RATIONALITY
AND LOGIC
ROBERT HANNA
Rationality and Logic
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Rationality and Logic
Robert Hanna
A Bradford Book
The MIT Press
Cambridge, Massachusetts
London, England
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© 2006 Massachusetts Institute of Technology
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This book was set in Sabon by SPI Publisher Services and was printed and bound in
the United States of America.
Library of Congress Cataloging-in-Publication Data
Hanna, Robert, 1957–.
Rationality and logic / Robert Hanna.
p. cm.
“A Bradford book.”
Includes bibliographical references and index.
ISBN 0-262-08349-3––ISBN 978-0-262-08349-2 (hc : alk. paper)
1. Logic. 2. Psychologism. 3. Reasoning (Psychology). I. Title.

volved many extended visits to the domains of logical theory and cognitive
psychology. But although I am a philosopher who by virtue of a deep inter-
est in human rationality is also deeply interested in logic and cognition, I am
neither a professional logician nor a professional cognitive psychologist. So
I want to make it very clear in advance that I am drawing and relying even
more heavily than is usual for philosophers on the theoretical expertise of
others. I hope to make my contribution at the synoptic level of the Big
Picture, and then turn this project back over to the specialists as a new and
important joint research program.
I am very grateful to the following people for conversations or correspon-
dence on and around my topic: Sean Anderson, Luc Bovens, Nicholas Denyer,
Christopher Green, Neil Manson, Arlo Murphy, Graham Oddie, Alex Oliver,
Eric Olson, Onora O’Neill, James Russell, Peter Strawson, Evan Thompson,
Dana Vanzanten, John Vejsada, and Jessica Wilson. Shards of the material
were presented to appropriately and helpfully skeptical audiences in talks at
Cambridge University; King’s College London; Trinity College Dublin; and
York University, Canada. Several of the central arguments were first sketched
or talked out during a visiting fellowship at Clare Hall, Cambridge, in
Michaelmas term 1998.
Institutionally speaking, the Social Sciences and Humanities Research
Council of Canada and York University generously gave me research grants
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for a sabbatical leave from York in 1998–1999; Fitzwilliam College,
Cambridge, generously gave me visiting fellowships for Lent term 2000,
Lent term 2001, and the academic year 2003–2004; and the Faculty of
Philosophy at the University of Cambridge generously gave me the unique
opportunity to lecture on Wittgenstein’s Tractatus and Investigations, back
to back, during Michaelmas term 2003 and Lent term 2004.
Personally speaking, Graham Oddie gave me encouragement at a crucial
moment. Thanks mate.

—Aristotle
1
Logic is a science of reason a science a priori of the necessary laws of thought, not
in regard to particular objects, however, but to all objects in general;—hence a science
of the correct use of the understanding and of reason in general, not subjectively,
however, i.e., not according to empirical (psychological) principles for how the under-
standing does think, but objectively, i.e., according to principles a priori for how it
ought to think.
—Immanuel Kant
2
[T]he word Logic in its primal sense means the Science of the Laws of Thought as
expressed. Considered in this sense, Logic is conversant about all thought which
admits of expression; whether that expression be effected by the signs of common lan-
guage or by the symbolic language of the mathematician.
—George Boole
3
If sheer logic is not conclusive, what is?
—W. V. O. Quine
4
The logical notions are embedded in our deepest nature, in the very form of our lan-
guage and thought, which is presumably why we can understand some kinds of logi-
cal systems quite readily, whereas others are inaccessible to us without considerable
effort . . . if at all.
—Noam Chomsky
5
For all we now know, cognition is saturated with rationality through and through.
—Jerry Fodor
6
This book is a philosophical study of the relation between human rationality
and logic. Its two central claims are (i) that logic is cognitively constructed

8
Of course philosophy, logic, and psychology have changed a lot since
those days. Most philosophers gave up classical analysis and replaced it with
scientific naturalism: the doctrine that all metaphysical, epistemic, and
methodological questions can ultimately be answered by the natural sciences
alone, without appeal to supernatural facts.
9
Most logicians went from
thinking that all logic is classical or elementary
10
to thinking that logic can
be conservatively “extended”
11
or radically “deviant,”
12
or even mind-blow-
ingly “paraconsistent”
13
or “dialetheic.”
14
And most psychologists dropped
behaviorism and adopted cognitivism: the thesis that the rational human
mind is essentially an active innately specified information-processor.
15
In other words, the philosophers, logicians, and psychologists loosened up
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significantly and moved on. But the old myths die hard. Even now, it remains
an almost unchallenged axiom of conventional philosophical wisdom that
the logical and the psychological are intrinsically incompatible.

