distinction between metaphysical exposition and transcendental deduction, a revised notion of metaphysical expo sition and of the philosophical tasks arising out of it.

L The General Notion oj a Transcendental Deduction

Making statements about the external world presupposes not

only a prior distinction between oneself and that world, but also a

method for differentiating, within one's experience of it, external

objects and attributes-properties and relations of which external

objects are the bearers. I shall say that such a method of external differentiation is associated with, or belongs to, a categorial schema

or, briefly, a "schema" of external differentiation if, and only if, the attributes employed comprise what may be called respectively, in accordance with philosophical tradition, "constitutive" and "in

dividuating" attributes. An attribute is constitutive (of external

objects) if, and only if, it is applicable to external objects and if, in addition, its applicability to an object logically implies, and is

logically implied by, the object's being an external object. I shall

say, more briefly, that a constitutive attribute is "comprehensively applicable" to external objects. An attribute is individuating (for external objects) if, and only if, it is applicable to every external

object and if, in addition, its applicability to an external object logically implies, and is logically implied by, the external object's being distinct from all other external objects. I shall say, more

briefly, that an individuating attribute "exhaustively individuates" external objects.

318 THE MONIST

Some comments on these definitions may be helpful. Although not yet fully general, they fit, for example, Kant's view of the attribute 'x is a substance* as constitutive of, and his view of the attribute 6x wholly occupies a region of absolute space during a

period of absolute time* as individuating for, external objects. The term "logically implies" is used to express the converse of the relation of logical deducibility with respect to some underlying logic, which at this stage need not be made explicit. An individuat

ing attribute the possession of which by an external object logi cally implies its being distinct from all others, must not be confused with any merely identifying attribute the possession of which by an

external object happens as a matter of fact to distinguish it from all others. Lastly it should be emphasised that a method of prior external differentiation does not necessarily belong to a categorial schema.

Statements about the external world are not the only ones

which presuppose a prior differentiation of experience into objects and attributes, and thus, possibly, a categorial schema consisting of constitutive and individuating attributes. We also make, at least

prima facie, statemer of other kinds, presupposing prior dif ferentiations of other gions of experience, e.g. sensory, moral and aesthetic experience, which may or may not belong to

categorial schemata. A schema of sensory differentiation would con

tain constitutive attributes of, and individuating attributes for, sen

sory objects. The* same would hold analogously for schemata of moral and aesthetic differentiation, if any. Such considerations per mit us to generalize the definition of a categorial schema as follows: A method of prior differentiation of a region of experience is as

sociated with, or belongs to, a categorial schema if, and only if, the attributes employed comprise attributes which are constitutive of the region's objects, and attributes which are individuating for them. For my purpose here it is not necessary to raise, much less to answer, the question why anybody uses the methods of prior differentiation

which he does in fact use, or why for him experience should fall into more or less clearly distinguishable regions and should fall into them in one way rather than in any other.

A transcendental deduction can now be defined quite generally as a logically sound demonstration of the reasons why a particular categorial schema is not only in fact, but also necessarily employed,

IMPOSSIBILITY OF TRANSCENDENTAL DEDUCTIONS 319

in differentiating a region of experience. This definition is very wide indeed and will presently be shown to cover Kant's conception of a transcendental deduction. Because of its generality it must

be protected against such charges of vagueness as would rob the

subsequent discussion of all cogency. Such protection can be achieved by the following characterization of the key-phrases which occur in the definition. Although a "logically sound demonstration" need not be a deductive argument, it may contain deductive argu ments in which case these must not be fallacious. Again, whatever else may be meant by the statement that a schema "is necessarily

employed in differentiating a region of experience" it logically

implies that any method actually or possibly employed in differ

entiating the region belongs to the schema. Apart from these pro visos no further restrictions are imposed on interpreting the definition.

