## 1. The Nature of Judgment



Theories of cognitive judgment both prior to and after Kant tend to
divide dichotomously into the *psychologistic* and
*platonistic* camps, according to which, on the one hand,
cognitive judgments are nothing but mental representations of
relations of ideas, as, e.g., in the Port Royal Logic (Arnaud &
Nicole 1996), or mentalistic ordered combinings of real individuals,
universals, and logical constants, as, e.g., in Russell's early
theory of judgment (Russell 1966), or on the other hand, cognitive
judgments are nothing but assertoric psychological states or attitudes
aimed at mind-independent, abstract propositions or thoughts, as,
e.g., in Bolzano's and Frege's theories of judgment
(Bolzano 1972, Frege 1979, Frege 1984). And, seemingly, never the
twain shall meet (Martin 2006, Hanna 2006a, ch. 1). But by sharp
contrast to both the psychologistic and platonistic camps,
Kant's theory of judgment is at once cognitivist,
anti-psychologistic, and anti-platonistic. More precisely, according
to Kant, judgments are complex conscious cognitions that (i) refer to
objects either directly (via intuitions) or indirectly (via concepts),
(ii) include concepts that are predicated either of those objects or
of other constituent concepts, (iii) exemplify pure logical concepts
and enter into inferences according to pure logical laws, (iv)
essentially involve both the following of rules and the application of
rules to the objects picked out by intuitions, (v) express true or
false propositions (truth-aptness), (vi) mediate the formation of
beliefs and other intentional acts, and (vii) are unified and
self-conscious.



The three leading features of this account are, first, Kant's
taking the innate capacity for judgment to be the central cognitive
faculty of the human mind, in the sense that judgment, alone among our
various cognitive achievements, is the joint product of all of the
other cognitive faculties operating coherently and systematically
together under a single higher-order unity of rational
self-consciousness (*the centrality thesis*); second,
Kant's insistence on the explanatory priority of the
propositional content of a judgment over its basic cognitive-semantic
constituents (i.e., intuitions and concepts), over the logical form of
judgments, over the inferential role of judgments, over the rule-like
character of the judgment, over the self-conscious psychological
states in which propositions are grasped as well as the
non-self-conscious psychological processes in which propositions are
synthetically generated, over epistemic beliefs in those propositions,
over all other propositional attitudes, and also over intentional acts
guided and mediated by those propositions, including non-epistemic
acts of various kinds (*the priority-of-the-proposition
thesis*); and third, Kant's background metaphysical doctrine
to the effect that judgments are empirically meaningful (objectively
valid) and true (objectively real) if and only if transcendental
idealism is correct (*the transcendental idealism thesis*).


### 1.1 The power of judgment and the other faculties of cognition



According to Kant, a "judgment" (*Urteil*) is a
specific kind of "cognition"
(*Erkenntnis*)--which he generically defines as any
conscious mental representation of an object (A320/B376)--that is
the characteristic output of the "power of judgment"
(*Urteilskraft*). The power of judgment, in turn, is a
cognitive "capacity" (*Fahigkeit*) but also
specifically a *spontaneous* and *innate* cognitive
capacity, and in virtue of these it is the "faculty of
judging" (*Vermogen zu urteilen*) (A69/B94), which
is also the same as the "faculty of thinking"
(*Vermogen zu denken*) (A81/B106).



For Kant the mind is essentially active and vital--"the
mind (*Gemut*) for itself is entirely life (the principle
of life itself)" (5: 278)--and a cognitive capacity in turn
is a determinate conscious propensity of the mind to generate
objective representations of certain kinds under certain conditions.
What do spontaneity and innateness add to a mere *capacity* for
cognition, so that it becomes a "*faculty* of
cognition" (*Erkenntnisvermogen*)? A cognitive
faculty is spontaneous in that whenever it is externally stimulated by
raw unstructured sensory data as inputs, it then automatically
organizes or "synthesizes" those data in an unprecedented
way relative to those inputs, thereby yielding novel structured
cognitions as outputs (B1-2, A50/B74, B132, B152). So cognitive
spontaneity is a *structural creativity* of the mind with
respect to its representations. It is a controverted question of
recent Kant-interpretation whether cognitive spontaneity derives
exclusively from the conceptual or discursive capacity of the rational
human mind (B152) (Longuenesse 1998, chs. 1-3, 5, 8), or can
also derive independently from the intuitional, non-conceptual, or
sensible capacity of the rational human mind, shared with minded
non-rational human or non-human animals (B151) (Hanna 2006b, ch. 1,
McLear 2011). Correspondingly, it is also a controverted question
whether according to Kant there is only one basic kind of synthesis,
i.e., conceptual/discursive synthesis, or two basic kinds, i.e.,
conceptual/discursive synthesis and
intuitional/non-conceptual/sensible synthesis. These controverted
questions, in turn, are closely connected with the recent vigorous
debate about Kant's conceptualism vs. Kant's
non-conceptualism in relation to his theory of judgment, and the
implications of this for interpreting and critically evaluating
Kant's transcendental idealism and the Transcendental Deduction
of the Pure Concepts of the Understanding, a.k.a. "the
Categories" (see the supplementary document
 The Togetherness Principle, Kant's Conceptualism, and Kant's Non-Conceptualism
 and Sections 4.1 to 4.2 below). 



Kant also uses the term 'spontaneity' in a somewhat
different sense in a metaphysical context, to refer to a mental cause
that can sufficiently determine an effect in time while also lacking
any temporally prior sufficient cause of itself (A445/B473). Call this
*practical* spontaneity. What is shared between the two senses
of spontaneity, practical and cognitive, is the unprecedented,
creative character of the mind's operations. But in the
cognitive sense of spontaneity, what is crucial is that the sensory
data manifest "poverty of the stimulus" (Cook & Newson
1996, 81-85)--significant underdetermination of the outputs
of an embodied cognitive capacity by the relevant inputs to that
capacity, plus previous experiences or habituation--although the
faculty's spontaneity must also always be minimally conditioned
by external sensory triggering (B1-2). Correspondingly, a
Kantian cognitive faculty is innate in the threefold sense that (i) it
is intrinsic to the mind, hence a necessary part of the nature of the
rational animal possessing that faculty, (ii) it contains internal
structures that are necessarily or strictly underdetermined by any and
all sensory impressions and/or empirical facts--which is the same
as their being *a priori* (B2), and (iii) it automatically
systematically synthesizes those sensory inputs according to special
normative rules that directly reflect the internal structures of the
faculty, thereby generating its correlatively-structured outputs. So
Kantian innateness is essentially a *procedure-based*
innateness, consisting in an a priori active readiness of the mind for
implementing normative rules of synthesis, as opposed to the
*content-based* innateness of Cartesian and Leibnizian innate
ideas, according to which an infinitely large supply of complete
(e.g., mathematical) beliefs, propositions, or concepts themselves are
either occurrently or dispositionally intrinsic to the mind. But as
Locke pointed out, this implausibly overloads the human mind's
limited storage capacities.



In contrast to both Rationalists and Empiricists, who hold that the
human mind has only one basic cognitive faculty--reason or sense
perception, respectively--Kant is a cognitive-faculty
*dualist* who holds that the human mind has *two* basic
cognitive faculties: (i) the "understanding"
(*Verstand*), the faculty of concepts, thought, and
discursivity, and (ii) the "sensibility"
(*Sinnlichkeit*), the faculty of intuitions/non-conceptual
cognitions, sense perception, and mental imagery (A51/B75). The
essential difference between the faculties of understanding and
sensibility, and correspondingly the essential difference between
concepts and intuitions (A50-52/B74-76), as distinct kinds
of cognition, is a fundamental commitment of Kant's theory of
cognition generally and of his theory of judgment more specifically.
Concepts are at once (a) general representations having the logical
form of universality (9: 91), (b) discursive representations
expressing pure logical forms and falling under pure logical laws
(A68-70/B92-94, A239/B298), (c) complex intensions ranging
over "comprehensions" (*Umfangen*) that contain all
actual and possible objects falling under those intensions, as well as
other narrower comprehensions (9: 95-96), (d) mediate or
indirect (i.e., attributive or descriptive) representations of
individual objects (A320/B376-377), (e) rules for classifying
and organizing perceptions of objects (A106), and (f)
"reflected" representations expressing the higher-order
unity of rational self-consciousness, a.k.a.
"apperception" (B133 and 133n.). Intuitions by contrast
are conscious object-directed representations that are (1) singular
(A320/B377) (9: 91), (2) sense-related (A19/B33, A51/B75), (3)
object-dependent (B72) (4: 281), (4) immediate, or directly
referential (A90-91/B122-123, B132, B145), and, above all,
(5) non-conceptual (A284/B340) (9: 99) (Hanna 2001, ch. 4).