Therefore, all politicians are liars.
Actually, Aristotle focuses not on concrete or complete syllogisms like these
three, but instead on abstracted or schematic syllogisms; and for special
Introduction xiii
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metaphysical and epistemological reasons, he was interested fundamentally
in general propositions and the logical import of general referring terms. But,
for expository convenience, we can also add to the Aristotelian notion of the
syllogism the later Stoic interests in the logical behavior of truth-functional
connectives (such as “not,” “and,” and “if
then”) and the logical import
of names, and derive schematic versions of the three syllogisms listed above:
All As are Bs.
a is an A.
Therefore, a is a B.
All As are Bs.
All Bs are Cs.
Therefore, all As are Cs.
If P, then Q.
P.
Therefore, Q.
Here the schematization of a concrete or complete syllogism is obtained by
uniformly substituting distinct capital letters (say, near the middle of the
alphabet) for distinct sentences;
16
distinct capital letters (say, near the begin-
ning of the alphabet) for distinct predicates; and distinct lowercase letters
(ditto) for distinct individual names. The alphabetic letters are nonlogical
constants. The words left over after the uniform substitution of nonlogical
constants for predicates, sentences, or individual names are logical con-

clusion of a valid argument is the relation of consequence.
17
Thus logic is the
science of the necessary relation of consequence.
So much for a preliminary internal characterization of the science of logic.
But what about the specifically philosophical question about the nature of
logic? My answer is that the nature of logic is explained by the logic faculty
thesis: logic is cognitively constructed by rational animals.
Obviously the fundamental notion lying behind this thesis is that of a
rational animal. For my purposes animals are sentient living organisms and for
simplicity’s sake I shall assume unless otherwise specified that all animals are
sound, that is, intact and mature. Even so, only some animals in this sense are
rational. On my view, rational animals are conscious, rule-following,
18
inten-
tional (that is, possessing capacities for object-directed cognition and purposive
action), volitional (possessing a capacity for willing),
19
self-evaluating, self-
justifying, self-legislating, reasons-giving, reasons-sensitive, and reflectively self-
conscious—or, for short, “normative-reflective”
20
—animals, whose inner and
outer lives alike are sharply constrained by their possession of concepts express-
ing strict modality. Modality in the philosophical sense comprises the concepts
of necessity, possibility, and contingency. Strict modality, in turn, includes the
concepts of logical necessity (truth in all logically possible worlds),
21
epistemic
necessity (certainty or indubitability), and deontic necessity (unconditional

talistic sense of rationality, between (a
1
) the rationality of animals, (a
2
), the
rationality of mental episodes or acts, and (a
3
) the rationality of mental
states. The important contrast here is that it is possible for something to be
a rational animal by having an overall mental capacity for rationality, yet fail
to be occurrently rational with respect to some of its mental episodes or men-
tal states, as in the case of someone who completely loses his temper tem-
porarily. Conversely, it is possible for an animal to be occurrently rational
with respect to some of its mental episodes or states, but lack an overall men-
tal capacity for rationality, as in the case of certain sorts of mental illness.
This point in turn implies another useful distinction, again within the men-
talistic sense of rationality, between (a
5
) an animal’s mental capacity for
rationality, and (a
6
) occurrent rationality with respect to the mental episodes
or mental states of an animal. And finally, for completeness, we can also dis-
tinguish, within occurrent mentalistic rationality, between (a
7
) the occurrent
rationality of mental episode or state types, and (a
8
) the occurrent rational-
ity of mental episode or state tokens. Here the contrast is that it is possible

term of art, “reflective equilibrium”) across a network or web of beliefs,
desires, emotions, intentions, and volitions.
25
In historical terms, this is the
Hegelian conception of rationality, according to which “the truth is the
whole.” And finally, in the instrumental sense, rationality means the posses-
sion of a capacity for generating or recognizing contingent truths, a posteri-
ori beliefs, contextually normative rules, consequentialist obligations, and
hypothetical “ought”-claims.
26
Put historically, this is the Humean concep-
tion of rationality, according to which “reason is the slave of the passions.”
The crucial three-way difference here is that whereas in the principled
sense, rationality means generating or recognizing rules that are absolute or
unconditional, in the holistic sense, by contrast, rationality means generating
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or recognizing rules or laws that are merely thoroughly interdependent or
mutually conditioned (hence none of those rules or laws can have a greater
degree of necessity or certainty, or be more binding, than the modally or
epistemically weakest proposition in the total holistic network of rules or
laws), and, by another contrast, rationality in the instrumental sense means
generating or recognizing rules that are merely empirically regular or condi-
tional (hence none of those rules or laws can be fully necessary or certain or
binding).
Unless otherwise noted, in what follows I will focus primarily on the men-
talistic, meeting-the-minimal-standards, and principled senses of rationality.
This is not to say that I reject or wish to depreciate in any way the proce-
dural, meeting-the-maximal-or-ideal-standards, holistic, or instrumental
senses of rationality. On the contrary, I am saying only that rationality in the

