A Priori and A Posteriori

The terms "a priori" and "a posteriori" refer primarily to how or on
what basis a proposition might be known. A proposition is knowable a
priori if it is knowable independently of experience. A proposition is
knowable a posteriori if it is knowable on the basis of experience.
The a priori/a posteriori distinction is epistemological and should
not be confused with the metaphysical distinction between the
necessary and the contingent or the semantical or logical distinction
between the analytic and the synthetic. Two aspects of the a priori/a
posteriori distinction require clarification: the conception of
experience on which the distinction turns; and the sense in which a
priori knowledge is independent of such experience. The latter gives
rise to important questions regarding the positive basis of a priori
knowledge.

1. An Initial Characterization

A priori" and "a posteriori" refer primarily to how, or on what basis,
a proposition might be known. In general terms, a proposition is
knowable a priori if it is knowable independently of experience, while
a proposition knowable a posteriori is knowable on the basis of
experience. The distinction between a priori and a posteriori
knowledge thus broadly corresponds to the distinction between
empirical and nonempirical knowledge.

The a priori/a posteriori distinction is sometimes applied to things
other than ways of knowing, for instance, to propositions and
arguments. An a priori proposition is one that is knowable a priori
and an a priori argument is one the premises of which are a priori
propositions. Correspondingly, an a posteriori proposition is knowable
a posteriori, while an a posteriori argument is one the premises of
which are a posteriori propositions. (An argument is typically
regarded as a posteriori if it is comprised of a combination of a
priori and a posteriori premises.) The a priori/a posteriori
distinction has also been applied to concepts. An a priori concept is
one that can be acquired independently of experience, which may – but
need not – involve its being innate, while the acquisition of an a
posteriori concept requires experience.

The component of knowledge to which the a priori/a posteriori
distinction is immediately relevant is that of justification or
warrant. (These terms are used synonymously here and refer to the main
component of knowledge beyond that of true belief.) To say that a
person knows a given proposition a priori is to say that her
justification for believing this proposition is independent of
experience. According to the traditional view of justification, to be
justified in believing something is to have an epistemic reason to
support it, a reason for thinking it is true. Thus, to be a priori
justified in believing a given proposition is to have a reason for
thinking that the proposition is true that does not emerge or derive
from experience. By contrast, to be a posteriori justified is to have
a reason for thinking that a given proposition is true that does
emerge or derive from experience. (See Section 6 below for two
accounts of the a priori/a posteriori distinction that do not
presuppose this traditional conception of justification.) Examples of
a posteriori justification include many ordinary perceptual, memorial,
and introspective beliefs, as well as belief in many of the claims of
the natural sciences. My belief that it is presently raining, that I
administered an exam this morning, that humans tend to dislike pain,
that water is H2O, and that dinosaurs existed, are all examples of a
posteriori justification. I have good reasons to support each of these
claims and these reasons emerge from my own experience or from that of
others. These beliefs stand in contrast with the following: all
bachelors are unmarried; cubes have six sides; if today is Tuesday
then today is not Thursday; red is a color; seven plus five equals
twelve. I have good reasons for thinking each of these claims is true,
but the reasons do not appear to derive from experience. Rather, I
seem able to see or apprehend the truth of these claims just by
reflecting on their content.

The description of a priori justification as justification independent
of experience is of course entirely negative, for nothing about the
positive or actual basis of such justification is revealed. But the
examples of a priori justification noted above do suggest a more
positive characterization, namely, that a priori justification emerges
from pure thought or reason. Once the meaning of the relevant terms is
understood, it is evident on the basis of pure thought that if today
is Tuesday then today is not Thursday, or when seven is added to five
the resulting sum must be twelve. We can thus refine the
characterization of a priori justification as follows: one is a priori
justified in believing a given proposition if, on the basis of pure
thought or reason, one has a reason to think that the proposition is
true.