Understanding and sensibility are both subserved by the faculty of
"imagination" (*Einbildungskraft*), which when
taken generically is the source or engine of all sorts of synthesis,
but which when taken as a "dedicated" or task-sensitive
cognitive faculty, construed as either "productive" or
"reproductive," more specifically generates (a) the
spatial and temporal forms of intuition, (b) novel mental imagery
in conscious sensory states, (g) reproductive imagery or
memories, and (d) "schemata," which are
supplementary rules for interpreting general conceptual rules in terms
of more specific figural (spatiotemporal) forms and sensory images
(A78/B103, B151, A100-102, A137-142/B176-181) (7:
167). At least in principle, then, the imagination mediates between
the understanding and the sensibility by virtue of being an autonomous
third basic cognitive capacity containing elements of each of the
basic dual capacities (see,e.g., A115-119 and
A139-142/B178-181)--which would, in effect, make Kant
a cognitive-capacity *trinitarian*. But sometimes, contrariwise
and somewhat incoherently, Kant seems instead to say that the
imagination at once (i) *belongs* to sensibility and yet also
(ii) *is caused* by the action of the understanding on
sensibility. This deep unclarity about the nature of the imagination,
in addition to being a flashpoint for important longstanding
disagreements in Kant-scholarship on his theory of judgment (see,
e.g., Heidegger 1990, Waxman 1991, Longuenesse 1998), also has some
serious implications for Kant's theory of judgment itself
(again, see the supplementary document
 The Togetherness Principle, Kant's Conceptualism, and Kant's Non-Conceptualism
 and Sections 4.1 to 4.2 below).



Just as understanding and sensibility are *sub*served by the
bottom-up cognitive processing of the imagination, so in turn they are
also *super*served by the top-down cognitive processing of the
faculty of "reason" (*Vernunft*), which produces
logical inferences, carries out pragmatic or moral choices and
decisions, a.k.a. "practical judgments"), imposes
coherence and consistency on all sorts of cognitions, and above all
recognizes and implements strongly modal and categorically normative
concepts such as necessary truth and unconditional obligation, in the
form of lawlike "principles" (*Principien*,
*Grundsatze*) (A299-304/B355-361,
A800-804/B828-832).



Finally, the objective unity of any judgment whatsoever is guaranteed
by the faculty of apperception or rational self-consciousness, which
plays the "executive" role in the corporate organization
of the mind by introducing a single higher-order unity into all of its
lower-order representations, via judgment, and whose characteristic
output is the cogito-like self-directed judgment-forming
representation "*I think*" (*Ich denke*): as
in "I think about *X*" (where *X* is some
concept, say the concept of being a philosopher) or "I think
that *P*" (where that-*P* is some proposition, say
the proposition that Kant is a philosopher) (B131-132). The
*I think* according to Kant is "the vehicle of all
concepts and judgments whatever" (A341/B399), because it is both
a necessary condition of the objective unity of every judgment and
also automatically implements one or another of a set of primitive
pure a priori logical forms or functions of unity in judgments or
thoughts--"the pure concepts of the understanding" or
"categories" (A66-83/B91-116)--in the
several semantic constituents of that judgment.



The power of judgment, while a *non-basic* faculty, is
nevertheless the *central* cognitive faculty of the human mind.
This is because judging brings together all the otherwise
uncoordinated sub-acts and sub-contents of intuition,
conceptualization, imagination, and reason, via apperception or
rational self-consciousness, for the purpose of generating a single
cognitive product, the judgment, under the overarching pure concepts
of the understanding or categories, thereby fully integrating the
several distinct cognitive faculties and their several distinct sorts
of representational information, and thereby also constituting a
single rational human animal. For Kant then, rational humans are
*judging animals*.


### 1.2 Judgments are essentially propositional cognitions



But what exactly *are* judgments? Kant's answer, in a
nutshell, is that they are essentially propositional
cognitions--from which it immediately follows that rational
humans are, more precisely, *propositional animals*. In what
sense, however, is this the case?



Logicians before Kant, e.g., the Port Royalists, tended to define
judgment as a "representation of a relation between two
concepts" (B140). This pre-Kantian definition implied that all
judgments are of subject-predicate form; but in fact, as Kant points
out (here following the Stoic logicians), some judgments--e.g.,
disjunctive judgments, and hypothetical conditional
judgments--are truth-valued relational complexes of
subject-predicate judgments and thus, apparently, have essentially
*truth-functional* form, not subject-predicate form. This idea
later heavily influenced George Boole's ground-breaking view of
logic as a set of a priori "laws of thought" governing a
formal calculus of binary functions that mimic the
"bipolar" behavior of the classical truth and falsity of
propositions (Boole 1854). Perhaps even more importantly however, the
pre-Kantian definition also failed to explain the *unity* of a
judgment, and the difference between a judgment and a mere list of
concepts. So in order to solve this
"unity-of-the-judgment" problem--which later
re-surfaced as "the problem of the unity of the
proposition" in early analytic philosophy (Hylton 1984, Linsky
1992)--Kant offers a radically new conception of the judgment as
a higher-order cognitive binding function for different types of
lower-order objective representational content. In a pre-Critical
essay, "The False Subtlety of the Four Syllogistic
Figures," he says that a judgment is an act of logical
predication whereby a concept is applied to a thing, as expressed by
the copula 'is' or 'are' (2: 47). In his
logical textbook, the *Jasche Logic*, he says that it is a
representation of the unity of consciousness linking together several
other representations, or a representation of their relation in a
single concept (9: 101). And in the *Critique of Pure Reason*
he characterizes judgment at least four times:



> 
> Judgment is ... the mediate cognition of an object, hence the
> representation of a representation of it. In every judgment there is a
> concept that holds of many [representations], and that among this many
> also comprehends a given representation, which is then immediately
> referred to the object. (A68/B93)
> 



> 
> All judgments are ... functions of unity among our
> representations, since instead of an immediate representation a higher
> one, which comprehends this and other representations under itself, is
> used for the cognition of the object, and many possible cognitions are
> hereby drawn together into one. (A69/B94)
> 



> 
> A judgment is nothing other than the way to bring given cognitions to
> the **objective** unity of apperception. That is the aim
> of the copula **is** in them: to distinguish the
> objective unity of given representations from the subjective. (B141).
> 



> 
> [Pure general logic] deals with **concepts**,
> **judgments**, and **inferences**,
> corresponding exactly to the functions and order of those powers of
> the mind, which are comprehended under the broad designation of
> understanding in general... If the understanding in general is
> explained as the faculty of rules, then the power of judgment is the
> faculty of **subsuming** under rules, i.e., of
> determining whether something stands under a given rule (*casus
> datae legis*) or not. (A130-132/B170-172)
> 



Despite the superficial differences in emphasis and formulation, these
six characterizations all converge on the same basic account: a
judgment is a higher-order complex conscious cognition that refers to
objects either directly (via the essentially indexical content of
intuitions/non-conceptual cognitions)or indirectly (via the
essentially attributive or descriptive content of concepts); in which
concepts are predicated either of those objects or of other
constituent concepts; in which concepts are intrinsically related to
one another and to intuitional/non-conceptual cognitions by pure
general logical forms/pure concepts of the understanding that express
various modifications and, apparently, truth-functional compounds of
the predicative copula; which enters into inferences according to a
priori laws of pure general logic; which essentially involves both the
following of rules and the application of rules to the perceptual
objects picked out by intuition/non-conceptual cognition; and in which
a composite objective representation is generated and unified by the
higher-order executive mental processing of a single self-conscious
rational subject. The crucial take-away points here are (a) a
judgment's referential bottoming-out in
intuitions/non-conceptual cognitions, which thereby constitute
directly-referential singular terms in singular categorical judgments,
that cannot be semantically replaced by individual concepts or
definite descriptions without change or loss of meaning (contrast,
e.g., Thompson 1972 and Hanna 2001, ch. 4), (b) the "privileging
of predication" (Longuenesse 1998, 104) over other sorts of
logical operations, (c) the intrinsic logico-syntactic and
logico-semantic form of the judgment, based on modifications or
compound truth-functional relations of the predicative copula, (d) the
rule-like character of the judgment, (e) the judgment's unified
conscious objective representational (i.e., semantic) content, and
above all (f) its higher-order rationally self-conscious ground of
objective unity. As such, Kantian judgments are *neither*
merely psychological objects or processes (as in psychologistic
theories of judgment), *nor* are they essentially
mind-independent, abstract objects (as in platonistic theories of
judgment), *nor* again are they inherently assertoric takings
of propositions to be true (as, e.g., in Frege's theory of
judgment). Instead, Kantian judgments are intersubjectively shareable,
rationally communicable, cognitively-generated mental-act structures
or types whose logically-structured truth-apt semantic contents can be
the targets of many different kinds of epistemic or non-epistemic
propositional attitudes. 



As just noted, every judgment has an intrinsic logical *form*
that is both syntactic and semantic in nature, centered on
predication. Even more fundamentally however, every judgment also has
an "intension" (*Inhalt*) or semantic
*content*: the "proposition" (*Satz*). A
propositional content is not monolithic but rather a unified composite
of individually meaningful proper parts. More specifically, a
proposition is the logically well-formed and semantically
well-composed, truth-valued, unified objective representational
content of a judgment; and more generally it is "what is
judged" in the act of putting forward any sort of rational claim
about the world (9: 109) (14: 659-660) (24: 934). Although a
proposition is always generated by means of psychological processes,
it is *not*, however, psychologically private and
incommunicable: on the contrary, it is intersubjectively shareable and
rationally communicable, due to the fact that the very same
propositional form-and-content can be individually generated by many
different judging animals, provided they are all equipped with the
same basic cognitive architecture. In this way judgments for Kant are
*essentially* propositional cognitions, in that the primary
function of the faculty of judgment is just to generate these
logically well-formed, semantically well-composed, truth-valued,
intersubjectively shareable, rationally communicable, unified
objective representational contents.