But it must also be frankly admitted that if someone upon serious reflection
simply does not believe that there is any such thing as rationality per se or
human rationality in particular, or that these are pseudo-concepts that ought
to be eliminated, then there is probably little I can do to convince him. I am
assuming that the existence of rationality and human rationality are primi-
tive and irreducible facts, and that as a consequence the prima facie case for
their reality and conceptual integrity is far more compelling than any
attempt to reject or eliminate them. Nevertheless, even allowing that it is
cognitively coherent to try to challenge rationality, a rationality-skeptic or
rationality-eliminativist might still find it interesting to inquire into the
extent that the nature of logic could be explained, if one were to take human
rationality seriously.
Whether or not there are rational animals other than humans, rational
human animals as a matter of fact constitute the basic class of cognizers or
thinkers studied by cognitive psychology. So if I am correct about the con-
nection between rationality and logic, it follows that the nature of logic is
significantly revealed to us by cognitive psychology. Correspondingly, I call
the overall view expressed by the conjunction of my two central claims log-
ical cognitivism.
Logical cognitivism has two important and rather controversial conse-
quences. First, the philosophers must reopen their door and civilly invite
the psychologists back in. As some people have been saying for two or
three decades now, we are all colleagues working in the very same metadis-
cipline: cognitive science. On this picture, analytic philosophy is at bottom
the same as the philosophy of rational human cognition. Second, however,
and perhaps even more controversially, a reconciliation between philoso-
phy and psychology by way of logical cognitivism must also be expected to
change cognitive science itself quite radically. Wittgenstein pregnantly
remarks in the Tractatus that “logic precedes every experience—that some-
thing is so.”

natural sciences cannot in and of themselves provide the foundations of cog-
nitive science. It is significantly odd that contemporary conventional philo-
sophical wisdom should include, simultaneously, strong commitments to
scientific naturalism and to the assumption that the logical and the psycho-
logical are incompatible.
31
I am interested in trying to formulate and defend
the broadly Kantian theory
32
of human rationality and logic that results if
we firmly reject both of these assumptions.
It may be useful to the reader, before pressing on, to have a sketch of the
overall argument in front of her.
In the first three chapters I explore three different philosophical approaches
to the nature of logic, each in the form of a basic problem. Chapter 1 deals
with the problem of logical psychologism: what is the relation between the
logical and the psychogical? Here I argue that logical psychologism is a
species of scientific naturalism; that scientific naturalism about logic is false;
and that logical cognitivism can effectively avoid both logical scientific natu-
ralism and the equally but oppositely flawed doctrine of logical platonism.
Chapter 2 addresses what I call the e pluribus unum problem: how can we
reconcile the unity of logic with the plurality of logical systems distinct from
classical or elementary logic? I argue that, despite their deep differences, all
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logical systems—whether classical, extended, or deviant—must presuppose a
single universal protologic, distinct in structure from all classical or nonclas-
sical systems, that is used to construct those systems. I then propose that this
protologic is contained in the logic faculty. If correct, my proposal implies
that the precise structural description of this protologic can be turned over to

tuition, in response to natural extensions of Wittgenstein’s famous worry
about “following a rule,” and Paul Benacerraf’s almost equally famous
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worry about reconciling our face-value or standard semantics of mathemat-
ical truth with our best epistemology of intuitive knowledge.
The seventh and last chapter subsumes the themes of the earlier chapters
under a discussion of the normativity of logic. The central claim is that logic
is a moral or “prescriptive” science and not merely a factual or “descriptive”
one, because the principles and concepts of the single universal protologic,
whatever they turn out to be, must be intrinsically categorically normative—
unconditionally obligatory—for human reasoning. The proper construal of
this claim leads to three further claims. First, the obvious fact that humans
persistently make logical gaffes does not count in any way against their being
logical animals but, on the contrary, counts all the more strongly in favor of
it: only a logical animal would ever care about committing fallacies, just as
only a moral animal would ever care about committing sins. Second, the obvi-
ous gap between abstract logical systems and concrete human reasoning does
not entail, as Gilbert Harman has argued, that logic has little or nothing to
do with reasoning. Third and finally, attempts by neo-Nietzscheans (and also
by some contemporary cognitive scientists) to defend the skeptical thesis that
humans are irrational and could at least in principle become logic-liberated
animals, because their logical reasoning abilities are nothing but expressions
of “the will-to-power” (or: “mechanisms of natural selection”), and because
logic itself is nothing but a social construct (or: the result of using “social con-
tract schemas”), while surprisingly resistant to philososophical refutation,
ultimately fail because they are cognitively self-defeating.
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Rationality and Logic