Among the most important and interesting examples of at

tempted transcendental deductions are, of course, those found in

Kant's philosophy, on which I shall be drawing for illustrations of

the general thesis that transcendental deductions are impossible. This choice will limit me to an examination of schemata of ex

ternal and practical differentiation. Kant's transcendental deduc

tions contain only such. He held that of all the methods of prior differentiation of experience which he investigated, only those of

external and practical differentiation-and not, for example, any method of aesthetic differentiation-belong to categorial schemata. It would not be difficult to find, in these or other fields, many

simpler or more simple-minded philosophical arguments easily rec

ognizable as attempts at transcendental deductions in the sense of our definition.

II. The Impossibility of Transcendental Deductions

I shall now examine the preconditions of the possibility of any transcendental deduction, and show that at least one of them is

such that it cannot be satisfied; from which result, of course, the

impossibility of transcendental deductions follows immediately. Be

fore a transcendental deduction can be attempted for any region of experience, a method of prior differentiation of the region must

first be exhibited and shown to belong to a schema. This, as was

320 THE MONIST

pointed out by and was perfectly clear to Kant, need not be the case. But if the method of prior differentiation does belong to a

schema the task of exhibiting the schema is feasible. It consists (a) in searching for nonempty attributes, e.g. an attribute P such that ?x is an object of the region* logically implies and is implied by, 'x is a P\ Sometimes one may succeed in the more ambitious task of giving a complete, finite enumeration of the simplest consti tutive attributes, i.e. such as are not logically equivalent to a con

junction of other constitutive attributes. We might, following Kant, call such simple and finitely enumerable attributes the "cate

gories" of the region and say that they are ultimately constitutive of the region's objects. But this pleasant possibility may be ignored.

The task further consists (b) in searching for at least one non

empty attribute, say such that Q is applicable to every object of the region, and is such that 'x is an object of the region and a Qf logically implies, and is logically implied by, *x is a distinct object of the region*. If another attribute say R, should also turn out to be an individuating attribute for the objects of the region then lx is an object of the region and an RJ logically implies, and is logical ly implied by, 'x is an object of the region and a Q*. We may again ignore this possibility. The fulfilment of the first precondition of the possibility of a transcendental deduction, i.e. of the above tasks

(a) and (b) may be called "the establishment of a schema"-on the basis of investigating a particular method of prior differentiation of a region of experience into objects and attributes.

With the establishment of a schema the preconditions for its transcendental deduction are, however, not yet satisfied. For to establish a schema is to establish that a particular method for dif

ferentiating a region of experience belongs to the schema, and not that any method which might actually or possibly be thus em

ployed, also belongs to it. Before one can show why any and every possible method belongs to the schema one has to show that any and every possible method belongs to it. One must, as I shall say, demonstrate the schema's uniqueness.

How could this be done? Prima facie three possibilities are

open. First, to demonstrate the schema's uniqueness by comparing it with experience undifferentiated by any method of prior differ entiation. But this cannot be done since the statements by which the comparison would have to be made, cannot be formulated with

IMPOSSIBILITY OF TRANSCENDENTAL DEDUCTIONS 321

out employing some prior differentiation of experience; and even if there were undifferentiated experience, one could at best show that a certain schema "reflects" it, and not that some other schema could not also reflect it. Second, to demonstrate the schema's

uniqueness by comparing it with its possible competitors. But this

presupposes that they all can be exhibited, and is self-contradictory in attempting a "demonstration" of the schema's uniqueness, by con

ceding that the schema was not unique. Thirdly, one might propose to examine the schema and its application entirely from within the schema itself, i.e. by means of statements belonging to it. Such an

examination, at best, could only show how the schema functions in the differentiation of a region of experience, not that it is the only

possible schema to which every differentiation of the region must

belong. The three methods include the possible grounds for a con

cordance between reality and its apprehension, mentioned in the

preface to the second edition of The Critique of Pure Reason. In order to avoid vague appeals to demonstrations of a categorial schema's uniqueness by other methods, e.g. some mystical insight or some special Logic, I am prepared to reduce my claim to the thesis that uniqueness demonstrations of a schema by comparing it

with undifferentiated experience, by comparing it with other sche mata, or by examining it from within, are impossible. It should be noted that I am speaking not of isolated concepts, such as 'per manence* or 'change*, which may or may not be indispensable to our thinking, but which by themselves are not constitutive of, or

individuating for, the objects of a region of experience-even though a demonstration of their uniqueness is, as I should be pre pared to argue, equally impossible.