Given the seminal role of the judgment's propositional content,
it is easy to see then that for Kant the propositional function of the
judgment is more basic than its inferential role--although every
judgment does indeed play an inferential role (Longuenesse 1998,
90-95)--and for this reason Kant's logical constants
(i.e., all, some, this/the, affirmation, propositional negation,
predicate-negation, the predicative copula, if-then, disjunction,
necessarily, possibly, and actually) are defined strictly in terms of
their specific roles in the propositional content of judgments, quite
apart from the ways those judgments can enter into inferences
(A69-76/B94-102). In recent years, however,
*inferentialist* treatments of Kant's theory of judgment
and Kant's logic, which treat the semantic contents and logical
constants of judgment as essentially dependent on and determined by
their inferential roles, have become increasingly popular and
influential (see, e.g., Landy 2009 and Leech 2012).


### 1.3 Judgments, objective validity, objective reality, and truth



The characteristically rational activity of taking-for-true implies
the subjective validity of a judgment, or its apparent meaningfulness
and apparent truth for an individual rational cognizer. By contrast,
the "objective validity" (*objektiv
Gultigkeit*) of a judgment is its empirical meaningfulness,
precisely because it is compositionally based on the empirical
"reference" (*Beziehung*)--whether singular or
comprehensional--of the basic constituent objective
representations of any judgment, namely intuitions and concepts. The
empirical reference of intuitions and concepts, in turn, is
necessarily constrained by the specifically aesthetic or sensible,
non-conceptual, non-discursive, and pre-rational or proto-rational
dimension of human experience, which itself is jointly determined by
(a) the brute givenness of material objects to our receptive capacity
for empirical intuition, via the relation of external affection, and
(b) the necessary and non-empirical forms of empirical intuition, our
representations of space and time (A19-22/B33-36), which
ultimately express the outer and inner sensory aspects of the
embodiment of our minds). In this way, an intuition is objectively
valid if and only if either (i) it directly refers to some individual
actual or possible external sensible object or to the subject's
phenomenally conscious inner response to this outer reference (this
accounts for the objective validity of *empirical* intuitions),
or else (ii) it represents a phenomenally immanent necessary condition
of empirical intuitions (this accounts for the objective validity of
the *forms* of intuition) (A239-240/B298-299). By
contrast, a concept is objectively valid if and only if either it
applies to some actual or possible objects of empirical intuition
(this accounts for the objective validity of *empirical*
concepts) or else it represents a necessary condition of empirical
concepts (this accounts for the objective validity of *pure*
concepts) (A239-240/B298-299,
A240-242/B299-300).



A necessary but not sufficient condition of the objective validity of
a judgment is its logico-syntactic well-formedness (grammatical
correctness) and logico-semantic well-formedness (sortal correctness)
(A73/98, A240-248/B300-305). So a judgment is objectively
valid if and only if it is logically well-formed and all of its
constituent intuitions and concepts are objectively valid
(A155-156/B194-195). Otherwise put, and fully spelled-out,
the objective validity of a judgment is its *anthropocentric
rational empirical referential meaningfulness*. Kant also
sometimes uses the notion of "objective reality"
(*objektive Realitat*) to characterize objectively valid
representations that apply specifically to actually or really existing
objects, and not to merely possible objects (A242 n.). True judgments
are thus objectively real propositions. Objective validity, in turn,
is a necessary but not sufficient condition of truth, and hence of
objectively real propositions, for false judgments are also
objectively valid (A58/B83). In this way the objective validity of a
judgment is equivalent to its *propositional truth-valuedness*,
but not equivalent to its propositional truth.



By contrast, all judgments that are not objectively valid are
"empty" (*leer*) or truth-valueless. Nevertheless,
it must be noted that for Kant empty judgments can still be rationally
intelligible and not in any way nonsensical, if all the concepts
contained within them are at least logically consistent or
"thinkable" (Bxxvi n.). In this way, e.g., some judgments
containing concepts of noumenal objects (things-in-themselves, or real
essences) or noumenal subjects (rational-agents-in-themselves, or
persons) are empirically meaningless and truth-valueless, hence empty,
yet *also* are rationally intelligible targets of what Kant
calls "doctrinal" belief (see the supplementary document
 Judging, Believing, and Scientific Knowing),
 and even, at least from a certain Critical meta-philosophical
standpoint, essential both to Kant's theoretical metaphysics
(A254-255/B309-310, A650-654/B678-682) and
also to his practical metaphysics of freedom and morality
(A530-558/B566-586).



So much for truth-valuedness: but what is truth? According to Kant,
truth is a predicate of whole judgments, and not a predicate of the
representational proper parts of judgments, i.e.,
intuitions/non-conceptual cognitions and concepts (A293/B350).
Furthermore we already know that objective validity is a necessary but
not sufficient condition of the truth of a judgment. Kant also holds
that logical consistency is a necessary but not sufficient condition
of the truth of a judgment (A60/B85). Most importantly however,
according to Kant the "nominal definition" of truth is
that it is the "agreement" or "correspondence"
(*Ubereinstimmung*) of a cognition (i.e., in this context,
an objectively valid judgment) with its object (A58/B82). Now a
Kantian nominal definition is a special type of analytic definition
that picks out the "logical essence" of that
concept--i.e., the generic and specific intensional criteria for
bringing things under that concept--but *without* also
picking out the "inner determinations" or real essences of
the things falling within the comprehension of that concept, which
would be the job of a *real* definition (9: 142-143). So
the nominal definition of truth means that for Kant truth *just
is* agreement or correspondence, which can then be further
unpacked as a relation between a judgment and an object such that (i)
the form or structure of the object is isomorphic with the
logico-syntactic and logico-semantic form of the proposition expressed
by the judgment, (ii) the judger cognitively orients herself in the
world by projecting the object under specific "points of
view" (*Gesichtspunkte*) or modes of presentation that
would also be typically cognitively associated with the constituent
concepts of the judgment by any other rational human animal in that
context (8: 134-137) (9: 57, 147) (24: 779), and (iii) the
object represented by the judgment really exists (Hanna 2006b, ch. 5).
Another way of putting this is to say that truth is *nothing but
the* *objective reality of the total propositional
form-and-content of the judgment*: that is, nothing but the real
existence of that which is precisely specified by the logico-syntactic
and logico-semantic features of the judgment taken together with the
judger's intersubjectively rationally communicable cognitive
orientation. Or in still other words, true judgments are *nothing
but ways of rationally projecting ourselves onto actual
truth-makers*. This is *not* what is nowadays called a
"deflationist" conception of truth, however, because Kant
is not saying that truth is nothing but asserting the corresponding
actual facts. On the contrary, for Kant truth is irreducible to merely
asserting the facts, because for him the concept of truth also
inherently expresses both the judger's fundamental rational
interest in "getting it right" (whether theoretically via
true judgment or practically via good intentional action) and also her
intersubjectively shareable and rationally communicable *cognitive
orientation*, as well as belonging intrinsically to the core moral
concept of *sincerity*.



In any case, the nominal definition of truth must be sharply
distinguished from the real definition of truth, i.e., the
"criterion" (*Kriterium*) of truth, which is a rule
for determining the truth or falsity of judgments in specific contexts
(A58/B82). According to Kant there is no all-purpose or absolutely
general criterion of truth (A58-59), such as the
"clarity-and-distinctness" criterion of the Cartesians.
Nevertheless there *are* special criteria of truth for each of
the basic classes of judgments: analytic judgments, synthetic a
posteriori (or empirical) judgments, and synthetic a priori judgments
(for more details about this threefold distinction and the special
truth-criteria, see
 Section 2).



The truth of empirical judgments is the bottom-level sort of truth for
Kant, in that all of the other kinds of truth presuppose it. In turn,
the proper object of an empirical judgment is an actual or possible
"object of experience" (*Gegenstand der
Erfahrung*), which is an empirical state-of-affairs, or a really
possible individual material object insofar as it has macroscopic
physical or "phenomenological" (in the Newtonian sense)
properties and can enter into causal or otherwise dynamical relations
in the spatiotemporal material world according to necessary laws of
nature (A176-218/B218-265). By the nominal definition of
truth as agreement or correspondence, this entails that actual objects
of experience are the *truth-makers* of empirical judgments. It
also leads to what Kant calls "the criterion of empirical
truth" which states that *since* the objectively valid
propositional content of an empirical judgment can be specified as a
necessary conceptual rule of sensory appearances, then *if*
that rule is effectively applied to the temporal succession of our
sensory representations of the phenomenal material world, *and*
that rule coheres with the causal-dynamic laws of nature,
*then* that judgment is true (A191/B236, A451/B479) (4: 290)
(18: 234).