It is the impossibility of demonstrating a schema's uniqueness that renders transcendental deductions impossible. The general argument just sketched rests mainly on two distinctions: the dis tinction between a method of prior differentiation and its cate

gorial schema, if any; and the distinction between (a) establish

ing that a method of prior differentiation belongs to a schema and

(b) demonstrating the uniqueness of the schema. In order to illus trate my conclusion with examples from Kant's work, I shall try to choose such as will not only serve to draw attention to errors, but will also suggest reasons why these errors are liable to escape

322 THE MONIST

undetected. I begin with what I consider to be a mistake which all the Kantian attempts at transcendental deductions have in common.

Assume that we have investigated a method of prior differentia tion of a region of experience and found that it belongs to a

schema. The result, as we have seen, is formulated (a) by state ments to the effect that some of the attributes employed by the method are constitutive of the objects of the region, e.g. that among the attributes is one, say P, such that P is applicable to objects of the region and such that *x is an object of the region* logically implies, and is implied by, (x is a P\ (b) by statements to the effect that one (or more) of the attributes employed are individuating for the objects of the region, e.g. that among the attributes is an at

tribute, say Q, such that Q applies to every object of the region and such that *x is an object of the region and a Q* logically implies, and is implied by, 'x is a distinct object of the region*. Let us now, as Kant did, examine the logical status of (a) statements of compre hensive applicability and (b) statements of exhaustive individuation.

Each of them is a conjunction of two statements. The first ex

presses that the extension of an attribute is, as a matter of fact, not

empty, that something exists, the existence of which could not be

guaranteed by logic or definitions alone. It is therefore a synthetic statement. The second is clearly logically necessary. Since a con

junction of a synthetic and a logically necessary statement is syn thetic, the statements of comprehensive applicability and exhaus tive individuation are all synthetic.

Moreover, each of these two kinds of statements in question, namely that of comprehensive applicability and that of exhaustive

individuation, is compatible with any statement about objects, i.e. with any statement expressing the applicability or inapplicability of attributes to objects-provided that such a statement is made

by a method of prior differentiation which belongs to the schema. The reason for this is that in that case no attribute can be applied or refused to any objects except such as are constituted and indi viduated by the schema's constitutive and individuating attributes. Thus no incompatibility can arise between the statements of com

prehensive applicability and exhaustive individuation of a cate

gorial schema on the one hand, and any statement expressed by a method of prior differentiation belonging to the schema on the

IMPOSSIBILITY OF TRANSCENDENTAL DEDUCTIONS 323

other. The statements of comprehensive applicability and exhaus tive individuation are thus a priori with respect to a particular rschema, namely the schema which comprises them. It does not fol low that they are also a priori with respect to any schema which can be claimed to be the only one possible, i.e. that they are

"uniquely a priori." Thus in establishing that a method of prior differentiation belongs to a schema one shows eo ipso that the statements of comprehensive applicability and of exhaustive indi viduation are synthetic and nonuniquely a priori. To show that

they are uniquely a priori would require a demonstration of the schema's uniqueness, which I have just argued to be impossible.

Kant did not see this, and he conflates uniquely a priori with

nonuniquely a priori statements. This conflation not only per vades his whole philosophy, but even determines its structure, espe cially the division of all his principal arguments into metaphysical expositions and transcendental deductions.1 A metaphysical exposi tion which exhibits a concept as, or exhibits it insofar as it is, a priori is always the result of inquiry into one actually employed method of differentiation. It can thus at best establish the schema, if any, to which the method belongs. A transcendental deduction, aimed at showing that and how a priori concepts are applicable or

possible, examines only the schema which has been established by the metaphysical exposition of this particular schema. It thus does

not examine a schema the uniqueness of which has been dem onstrated. Kant's failure even to consider the need for interpolating a uniqueness-demonstration between any metaphysical exposition and a corresponding transcendental deduction and his conflation of

nonuniquely and uniquely a priori statements are so intimately related that they deserve to be regarded as two aspects of the same error.

The reasons why these points, which in our own day are not too difficult to see, have escaped Kant, are partly historical and

partly logical. The historical ones, are, of course, that like most of his contemporaries, Kant considered the mathematics and physics of his day and the moral code by which he found himself bound, to be true beyond doubt; he felt in no way compelled to consider, therefore, the question of schemata other than those to which be

l See Critique of Pure Reason, B. 38, 80 etc.

324 THE MONIST

long the methods of differentiation employed by him in his mathe

matical, physical and moral thinking. The logical reasons are that his various attempts at transcendental deductions contain sub

sidiary assumptions which tend to reinforce the common error

underlying all of them. The Transcendental Aesthetic which exhibits the individuat

ing attributes of the Kantian schema is based on the assumption that the propositions of Euclidean geometry describe the spatial relations between external objects; also the more general assump tion that ii-per impossibile-two different geometries were con

ceivable, then at most one of them would describe, and at least one would misdescribe, these relations. However, neither Euclidean

geometry, nor any other, describes the spatial structure of external

objects or the spatial relations between them. A physical triangle, for example, is not an instance of the concept 'Euclidean triangle*, or for that matter 'non-Euclidean triangle', just as neither a Euclid ean triangle nor a non-Euclidean one is an instance of the con

cept 'physical triangle*. To "apply geometry to the external world" is not to assert geometrical attributes of external objects, but to

identify external objects with instances of geometrical attributes in certain contexts and for certain purposes, i.e. to treat them as if they were identical. The applicability, in this sense of one geometry does not exclude the applicability of another. Kant assumes the

unique applicability to external objects of Euclidean geometry, without even attempting to establish the assumption. Yet the

assumption of the unique applicability of Euclidean geometry to external objects is a key premiss in the very argument by which he tries to establish that spatio-temporal location in Euclidean space and Newtonian time is the principle of individuation for all ex ternal objects-a principle which he shows to be synthetic, and non

uniquely (not, as he thinks, uniquely) a priori. Again, the Transcendental Analytic, which exhibits the consti

tutive attributes of the Kantian schema, assumes as a principle that the categories must be recognized as conditions a priori of the pos sibility of experience2 conceived as differentiated into distinct exter nal objects and attributes of such. Sufficient conditions are not

distinguished from sufficient and necessary conditions. The former,

2 See e.g. B 126.

IMPOSSIBILITY OF TRANSCENDENTAL DEDUCTIONS 325

which Kant tries to establish, are satisfied by the establishment of a schema. The latter would be satisfied only if the schema's unique ness were also demonstrated. Failure to distinguish between the two

lands of conditions thus supports the conflation of statements

synthetic and nonuniquely a priori, with synthetic and uniquely a priori statements of comprehensive applicability.

The most convincing way to expose Kant's failure to give a transcendental deduction of the schema of external differentiation established in the Critique of Pure Reason, is simply to provide an example of a different schema of external differentiation. Since I have gone into this point in detail elsewhere,3 I may put it here

quite briefly. Grant that determinate spatio-temporal location, as conceived by Newton and Kant, exhaustively individuates exter nal objects of which the Kantian categories of substance, causality and the rest, are the constitutive attributes; and grant also that the statements to this effect are synthetic a priori. The existence of relativistic quantum-mechanics compels us to grant equally that determinate spatio-temporal location in a spatio-temporal con tinuum of an altogether different kind exhaustively individuates ex ternal objects of which the constitutive attributes are quite other than the Kantian categories; and to grant equally that the state

ments to this effect are synthetic a priori. But neither schema of external differentiation is unique; and the synthetic a priori state ments about the comprehensive applicability of, and the exhaustive individuation for, external objects with respect to either schema are non-uniquely a priori.