See the supplementary documents:



> 
> 
> The Togetherness Principle, Kant's Conceptualism, and Kant's Non-Conceptualism
> 
> 
> 
> 
> Judging, Believing, and Scientific Knowing
> 
> 
> 
> 


## 2. Kinds of Judgments



One of the most controversial, influential, and striking parts of
Kant's theory of judgment is his multiple classification of
judgments according to kinds of logical form and kinds of semantic
content. Indeed the very importance of Kant's multiple
classification of judgments has sometimes led to the misconception
that his theory of judgment will stand or fall according to the fate
of, e.g., his analytic-synthetic distinction, or his doctrine of
synthetic a priori judgments. Important as these classifications are
however, it is crucial to remember that the core of Kant's
theory of judgment consists in the centrality thesis, the
priority-of-the-proposition thesis, and the transcendental idealism
thesis, all of which can still hold even if some of his
classifications of judgments are rejected.


### 2.1 Kinds of logical form



The modern conception of logical form--as found, e.g., in the
symbolic and mathematical logic of Gottlob Frege's
*Begriffsschrift* ("Conceptual Notation") (Frege
1972), Bertrand Russell and A.N. Whitehead's *Principia
Mathematica* (Whitehead and Russell 1962), and Ludwig
Wittgenstein's *Tractatus Logico-Philosophicus*
(Wittgenstein 1922)--owes much to Kant's conception of
logical form, if not so very much to his particular conception of
logic, which from a contemporary point of view can seem
"terrifyingly narrow-minded and mathematically trivial,"
as Allen Hazen has drily put it (Hazen 1999). On the other hand,
however, it is clearly true that Kant's conception of
*mathematical* form, which is found in his theory of pure or
formal intuition, substantially influenced Wittgenstein's view
of logical form in the *Tractatus* (Wittgenstein 1922, props.
2.013, 5.552, 5.61, and 6.13). There is an ongoing scholarly debate
about whether Kant's conception of mathematical form is a direct
expression of the narrow-mindedness of his logical theory, or instead
a direct expression of the striking originality of his philosophy of
mathematics (Parsons 1983, Friedman 1992, Shabel 2003, Hanna 2006b,
ch. 6, Shabel 2006). But even more importantly, Kant's deep idea
*that logic and logical form can exist only in the context of the
judging activities and judging capacities of rational human
animals*, has heavily influenced some heavily influential
philosophers of logic, linguists, philosophers of language, and
cognitive scientists from Boole and Wilhelm von Humboldt (Von Humboldt
1988), to Frege, the later Wittgenstein, and Noam Chomsky
(Wittgenstein 1953, para. 241-242, Chomsky 1975, Bell 1979, Bell
1987).


#### 2.1.1 Pure general logic and the table of judgments



As mentioned in
 Section 1,
 every judgment for Kant has an intrinsic logical form. These logical
forms correspond one-to-one to the pure concepts of the understanding
or categories, a claim which is argued-for in what Kant calls the
**metaphysical deduction** of the categories
(A76-83/B102-109, B159). On the basis of this, it is
possible to argue that all concepts, whether pure or empirical, have a
logical ground (Newton 2015). In any case, the total set of such
logical forms/pure concepts is the "table of judgments,"
which Kant also describes as "the functions of unity *in
judgments*" (A69/B94, emphasis added). He does this in order
to draw special attention to the fact that for him the very idea of a
logical form/pure concept is essentially judgment-based: logical form
is nothing but the intrinsic logico-syntactic and logico-semantic form
*of* and *in* a proposition. So for Kant the
propositional content of a judgment is more explanatorily basic than
its logical form or pure-conceptual structure.



The table of judgments, in turn, captures a fundamental part of the
science of pure general logic: *pure*, because it is a priori,
necessary, hence strictly universally true, and also without any
associated sensory content; *general*, because it is strictly
underdetermined by all objectively valid representational contents and
also abstracts away from all specific or particular differences
between represented objects (cf. MacFarlane 2002), and thereby
"has to do with nothing but the mere form of thinking"
(A54/B78); and *logic* because, in addition to the table of
judgments, it also systematically provides categorically normative
*conditio sine qua non* rules for the truth of judgments (i.e.,
the law of non-contradiction or logical consistency) and for valid
inference (i.e., the law of logical consequence)
(A52-55/B76-79) (9: 11-16).



In this connection, there are two crucial points to note about
Kant's pure general logic.



First, pure general logic is sharply distinct from
*transcendental* logic, in that, although both logics are pure
and a priori, whereas pure general logic is "general" in
that it is strictly underdetermined by all objectively valid
representational contents and also abstracts away from all specific or
particular differences between represented objects, hence is
*ontically unrestricted*, nevertheless transcendental logic is
"special" in that it is *ontically restricted*,
i.e., objectually-committed, and thereby presupposes the existence of
certain specific categories or kinds (including natural kinds) of
objects (A55-57/B79-82). In this way, transcendental logic
presupposes pure general logic, and is synthetic a priori, not
analytic. Some recent Kant-commentators, however, have argued that on
the contrary, pure general logic presupposes transcendental logic
(see, e.g., Rodl 2008, Tolley 2012), on the grounds that for
Kant, thought by its very nature is object-directed. But the
generality and inherently formal character of pure general logic is
fully consistent with its being objectively valid: hence the fact that
thought by its very nature is *object-directed* does not by
itself imply that the logic governing thought is *ontically
restricted* or objectually-committed.



Second, pure general logic is absolutely binding on any rational human
thinker and provides an unconditional logical *ought*: the laws
of logic are the categorically normative laws of thought for all
actual and possible rational animals. Thus pure general logic is both
a *formal* science and also a *moral science*, but not a
*natural science*. As such, pure general logic fully heeds the
lesson of the Naturalistic Fallacy, that is, the irreducibility of the
*ought* to the *is*. Correspondingly, just like the
unconditional moral *ought*, as expressed by the Categorical
Imperative, the logical *ought*, as expressed by, e.g., the law
of non-contradiction, is rarely correctly obeyed in the real world by
finite flawed thinkers like us, who commit logical fallacies and moral
sins with comparable frequency: sadly, *ought* does not entail
*is*. Still, as non-naturalistic, Kant's pure general
logic is irreducible to all contingent facts and especially to all
empirical psychological facts; hence his logic is thoroughly
anti-psychologistic, which exploits the flip-side of unconditional
obligation, whether logical or moral: happily, *is* does not
entail *ought*.



Kant's table of judgments lays out a (putatively) exhaustive
list of the different possible logical forms of propositions under
four major headings, each major heading containing three sub-kinds, as
follows.



> 
> *Table of Judgments*
> 1. Quantity of Judgments: Universal, Particular, Singular.
> 2. Quality: Affirmative, Negative, Infinite
> 3. Relation: Categorical, Hypothetical, Disjunctive
> 4. Modality: Problematic, Assertoric, Apodictic (A70/B95)
> 
> 
> 



Consistently with Kant's "privileging of
predication," it is arguable that his logical forms are all
either modifications or else truth-functional compounds of simple
monadic (i.e.,1-place) categorical (i.e., subject-predicate)
propositions of the general form "*Fs* are
*Gs*."



In this way, e.g., the three kinds of *quantity* of judgments
are supposed by Kant to capture the three basic ways in which the
comprehensions of the two constituent concepts of a simple monadic
categorical proposition are logically combined and separated. So Kant
says that universal judgments are of the form "All *Fs*
are *Gs*"; that particular judgments are of the form
"Some *F*s are *G*s"; and that singular
judgments are of the form "This *F* is *G*"
or "The *F* is *G*."



By contrast, the three kinds of *quality* of judgments are
supposed by Kant to capture the three basic ways in which the
constituent concepts of a simple monadic categorical judgment can be
either existentially posited or *gesetzt*, or else
existentially cancelled or *aufhebe*, by respectively assigning
non-empty actual extensions to concepts, or null actual extensions to
concepts (A594-595/622-623). So Kant says that affirmative
judgments are of the form "it is the case that *F*s are
*G*s" (or more simply: "*F*s are
*G*s"), negative judgments are of the form "no
*F*s are *G*s"; and infinite judgments are of the
form "*F*s are non-*G*s."



By contrast again, the three kinds of *relation* of judgments
are supposed by Kant to capture the three basic ways in which simple
1-place subject-predicate propositions can be either atomic
(elementary) or molecular (compound) in respect of their truth-values.
So Kant says that categorical judgments repeat the simple atomic
1-place subject-predicate form "*F*s are
*G*s"; molecular hypothetical judgments are of the form
"If *F*s are *G*s, then *H*s are
*I*s" (or: "If *P* then *Q*");
and molecular disjunctive judgments are of the form "*Fs*
are either *G*s or *H*s or ..." (where each
partition of the total domain is mutually exclusive and the total set
of partitions is exhaustive).



By contrast yet again and finally, the three kinds of
*modality* of a judgment are supposed by Kant to capture the
three basic ways in which the copula of a simple 1-place
subject-predicate proposition "contributes nothing to the
content of the judgment ... but rather concerns only the value of
the copula in relation to thinking in general"
(A74/B99-100). This doctrine might seem to confuse the three
propositional attitudes of "opining" (*Meinen*),
epistemic belief, and certainty (A820-823/B848-851), as
discussed in the supplementary document
 Judging, Believing, and Scientific Knowing,
 with the alethic modal notions of possibility, actuality, and
necessity. Or even worse, it might seem to psychologize modality.