In Kant's practical philosophy he investigates a method for dif

ferentiating objects and attributes within the experience of the

practicable. The objects might be called "morally relevant" objects since their attributes include moral attributes. By exhibiting the constitutive and individuating attributes employed by the method, the method is shown to belong to a schema. Again no attempt is

made to demonstrate the uniqueness of the schema. Such an at

tempt could not, as I have argued, in any case have been successful, from which circumstance the impossibility of any transcendental deduction of the schema immediately follows.

3'Zur Kantischen Begr ndung der Mathematik und der Naturwissenschaften* Kant Studien, 56, No. s/4 (1966).

326 THE MONIST

At this point, however, Kant varies his usual procedure. Hav

ing established the schema, he does not immediately attempt its transcendental deduction. Instead he tries to derive a new principle from it, namely the categorical imperative, the applicability of

which does not only characterize the merely morally relevant ob

jects, which are constituted and individuated by the schema, but also those among the morally relevant objects which are the bearers of moral value. Only after the alleged derivation of the cate

gorical imperative is completed, does he attempt a transcendental deduction of it and the schema.

Kant's belief that an examination of his schema of practical differentiation yields the categorical imperative, which he regarded as a necessary and sufficient criterion of the morality of any action, was one of the main reasons why, in his practical philosophy, he overlooked the circumstance that to establish a schema is not to demonstrate its uniqueness; and why consequently there too he conflated synthetic statements which are nonuniquely a priori with

uniquely a priori ones. I shall not consider Kant's derivation of the

categorical imperative from the allegedly unique schema of practi cal differentiation. Instead I shall compare that schema with a dif ferent one, thus providing the strongest possible kind of argu ment against the assumption of its uniqueness, and, therefore,

against the soundness of the attempted transcendental deduction of it.

Since what is practicable is practicable in the external world,

any method of practical differentiation will depend on, and vary with, the adopted method of external differentiation and even

with substantive assumptions about the external world, formulated

by means of this method. Let us ignore such variations, however

important they may be. Kant's metaphysical exposition as a search

for the constitutive and individuating attributes employed in his

method of practical differentiation leads him to the following con

clusions: (a) the attribute 'x is a morally relevant object* is not

empty; and it logically implies, and is logically implied by, lx is a

type of act and x is performed in accordance with a maxim, chosen

by an agent*, (b) The latter attribute is not only constitutive of

morally relevant objects, but also individuates them exhaustively. The key-terms of the bilateral implication require comment.

IMPOSSIBILITY OF TRANSCENDENTAL DEDUCTIONS 327

An act is the intentional initiation (prevention or nonpreven

tion) by a person of a change in the situation which confronts him. A maxim is a rule of the general form: 'If in a situation of

type S, perform an act of type A\ S and A are not the unmanage

ably long, and possibly unlimited, conjunctions of attributes which are respectively characteristic of concrete situations and particular acts. They are manageable conjunctions of relevant attributes their relevance or irrelevance being determined by the person who chooses the maxim before acting, who formulates it retrospectively or who is at least assumed to be capable of doing so. S may, and

usually does, comprise some reference to the person's desires and intentions other than the intention involved in performing the act. A need not, usually does not, and-on some interpretations of Kant's theory-must not, comprise such a reference. Examples of maxims where A does not comprise it are: If in . . . help (or don't

help) your neighbour, commit (or don't commit) suicide etc.

According to Kant an act by itself is not a morally relevant ob

ject. What constitutes and individuates the bearers of moral at

tributes, i.e. of moral value, disvalue and indifference, is the type A under which a person subsumes his act, and the maxim to which he conforms in acting. At this point a glance at the history of moral

philosophy is sufficient to provide examples of schemata of practical differentiation, which are internally consistent, have been actually employed and are quite different from the Kantian. According to a whole class of such schemata a morally relevant object is a com

plicated relation between an act, the agent's beliefs, the truth or falsehood of his beliefs and his desires. Such a relation need not

depend on the person's chosen maxims; and is quite compatible with the reasonable assumption that not every act is governed by a maxim. The Kantian schema of practical differentiation is non

unique and its transcendental deduction therefore impossible.