And this in turn raises in a pointed way a general difficulty in the
common interpretation of Kant's theory of judgment: the tendency
to hold that his logic and theory of judgment are at bottom
epistemological or empirical psychological theories. But this common
interpretation, as specifically applied to Kant's view of the
modality of judgments, should be rejected for four reasons. First, he
explicitly isolates and discusses propositional attitudes in the
context of his epistemology of judgment and his ethics of belief, so
it is obvious that he does not confuse logical modality with
propositional attitudes. Second, he firmly rejects logical
psychologism, as we have already seen. Third, the notion of
"value" (*Wert*) here clearly means the
*truth*-value of a whole proposition, not its propositional
*content* specifically, which explains why a modal predicate
"contributes nothing to the content of a judgment," i.e.,
it contributes nothing to the *specific* content of a judgment
over and above its truth-value. Fourth and most importantly, the
notion of "thinking in general" for Kant is the conceptual
equivalent of Leibnizian logically possible worlds (Bxvii n.,
A573/B601). Thus the three kinds of modality of a judgment for Kant
are, at bottom, the three basic ways in which truth can be assigned to
simple 1-place subject-predicate propositions, or to non-categorical
sentential propositions, across logically possible
worlds--whether to some worlds (possibility), to this world alone
(actuality, as essentially indexically determined by human sensory
intuition/non-conceptual cognition), or to all worlds (necessity). So
Kant says that problematic judgments are of the form "Possibly,
*F*s are *G*s" (or: "Possibly
*P*"); assertoric judgments are of the form
"Actually, *F*s are *G*s" (or:
"Actually *P*"); and apodictic judgments are of the
form "Necessarily, *F*s are *G*s" (or:
"Necessarily *P*").



See the supplementary document:



> 
> Do the Apparent Limitations and Confusions of Kant's Logic Undermine his Theory of Judgment?
> 


### 2.2 Kinds of propositional content



For Kant, as we have seen, the propositional content of a judgment is
more basic than its logical form. The propositional content of a
judgment, in turn, can vary along at least three different dimensions:
(1) its relation to sensory content, (2) its relation to the
truth-conditions of propositions, and (3) its relation to the
conditions for objective validity.


#### 2.2.1 A priori judgments and a posteriori judgments



The notion of "cognitive content" for Kant has two sharply
distinct senses: (i) intension or *Inhalt*, which is objective
and representational (semantic content); and (ii) sensory matter or
*Materie*, which is subjective and non-representational,
reflecting only the immediate conscious response of the mind to the
external impressions or inputs that trigger the operations of the
faculty of sensibility (phenomenal qualitative content)
(A19-20/B34, A320/B376). To be sure, for Kant just as for the
Empiricists, all cognition "begins with" (*mit ...
anfange*) the raw data of sensory impressions. But in a crucial
departure from Empiricism and towards what might be called a
*mitigated rationalism*, Kant also holds that not all cognition
"arises from" (*entspringt ... aus*) sensory
impressions: so for him, a significant and unique contribution to both
the form and the objective representational content of cognition
arises from the innate spontaneous cognitive capacities (B1). This
notion of cognition's "arising from" either sensory
impressions or innate spontaneous cognitive capacities can best be
construed as a strict determination relation (similar to what is
nowadays called "strong supervenience") such that
*X* strictly determines *Y* if and only if the
*X*-features of something are sufficient for its
*Y*-features, and there cannot be a change in anything's
*Y*-features without a corresponding change in its
*X*-features. This allows us to say that a cognition is a
posteriori, empirical, or *dependent on sensory impressions and/or
contingent natural objects or facts* just in case it is strictly
determined in its form or in its semantic content by sensory
impressions and/or contingent natural objects or facts; but a
cognition is a priori, non-empirical, or *absolutely independent of
all sensory impressions and/or contingent natural objects or
facts* just in case it is not strictly determined in its form or
in its semantic content by sensory impressions and/or contingent
natural objects or facts and is instead strictly determined in its
form or in its semantic content by our innate spontaneous cognitive
faculties (B2-3). It should be noted that the apriority of a
cognition in this sense is perfectly consistent with all sorts of
associated sensory impressions and also with the actual presence of
sensory matter in that cognition, caused by contingent natural objects
or facts, so long as neither the form nor the semantic content is
strictly determined by those sensory impressions and/or contingent
natural objects or facts. "Pure" a priori cognitions are
those that in addition to being a priori or absolutely independent of
all sensory impressions and/or contingent natural objects or facts,
also contain no sensory matter whatsoever (B3). So in other words,
some but not all a priori cognitions are pure.



Applying these notions to judgments, it follows that a judgment is a
posteriori if and only if either its logical form or its propositional
content is strictly determined by sensory impressions and/or
contingent natural objects or facts; and a judgment is a priori if and
only if neither its logical form nor its propositional content is
strictly determined by sensory impressions and/or contingent natural
objects or facts, and both are instead strictly determined by our
innate spontaneous cognitive faculties, whether or not that cognition
also contains sensory matter. Kant also holds that a judgment is a
priori if and only if it is necessarily true (Axv, B3-4,
A76/B101). This strong connection between necessity and apriority
expresses (i) Kant's view that the contingency of a judgment is
bound up with the modal dependence of its semantic content on sensory
impressions and/or contingent natural objects or facts, i.e., its
aposteriority (B3), (ii) his view that necessity is equivalent with
strict universality or *strenge Allgemeinheit*, which he
defines in turn as a proposition's lack of any possible
counterexamples or falsity-makers (B4), and (iii) his view that
necessity entails truth (A75-76/B100-101). Furthermore
Kant explicitly holds that not only do a priori judgments really exist
in various sciences, including physics and legitimate (i.e.,
transcendental idealist) metaphysics, but also that there really are
some *pure* a priori judgments, e.g., in mathematics
(B4-5, B14-18).


#### 2.2.2 Analytic judgments and synthetic judgments



Kant's distinction between analytic and synthetic judgments is
the historical origin of, and therefore significantly related to,
but--crucially--not precisely equivalent, either in
intension or extension, with the nowadays more familiar
analytic-synthetic distinction, according to which (1) analyticity is
truth by virtue of linguistic meaning alone, exclusive of empirical
facts, (2) syntheticity is truth by virtue of empirical facts, and (3)
the necessary statement vs. contingent statement distinction is
formally and materially equivalent to the analytic-synthetic
distinction. By 1950 this more familiar distinction was accepted as
gospel truth by virtually all analytic philosophers: but in the two
decades after the publication of W.V.O. Quine's iconoclastic
"Two Dogmas of Empiricism" in 1951 (Quine 1961), it was
gradually replaced by the new-and-improved post-Quinean gospel truth
that there is no such thing as an acceptable analytic-synthetic
distinction. This plain historical fact is closely related to the
highly regrettable further fact that Kant's analytic-synthetic
distinction is nowadays often wrongly interpreted (i) in terms of the
more familiar and now largely discredited analytic-synthetic
distinction, and also (ii) as reducible to an epistemic distinction
between uninformatively or trivially true a priori judgments and
informative judgments. Ironically Frege, the father or grandfather of
analytic philosophy, was much nearer the mark in the *Foundations
of Arithmetic* when he correctly construed Kant's theory of
analyticity *semantically*, as a theory about necessary
internal relations between concepts; although at the same time he not
quite so correctly said that Kantian analyticity boils down to
"simply taking out of the box again what we have just put into
it" (Frege 1953, 101). Frege's 19th century
characterization of Kantian analyticity, it turns out, has significant
parallels with the 18th century Leibnizian and Wolffian theories of
conceptual and/or logical truth that heavily influenced Kant's
work on analyticity (Anderson 2015). Backing away now from Frege and
the Leibniz-Wolff tradition, however, the crucial fact is that
Kant's analytic-synthetic distinction concerns two irreducibly
different kinds of semantic content within objectively valid
propositions (Hanna 2001, chs. 3-4), and this distinction is
neither primarily epistemic in character (although it does have some
important epistemic implications [Hanna 2006b, 362-379]) nor
does it specifically concern the logical form of judgments (4:
266).



Frege regarded Kant's notion of analyticity as trivial; and,
correspondingly, it is also true that if the Leibniz-Wolff approach to
conceptual and/or logical truth largely determined Kant's theory
of analyticity, then Kant's notion of analyticity is
impoverished (Anderson 2015). But on the contrary Kant's notion
of analyticity is substantive, by virtue of five important ideas:
first, Kant's *pro-Leibnizian* idea that all concepts
have intensional microstructures, or what he calls "logical
essences" or "conceptual essences" (9: 61); second,
his *anti-Leibnizian* idea that logically possible worlds are
nothing but maximal logically consistent sets of concepts, not
things-in-themselves (A571-573/B599-601); third, his
*referentialist* idea that all grammatically well-formed,
sortally correct, and logically consistent concepts have non-empty
cross-possible-worlds extensions (a.k.a. "comprehensions")
(A239/B298-299) (9: 95-96); fourth, his *semantic
restrictionist* idea that all and only objectively valid
propositions have truth-values; and fifth, finally, and most
importantly, his *logical analyticity* idea that the notion of
analyticity covers not only the so-called "containment"of
predicate-concepts in subject-concepts in categorical propositions,
and not only the intensional identity of subject-concepts and
predicate-concepts, *but also* all the logical truths of
truth-functional logic and monadic predicate logic. Then for Kant a
judgment is analytic if and only if its propositional content is
necessarily true either by virtue of necessary internal relations
between its objectively valid conceptual microstructures and/or its
conceptual comprehensions, or by virtue of its truth-functional
logical connectives, or by virtue of its monadic predicate logical
connectives (Hanna 2001, ch. 3), leaving open the question of whether
for Kant all logical connectives are strictly truth-functional. In any
case, let this be repeated with strong emphasis: Kant does
*not* define analyticity in terms of either the containment or
the identity of concepts, which are at best sufficient conditions for
analyticity and *not* also necessary conditions for
analyticity. On the contrary, Kant explicitly states a universal,
necessary, and sufficient semantic criterion for the truth of analytic
judgments, namely that a judgment is analytically true if and only if
its denial entails a contradiction, in a broad sense of
"entailment" that includes intensional entailment and not
merely classical deductive entailment (A151/B190-191). This
criterion also directly connects the notion of an *analytic
truth* with the notion of a *logical truth* in a
correspondingly broad sense that fully includes the tautologies and
valid sentences of truth-functional logic and monadic predicate logic,
but is neither restricted to nor reducible to (with the addition of
"logical definitions" [Frege 1953], whatever *they*
actually turn out to be on Frege's account, which is not at all
clear [Benacerraf 1981]) the truth-functional tautologies and valid
sentences of classical polyadic predicate logic.



Needless to say, however, if one holds that the Kantian definition of
analyticity is truth-in-virtue-of-containment, and also that the
Kantian definition of syntheticity is
truth-in-virtue-of-non-containment, together with a Kantian
conceptualist view of the nature of judgment, then one's
conception of Kant's analytic and synthetic judgments will be
correspondingly different (Anderson 2004, Anderson 2005, Anderson
2009, Anderson 2015).



But what about syntheticity? Since for Kant the analytic-synthetic
distinction is exhaustive in the sense that every proposition is
either analytic or synthetic but not both, his two-part doctrine of
analyticity in turn provides him with a two-part negative doctrine of
syntheticity: A proposition is synthetic if and only if its truth is
*not* strictly determined by relations between its conceptual
microstructures or conceptual comprehensions alone, or by
truth-functional logic or monadic predicate logic alone (which for
Kant is expressively captured by the table of judgments and the table
of pure concepts of the understanding); and a judgment is
synthetically true if and only if it is true and its denial does
*not* entail a contradiction. But this negative
characterization of course does not tell us what the truth of
synthetic judgments positively consists in. In order to do this, Kant
directly connects the semantics of syntheticity with the semantics of
intuitions, just as he directly connects the semantics of analyticity
with the semantics of concepts (including both empirical concepts and
the pure concepts of the understanding). Then positively put, a
judgment is synthetic if and only if its meaning and its truth are
strictly determined by its constituent intuitions, whether empirical
intuitions or pure intuitions (A8, A154-155/B193-194,
A721/B749) (8: 245) (11: 38). This is not to say either that synthetic
judgments do not contain any concepts (in fact they always *do*
contain empirical or pure concepts), or even that the conceptual
components of a synthetic judgment are irrelevant to its meaning or
truth (in fact empirical or pure concepts always *are*
semantically relevant), but only to say that in a synthetic judgment
it is the intuitional components that *strictly determine* its
meaning and truth, not its empirical-conceptual or pure-conceptual
components. In short, a synthetic judgment is *an intuition-based
proposition*.


#### 2.2.3 Synthetic a priori judgments



Every reader of the *Critique of Pure Reason* knows that Kant
glosses his philosophical project in that book as a complete and
systematic answer to the question, "how are synthetic *a
priori* judgments possible?" (B19). Also every reader of the
first *Critique* knows that Kant asserts the existence of
synthetic a priori judgments in mathematics, physics, and metaphysics
(B14-18, A158/B197). But fewer readers are aware that this
assertion, whether right or wrong, is certainly the boldest and
perhaps also the most important claim in post-Cartesian metaphysics.
This is because it posits the thesis of *modal dualism*, or the
claim that there are two irreducibly different basic types of
necessary truth, in the face of the almost universally-held
counter-thesis of *modal monism*, or the claim that there is
one and only basic type of necessary truth, i.e., analytically or
logically necessary truth. Given Kant's theory of truth, modal
dualism also implies the worldly existence of two irreducibly
different types of modal facts as truth-makers for analytically and
synthetically necessary truths respectively. In short if Kant is
right, then there are fundamentally more things in heaven and earth
than modal monists are prepared to acknowledge. Moreover Kant holds
that all the basic statements of traditional metaphysics are, at least
in intention, synthetic a priori judgments (B18). Hence his famous
critique of traditional metaphysics in the Transcendental Dialectic is
nothing but a deepened and extended investigation of the possibility
of synthetic a priori judgments.



But what *is* a synthetic a priori judgment? Combining the a
priori-a posteriori distinction with the analytic-synthetic
distinction, Kant derives four possible kinds of judgment: (1)
analytic a priori, (2) analytic a posteriori, (3) synthetic a priori,
and (4) synthetic a posteriori. By virtue of the fact that analytic
judgments are necessarily true, and given Kant's thesis that
necessity entails apriority, it follows that all analytic judgments
are a priori and that there is no such thing as an analytic a
posteriori judgment. By contrast, synthetic judgments can be either a
priori or a posteriori. Synthetic a posteriori judgments are
empirical, contingent judgments, although they may vary widely as to
their degree of generality. Synthetic a priori judgments, by contrast,
are non-empirical, non-contingent judgments.



More precisely however, synthetic a priori judgments have three
essential features. First, because a synthetic a priori judgment is a
priori, its meaning and truth are strictly underdetermined by sensory
impressions and/or contingent natural objects or facts, and it is also
necessarily true. Second, because a synthetic a priori judgment is
synthetic, not analytic, its truth is not determined by
conceptual/truth-functional-logical/monadic-predicate-logical factors
alone, and its denial is logically consistent. Third, as is the case
with all synthetic judgments, the meaning and truth of a synthetic a
priori judgment is intuition-based. This third factor is the crucial
one. For while the meaning and truth of synthetic a posteriori
judgments is based on *empirical* *intuitions*, the
meaning and truth of synthetic a priori judgments is based on *pure
intuitions* or our a priori formal representations of space and
time (B73) (8: 245) (11: 38). Now since according to Kant our a priori
formal representations of space and time are both necessary conditions
of the possibility of human experience and *also* necessary
conditions of the objective validity or empirical meaningfulness of
judgments, which in turn confers truth-valuedness upon propositions,
it then follows that a synthetic a priori judgment is a proposition
that is true in all and only the humanly experienceable possible
worlds and truth-valueless otherwise (Hanna 2001, 239-245). By
sharp contrast, analytic judgments, as logical truths in either a
narrow (truth-functional or syllogistic) or broad (intensional logic)
sense, are true in all logically possible worlds, including those
logically possible worlds in which human experience is *not*
possible, i.e., the worlds containing non-phenomenal or non-apparent
entities, especially including things-in-themselves, i.e., the
"noumenal worlds."



So analytic and synthetic a priori judgments sharply differ not only
in the nature of their semantic content (i.e.,
concept-based/truth-functional-logic-based/monadic-predicate-logic-based
vs. intuition-based) but also in their modal scope (true in all
logically possible worlds vs. true in all and only humanly
experienceable worlds and truth-valueless otherwise). Nevertheless,
despite this sharp difference in modal scope--from which it
follows, perhaps surprisingly, that for Kant there are logically
possible worlds in which synthetic a priori propositions such as
"7+5=12" are thinkably deniable--since synthetic a
priori judgments are *either true or truth-valueless in every
logically possible world*, it also follows that they are *never
false in any logically possible world* and thus satisfy
Kant's general definition of a necessary truth, i.e., that a
proposition is necessary if and only if it is strictly universally
true, in that it is true in every member of a complete class of
possible worlds and has no possible counterexamples or falsity-makers
(Hanna 2001, ch. 5). Less abstractly and gallumphingly put, a
synthetic a priori judgment is *a necessary truth with a human
face*.



In the discussion so far, judgments are essentially identified with
their propositional contents. But according to Kant it is also
possible for a rational cognizer to *use* the very same
propositional content in different ways. The fundamental difference in
uses of judgments is between (a) theoretical judgments and (b)
non-theoretical judgments. But there are also some crucial differences
between theoretical uses of judgments. For a discussion of these kinds
of use, see the following supplementary document:



> 
> Kinds of Use
> 


## 3. The Metaphysics of Judgment: Transcendental Idealism



There is a very real sense in which Kant's positive metaphysics
in the *Critique of Pure Reason* is essentially an elaboration
of his theory of judgment: "it is not at all [traditional]
metaphysics that the *Critique* is doing but a whole new
science, never before attempted, namely the critique of an a priori
judging reason" (10: 340). This results directly from the
conjunction of the centrality thesis and the transcendental idealism
thesis: judgment is the central cognitive activity of the human mind,
and judgments are objectively valid and true if and only if the
metaphysics of transcendental idealism is correct. In this section,
the crucial connection between judgment and transcendental idealism
will be spelled out in more detail.