III. A Revised Notion of Metaphysical Exposition

Before arguing that the spurious distinction between meta

physical exposition and transcendental deduction should be re

placed by a revised notion of metaphysical exposition and showing how much in harmony such replacement is with some of Kant's

insights, another attempt must be briefly examined at reconstruct

328 THE MONIST

ing the strategy of the transcendental philosophy. It sees the fundamental error not in neglecting the problem of demonstrating the (undemonstrable) uniqueness of any schema of differentiation, but merely in a narrowness of the methods investigated by Kant of prior differentiation and a corresponding narrowness of the schemata established by him.

On this view the post-Kantian development of physics and

mathematics, for example, would merely show the Kantian schema of external differentiation as having to be widened before a

transcendental deduction is attempted; one need not regard a

transcendental deduction as in principle impossible. Thus the indi

viduating attribute for external objects 'x wholly occupies a region of space and an interval of time as conceived by Newton* is to be

replaced by *x wholly occupies a region of space and an interval of time as conceived by Newton or a spatio-temporal region as conceived by Einstein*. In a similar manner the Kantian con stitutive attributes are to be replaced by unions of them with other

corresponding constitutive attributes. But, then, how could one show that the available constitutive and individuating attributes exhaust all the conceivable ones, or that all those conceivable have been conceived? To show this, one would have to produce a dem onstration of the widened schema's uniqueness and, as has been

argued quite generally, such a demonstration is impossible. In his metaphysical expositions of a particular method of prior

external and a particular method of prior practical differentiation, Kant has established that they belong to schemata, i.e. that they employ constitutive and individuating attributes. The statements to

the effect that the constitutive attributes are comprehensively ap plicable to the objects of the differentiated region of experience and that the individuating are exhaustively individuating for them, are synthetic and nonuniquely a priori-not as Kant thought uniquely a priori. These statements do not demarcate the structure of any method of external or of practical differentiation, as neces

sarily unchangeable; they are compatible with the assumption-and the historical truth-that schemata of external and practical dif ferentiation can change and become obsolete.

The constitutive and individuating attributes of a schema which is no longer employed, may even turn out, or be judged, to be empty. Having e.g. abandoned the Kantian schema of external

IMPOSSIBILITY OF TRANSCENDENTAL DEDUCTIONS 329

differentiation in favour of another, it becomes possible-looking as it were from the outside-to assert that the Kantian attribute of substance is empty, i.e. that the synthetic, nonuniquely a priori statement asserting its comprehensive applicability to external ob

jects is false. A social anthropologist may in a similar manner

judge that the constitutive and individuating attributes of a de

monology, which he has investigated, are empty, even though a cer

tain way of life might be inseparably bound up with it. In order to do justice to such possibilities I now define a revised

notion of metaphysical exposition, which relativizes the Kantian absolute notion in a number of ways. It is the analysis of methods for the differentiation of more-or-less-well-demarcated domains into

objects and attributes which aims at the exhibition of synthetic and nonuniquely a priori statements, by exhibiting the schemata in respect of which the statements are a priori. The differentiated

domain, as became clear in discussing geometrical statements, need not be a region of experience. It may be a domain of ideal ob

jects. A method of differentiation belongs, we remember, to a schema if, and only if, it employs attributes which are constitutive of all objects of the domain and attributes which individuate all of them. The constitutive and individuating attributes are the schema. A statement is synthetic if, and only if, it is not logically valid with respect to the logic underlying the methods of dif ferentiation being considered. Thus we must, distinguish e.g. statements synthetic with respect to classical from those synthetic

with respect to intuitionist logic. A statement is a priori with re

spect to a schema if, and only if, it is compatible with any statement in which an attribute is applied to one or more distinct objects by means of any method which belongs to the schema.