### 3.1 Judgment, transcendental idealism, and truth



Transcendental idealism is the conjunction of two theses: (1)
*cognitive idealism*, which says that all the proper objects of
human cognition are nothing but mind-dependent sensory appearances or
phenomena, not things-in-themselves or noumena (A369), and (2)
*representational transcendentalism* , which says that all
representations and their contents necessarily conform to the forms or
structures of our innate spontaneous cognitive capacities (Bxvi,
A11/B25) (4: 373 n.). There are weaker and stronger interpretations of
these theses (see, e.g., Allais 2015), but in any case transcendental
idealism in its *strongest* version directly entails that all
the objects of human experience are token-identical with
objectively-valid sensory representational contents:



> 
> You put the matter quite precisely when you say The content
> (*Innbegriff*) of a representation is itself the object; and
> the activity of the mind whereby the content of a representation is
> represented is what is meant by 'referring to the object. (11:
> 314)
> 



Longuenesse aptly dubs this Kantian thesis "the internalization
to representation of the object of representation" (Longuenesse
1998, 20, 108). But perhaps even more importantly, Kant's
"internalization to representation of the object of
representation" entails that all the basic phenomenal forms or
structures of those objects of experience are type-identical with the
forms or structures introduced into representations by the innately
pre-programmed spontaneous operations of our cognitive faculties, and
in particular with the spatiotemporal structures of our subjective
forms of sensory intuition. Indeed, Kant explicitly holds that space
and time are *nothing but* our subjective forms of intuition,
which is his controversial thesis of "the transcendental
ideality of space and time" (A28-30/B44-45,
A36/B52-53, A42-43/B59-60). The upshot is that
according to the strongest version of transcendental idealism, all the
objects of human experience are *nothing but what we represent them
to be, when we represent sensory objects according to the a priori
normative principles of our understanding and our reason*: so our
cognition does not conform to the objects we cognize, rather those
objects necessarily conform to our innate a priori
normatively-governed faculties of cognition (Bxvi,
A92/B125-126).



Now assume that this strongest version of transcendental idealism is
correct. Then add to this assumption Kant's centrality thesis,
to the effect that judgment is the central human cognitive faculty,
and also the priority-of-the-proposition thesis. It follows
immediately that all the objects of human experience are
token-identical with *the propositional contents of objectively
valid empirical judgments*, and also that all the basic phenomenal
forms or structures of objects of human experience are type-identical
with the spatiotemporal and logico-syntactic and logico-semantic forms
or structures that are inherent in the propositional contents of
empirical judgments, which we can now see to be forms or structures
that have been introduced directly into nature by the acts of the
cognitive faculties of sensibility, imagination, understanding,
apperception, and reason, *which are all brought together and fused
in the unifying act of judgment or thought* . In short, the
strongest version of Kant's transcendental idealism is also a
*judgment-based idealism*, according to which actual or
non-actual/merely possible empirical objects or states-of-affairs are
nothing but true or false empirical propositions, and according to
which the basic phenomenal contours of the world we cognize are
precisely the same as the innate intuitional, formal-syntactic, and
semantic contours of the several cognitive faculties that jointly
generate our judgments.



Kant's judgment-based idealism has some crucial consequences for
his theory of truth. If the strongest version of transcendental
idealism is correct, then to every true empirical judgment there
necessarily corresponds an actual empirical fact, and conversely, and
also to every true a priori judgment there necessarily corresponds
some objectively real conceptually-represented or
intuitionally-represented structure across a complete set of logically
or experientially possible worlds. What this means is that whereas
Kant's theory of truth is explicitly realistic at the empirical
level--which is what he calls his "empirical realism"
(A28/B44, A35/B52, A370-373)--in that actual empirical
facts or modal facts (whether these are conceptually-represented
logical world-structures or intuitionally-represented non-logical
world-structures) always present themselves as in some irreducible
respects external or extrinsic to our cognition, and therefore not
controlled by us, nevertheless at the transcendental level his theory
of truth is fully anti-realistic: transcendentally speaking, we
*impose* truth upon the world . In short, the strongest version
of transcendental idealism plus the centrality thesis plus the
priority-of-the-proposition thesis *jointly* necessarily
guarantee that all and only the cognitively well-generated judgments
are true. This is what Kant calls the "transcendental
truth" of judgments (A146/B185). Transcendental falsity, by
contrast, is always the result of some special idiosyncrasy or
accidental glitch in the cognitive generation of a given judgment, and
thus represents a mere "performance error" in the
operation of our cognitive faculties, and not a gap in our
transcendental cognitive "competence." Thus any sort of
serious skepticism at the transcendental level of Kant's theory
of judgment is automatically ruled out of court.


### 3.2 Is Kant a verificationist?



One important critical question that needs to be raised is whether, in
view of the strongest version of his transcendental idealism,
Kant's theory of judgment is reductionist in some basic
respects, and in particular whether he reduces the meaning or
propositional content of a judgment to a rule for confirming or
disconfirming the assertion of that propositional content in the
tribunal of sensory experience. This is of course the thesis of
verificationism. Several important Kant commentators--e.g., Bird
1962, Strawson 1966, and Stroud 1968--have held that Kant's
theory of judgment is verificationist. Familiar problems with
verificationism include its susceptibility to epistemic skepticism,
its commitment to an implausible coherence theory of truth, and
specific difficulties about how to confirm or disconfirm judgments
about the non-immediate past or future.



It cannot be denied that there are some verificationist strands in
Kant's theory. For one thing, his "criterion of empirical
truth" (see Section 1.3 above) is in effect verificationist.
Moreover, to the extent that both Kant's theory of
transcendental truth and also his verificationism are anti-realist and
judgment-based, there is at least an elective affinity if not
precisely an equivalence between the two doctrines. Nevertheless, Kant
is not a reductionist about meaning. In other words, he is not
committed to the thesis that the propositional content of a judgment
is *nothing but* a rule for confirming or disconfirming the
assertion of that propositional content in the tribunal of sensory
experience. While he does seem to be committed to the thesis that the
propositional content of a judgment will be empirically meaningful or
objectively valid *only if* it contains a rule for confirming
or disconfirming the assertion of that propositional content in the
tribunal of sensory experience, this does not by any means exhaust the
propositional content of that judgment. Over and above its
verificationist element, the propositional content of every judgment
also contains a "thick" or non-deflationary
correspondence-relation to relatively external or extrinsic actual
facts (see Section 1.3 above). Furthermore the propositional content
of every judgment contains a set of a priori logical forms deriving
from the pure understanding, as well as a higher-order a priori
rational subjective unity deriving from the faculty for apperception
or rational self-consciousness (see Section 2.1.1 above). What this
means is that Kant is at most a weak verificationist, and that the
verificationist elements of his theory of judgment are significantly
tempered by his semantic non-reductionism, his empirical realism, and
his mitigated rationalism.



A more complete picture of Kant's metaphysics of judgment is
obtained by sketching in accounts of judgments of experience and
transcendental judgments. These are discussed in the following
supplementary document:



> 
> Completing the Picture of Kant's Metaphysics of Judgment
> 


## 4. Problems and Prospects



The basic parts of Kant's theory of judgment are now all in
place. In this concluding section, we will look briefly at several
serious problems for Kant's theory. These problems, which come
to a head in the debate about Kant's conceptualism vs.
Kant's non-conceptualism (see the supplementary document
 The Togetherness Principle, Kant's Conceptualism, and Kant's Non-Conceptualism),
 all ultimately stem from the interplay between either the centrality
thesis or the priority-of-the-proposition thesis, and the
transcendental ideality thesis. This in turn suggests that the other
two parts of Kant's theory can be logically detached from his
transcendental idealism and defended independently of it.


### 4.1 The bottom-up problem: essentially non-conceptual intuitions, rogue objects, and the gap in the B Deduction



What can be called *the bottom-up problem* for Kant's
metaphysics of judgment follows directly from his non-conceptualism
(see the supplement
 The Togetherness Principle, Kant's Conceptualism, and Kant's Non-Conceptualism),
 and exposes a fundamental gap in the B Deduction. In our discussion
of the B Deduction (see the supplement
 Completing the Picture of Kant's Metaphysics of Judgment)
 it was noted that Kant's argument for the objective validity of
the categories will go through only if all the objects of human
intuition are necessarily *also* objects of human experience,
that is, are necessarily *also* objects correctly represented
by true judgments of experience, that is, are necessarily
*also* objects falling under all of the categories, or at the
very least under the principle of the Second Analogy of Experience,
which provides the criterion of the objectivity of objects of
experience. But if this claim fails, then there can in principle be
nomologically ill-behaved or "rogue" objects of human
intuition that fall outside the scope of judgments of experience and
thus also outside the categories, or at least outside the scope of the
Second Analogy. As several Kant-interpreters have pointed out, given
the possibility of essentially non-conceptual intuitions, then the B
Deduction is in big trouble (Kitcher 1990, Hanna 2016b). More
precisely, Kant's non-conceptualism entails that there can be
objectively valid empirical intuitions that are both autonomous from
and also independent of concepts, and thereby directly refer to
objects. Since the cognition of these objects does not require either
concepts or the faculty of understanding, and since these intuitions
consciously represent objects over and above any conceptual content
whatsoever, then some of these intuitions can pick out rogue objects
that fall outside the constraints of all the categories, and thereby
outside the constraints of the Second Analogy in particular. So it is
not true that the categories and principles of pure understanding
*necessarily* apply to all objects of conscious human
perception, and the categorial anarchy of at least some sensory
objects is really possible. Therefore the B Deduction is unsound. 


### 4.2 The top-down problem: judgment, transcendental affinity, and the systematic unity of nature



The bottom-up problem has a metaphysical mirror-image, which can be
called *the top-down problem*. This problem afflicts
Kant's transcendental doctrine of judgment, and consequently
also his theory of the principles of pure understanding (see the
supplement
 Completing the Picture of Kant's Metaphysics of Judgment).
 The worry here is simply that even allowing for the transcendental
schematism of the judgment, there is still no absolute guarantee that
a given universal transcendental principle or transcendental concept
of the understanding, construed as a rule for ordering sensory
appearances or sensory objects, has been *completely* applied
to sensory appearances or objects. In other words, even allowing for
his transcendental doctrine of the judgment, Kant has not given us
good reason to think that there cannot be any sensory appearances or
objects that fail to be subsumed under the transcendental principles
of nature. In the *Critique of Pure Reason*, Kant calls the
specifically causal-law-governed or nomological interconnection of all
sensory appearances or objects under transcendental principles the
"transcendental affinity"of the sensory manifold of
intuitions (A114). In the A edition of the first Critique, Kant
asserts that if the categories are objectively valid, then the
transcendental affinity of the manifold automatically follows. Then,
assuming the strongest version of transcendental idealism, he further
asserts that from transcendental affinity, an "empirical
affinity" of the sensory manifold of intuitions also directly
follows (A115). Now since empirical affinity is the complete
application to actual empirical nature of the system of causal laws
under transcendental principles, it follows that empirical affinity is
the same as *the systematic unity of nature*. So Kant is saying
that the systematic unity of nature is a trivial consequence of
transcendental affinity.



In the first *Critique*'s Appendix to the Transcendental
Dialectic however, Kant quietly but very significantly backtracks on
this crucial point and treats the principle of the systematic unity of
nature as stemming only from a *regulative* but not a
constitutive use of judgment, although this principle is also asserted
to have some sort of transcendental force (see the supplement
 Kinds of Use).
 Then in the first Introduction to the *Critique of the Power of
Judgment*, Kant explicitly says that



> 
> [it] is quite possible in itself (at least as far as the understanding
> can make out a priori), [that] the multiplicity of these [empirical]
> laws, along with the natural forms corresponding to them, being
> infinitely great, [could] ... present to us a raw chaotic
> aggregate and not the least trace of a system, even though we must
> presuppose such a system in accordance with transcendental laws. (20:
> 209)
> 



In other words, now Kant is saying that the transcendental affinity of
the manifold does *not* entail an empirical affinity of the
manifold or the systematic unity of nature. To be sure, in the third
*Critique*, he also explicitly ties together the principle of
systematic unity with the regulative use of reflective judgments of
taste, and says that it is a subjectively necessary transcendental
principle presupposed by legitimate judgments of taste (see the
supplement
 Kinds of Use).
 But if the principle of systematic unity is only subjectively and not
in fact *objectively* necessary, then Kant has *not*
shown us that the system of causal laws of nature *must be*
completely applied to sensory appearances or objects. Rather he has
shown only that we *must epistemically believe it to be*
completely applied to sensory appearances or objects. So there remains
the real possibility of relatively or absolutely chaotic aggregates of
sensory appearances or objects that are not subsumed or even in
principle cannot be subsumed under the transcendental affinity of the
manifold, i.e., the real possibility of the categorial anarchy of
rogue objects. In other words, for all that Kant has argued, and by
his own reckoning, even assuming transcendental affinity there might
still be no complete application of transcendental laws to nature. So
the transcendental schematism of the pure concepts is insufficient to
bridge the gap between categories and sensory appearances, and the
transcendental doctrine of judgment fails.


### 4.3 The dream-skeptical problem: judgment, problematic idealism, and the gap in the Second Analogy



As we saw in the supplement
 Completing the Picture of Kant's Metaphysics of Judgment,
 the Second Analogy of Experience, if true, guarantees both the
objectivity and the universal diachronic or temporally successive
causal necessitation of objects of experience and all of their parts,
under natural laws. As we also saw in Section 1.3, the
"criterion of empirical truth" for a judgment of
experience says that since the objectively valid propositional content
of an empirical judgment can be specified as a necessary conceptual
rule of sensory appearances or objects, then *if* that rule is
effectively applied to the temporal succession of our sensory
representations of the phenomenal material world, *and* that
rule coheres with the causal-dynamic laws of nature, *then*
that judgment is true. And finally, as we also saw in Section 3.1, the
centrality thesis, the priority-of-the-proposition thesis, and the
transcendental idealism thesis jointly entail the
"transcendental truth" of judgment, which is that
necessarily every well-generated judgment of experience is true and
corresponds to an actual object of experience, that is, to an actual
empirical fact.



But here is a simple objection to this three-part doctrine, borrowed
from Descartes's famous "dream skepticism" in the
first of the *Meditations on First Philosophy*. Kant calls this
form of skepticism "problematic idealism" (B274). To
generate the relevant version of problematic idealism, suppose that
all the sensory appearances or objects currently falling under the
Second Analogy, the criterion of empirical truth, and the principle of
transcendental truth are *nothing but causally well-ordered parts
of my inner sense alone*. Then any object of experience
corresponding to my currently true judgment of experience might be
nothing but a very coherent dream or a hallucination. Nothing Kant has
said can rule this out. Even the famous Refutation of Idealism in the
first *Critique*, if sound, says only that "inner
experience is possible only through outer experience in general"
(B278-279), and Kant explicitly concedes that at any given time,
for all we know, we could be dreaming or hallucinating:



> 
> from the fact that the existence of outer objects is required for the
> possibility of a determinate consciousness of our self it does not
> follow that every intuitive representation of outer things includes at
> the same time their existence, for that may well be the mere effect of
> the imagination (in dreams as well as delusions). (B278)
> 



So even if inner experience and outer experience are necessarily
connected in general, the truth and objectivity of any
*particular* judgment of experience, by Kant's own
criteria for truth and objectivity, are consistent with the
possibility that the particular object of experience corresponding to
that judgment is nothing but very coherent dream or a hallucination.
After all, I can perfectly well *dream or hallucinate* a boat
going downstream, as well as actually *seeing* one. It is true
that Kant does remark in the General Note on the System of Principles
in the B edition of the first *Critique* that "in order
to understand the possibility of things in accordance with the
categories, and thus to establish the objective reality of the latter,
we do not merely need intuitions, but always outer intuitions"
(B291). This seems correct. But unfortunately, given what Kant says at
B278, nothing in his transcendentally idealistic metaphysics of
judgment will guarantee that any set of sensory appearances or objects
satisfying his criteria for the truth and objectivity of judgments of
experience on any particular occasion will in fact be material objects
in space corresponding to outer intuitions, and not merely causally
well-ordered mental imagery corresponding to inner intuitions, i.e.,
mere "phantoms of my brain." So the Second Analogy's
criterion of objectivity is ultimately insufficient to yield the
empirical truth of judgments of experience, despite Kant's
explicit claim that this criterion does yield both their objective
validity and their empirical truth (A202/B247).


### 4.4 Conclusion: judgment without strong transcendental idealism?



As we have seen in Sections 4.1 to 4.3, Kant's theory of
judgment leads to at least three serious problems when it is taken in
conjunction with the issue about his conceptualism vs. his
non-conceptualism (in the supplement
 The Togetherness Principle, Kant's Conceptualism, and Kant's Non-Conceptualism)
 and his metaphysics of strong transcendental idealism (Section 3.1
and the supplement
 Completing the Picture of Kant's Metaphysics of Judgment).
 Does this mean his theory of judgment is philosophically unacceptable
and at best an antiquarian curiosity of 18th century German
philosophy? No. This is because it seems very likely that the problems
in Kant's theory of judgment are principally due to his
conjoining the centrality thesis and the priority-of-the-proposition
thesis with the thesis of transcendental idealism. But suppose that
the strongest version of transcendental idealism is false, and that
the transcendental idealism thesis is either logically detached from
the other two theses or else retained but instead based on a
significantly weaker version of transcendental idealism (Hanna 2006b,
ch. 5): what remains? We are left with a general Kantian theory of
human rationality that is essentially oriented towards judgment, and
then in turn with specific Kantian accounts of the nature of judgment
and of the various irreducibly different kinds of judgment, that are
essentially oriented towards the anthropocentric empirical
meaningfulness and truth of the proposition. As such, Kant's
theory of judgment is thoroughly cognitivist but also
anti-psychologistic and anti-platonistic, and it thereby smoothly
combines the several "faces" of judgment into a unified
doctrine. So the fact that Kantian non-conceptualism (see the
supplement
 The Togetherness Principle, Kant's Conceptualism, and Kant's Non-Conceptualism)
 makes serious trouble for the B Deduction (Section 4.1), together
with the further fact that the strongest version of transcendental
idealism is very likely false--since the unqualified
transcendental ideality thesis, when conjoined with the centrality
thesis and the priority-of-the-proposition thesis, collectively entail
contradictions in Kant's theory that are not entailed by the
conjunction of the other two theses alone--do not ultimately
compromise the inherent philosophical interest, contemporary
relevance, and critical defensibility of the other basic parts of
Kant's theory of judgment.