Among the kinds of schemata which a metaphysical exposition (in the revised sense) of various methods of differentiation may

establish for them are the following: Schemata (a) of external

differentiation, including the schema established in the Critique of Pure Reason for the method of external differentiation investigated by it. But there are other, methods of external differentiation be

longing to the same or other schemata. Schemata (b) of practical differentiation, including the schema established in the Critique of Practical Reason for the method of practical differentiation in

vestigated by it. But there are other methods of practical differentia

330 THE MONIST

tion belonging to the same or other schemata. Schemata (c) of idealized external or, briefly, mathematical differentiation of a do

main which is an idealization of some aspects of external experience. The methods of differentiating such a domain and the statements which are true about it, are sometimes expressed in axiomatic mathematical theories, even though a large class of such theories cannot, as G del has shown, comprise all the statements which are true about the domain. Kant, as was pointed out earlier, failed to recognize the multiplicity of possible mathematical schemata and confused mathematical with external differentiation. Schemata (d) of idealized practical differentiation, which are of interest in the

study of certain normative, e.g. legal, systems. Schemata (e) of

logical differentiation. Their establishment results in synthetic non

uniquely a priori statements of comprehensive applicability. Such a statement is a conjunction consisting of two statements, an ana

lytic statement asserting that certain statement-forms are true of all

objects constituted and individuated by any of the available meth ods of differentiation, and a synthetic statement asserting that the domain of these objects is not empty. Kant, who was not faced with the problem of alternative logics, naturally did not consider this

possibility. Every synthetic, nonuniquely a priori statement is a priori with

respect to at least one schema. Thus statements of comprehensive applicability and exhaustive individuation are a priori with respect to the schema to whose constitutive and individuating attributes

they refer. Next, all synthetic, ideal statements are a priori with

respect to any schema of external differentiation, because no state ment solely about ideal objects can be incompatible with any state ments solely about external objects, however these may be consti tuted or individuated. Again the question how far statements which

belong to a schema of practical differentiation are a priori with re

spect to a schema of external differentiation cannot be answered in general, since methods of external differentiation and methods

of practical differentiation (and their schemata, if any) may stand in a variety of relations to each other.

The important Kantian distinction between synthetic a priori statements and regulative principles remains valid. We might de fine a regulative principle as being synthetic if, and only if, the statement describing the type of action prescribed by the principle

IMPOSSIBILITY OF TRANSCENDENTAL DEDUCTIONS 331

is synthetic; and as a priori with respect to a schema of differentia tion if, and only if, the descriptive statement is compatible with any statement in which attributes are applied to objects by a method of differentiation which belongs to the schema. Regulative prin ciples which are in this sense synthetic and nonuniquely a priori dif

fer, of course, from synthetic and nonuniquely a priori statements

by having no truth-value. In the course of a metaphysical exposition such principles will often be uncovered, whether or not we decide to include their exhibition among its explicit aims. Epistemologi cally of greatest interest are those regulative principles which regu late the construction of theories and those which express preferences for some schemata over others.

Transcendental deductions of schemata and of synthetic a priori statements are, as I have argued, impossible because their unique ness cannot be demonstrated. The Kantian question as to how

synthetic and uniquely a priori judgements are possible does not arise. In its place, however, there arises another question: How are

synthetic and nonuniquely a priori statements possible? To answer this question is, as we have learned from Kant, to examine the function of such statements, that is to say their relations to each

other, to analytic and to empirical statements. The task is by no means simple or trivial as can be seen, for example, by considering the relation in scientific thinking between various schemata of ex

ternal, ideal and logical differentiation. Moreover, since contrary to Kant's convictions, not only methods of differentiation but also the schemata to which they belong can and do change, the task cannot be completed once and for all, but must be undertaken over and over again.

S. K RNER THE UNIVERSITY, BRISTOL