These initial considerations of the a priori/a posteriori distinction
suggest a number of important avenues of investigation. For instance,
on what kind of experience does a posteriori justification depend? In
what sense is a priori justification independent of this kind of
experience? And is a more epistemically illuminating account of the
positive character of a priori justification available: one that
explains how or in virtue of what pure thought or reason might
generate epistemic reasons? But before turning to these issues, the a
priori/a posteriori distinction must be differentiated from two
related distinctions with which it is sometimes confused:
analytic/synthetic; and necessary/contingent.
2. The Analytic/Synthetic Distinction

The analytic/synthetic distinction has been explicated in numerous
ways and while some have deemed it fundamentally misguided (e.g.,
Quine 1961), it is still employed by a number of philosophers today.
One standard way of marking the distinction, which has its origin in
Kant (1781), turns on the notion of conceptual containment. By this
account, a proposition is analytic if the predicate concept of the
proposition is contained within the subject concept. The claim that
all bachelors are unmarried, for instance, is analytic because the
concept of being unmarried is included within the concept of a
bachelor. By contrast, in synthetic propositions, the predicate
concept "amplifies" or adds to the subject concept. The claim, for
example, that the sun is approximately 93 million miles from the earth
is synthetic because the concept of being located a certain distance
from the earth goes beyond or adds to the concept of the sun itself. A
related way of drawing the distinction is to say that a proposition is
analytic if its truth depends entirely on the definition of its terms
(that is, it is true by definition), while the truth of a synthetic
proposition depends not on mere linguistic convention, but on how the
world actually is in some respect. The claim that all bachelors are
unmarried is true simply by the definition of "bachelor," while the
truth of the claim about the distance between the earth and the sun
depends, not merely on the meaning of the term "sun," but on what this
distance actually is.

Some philosophers have equated the analytic with the a priori and the
synthetic with the a posteriori. There is, to be sure, a close
connection between the concepts. For instance, if the truth of a
certain proposition is, say, strictly a matter of the definition of
its terms, knowledge of this proposition is unlikely to require
experience (rational reflection alone will likely suffice). On the
other hand, if the truth of a proposition depends on how the world
actually is in some respect, then knowledge of it would seem to
require empirical investigation.

Despite this close connection, the two distinctions are not identical.
First, the a priori/a posteriori distinction is epistemological: it
concerns how, or on what basis, a proposition might be known or
justifiably believed. The analytic/synthetic distinction, by contrast,
is logical or semantical: it refers to what makes a given proposition
true, or to certain intentional relations that obtain between concepts
that constitute a proposition.

It is open to question, moreover, whether the a priori even coincides
with the analytic or the a posteriori with the synthetic. First, many
philosophers have thought that there are (or at least might be)
instances of synthetic a priori justification. Consider, for example,
the claim that if something is red all over then it is not green all
over. Belief in this claim is apparently justifiable independently of
experience. Simply by thinking about what it is for something to be
red all over, it is immediately clear that a particular object with
this quality cannot, at the same time, have the quality of being green
all over. But it also seems clear that the proposition in question is
not analytic. Being green all over is not part of the definition of
being red all over, nor is it included within the concept of being red
all over. If examples like this are to be taken at face value, it is a
mistake to think that if a proposition is a priori, it must also be
analytic.

Second, belief in certain analytic claims is sometimes justifiable by
way of testimony and hence is a posteriori. It is possible (even if
atypical) for a person to believe that a cube has six sides because
this belief was commended to him by someone he knows to be a highly
reliable cognitive agent. Such a belief would be a posteriori since it
is presumably by experience that the person has received the testimony
of the agent and knows it to be reliable. Thus it is also mistaken to
think that if a proposition is a posteriori, it must be synthetic.

Third, there is no principled reason for thinking that every
proposition must be knowable. Some analytic and some synthetic
propositions may simply be unknowable, at least for cognitive agents
like us. We may, for instance, simply be conceptually or
constitutionally incapable of grasping the meaning of, or the
supporting grounds for, certain propositions. If so, a proposition's
being analytic does not entail that it is a priori, nor does a
proposition's being synthetic entail that it is a posteriori.

This raises the question of the sense in which a claim must be
knowable if it is to qualify as either a priori or a posteriori. For
whom must such a claim be knowable? Any rational being? Any or most
rational human beings? God alone? There may be no entirely
nonarbitrary way to provide a very precise answer to this question.
Nevertheless, it would seem a mistake to define "knowable" so broadly
that a proposition could qualify as either a priori or a posteriori if
it were knowable only by a very select group of human beings, or
perhaps only by a nonhuman or divine being. And yet, the more narrow
the definition of "knowable," the more likely it is that certain
propositions will turn out to be unknowable. "Goldbach's conjecture" –
the claim that every even integer greater than two is the sum of two
prime numbers – is sometimes cited as an example of a proposition that
may be unknowable by any human being (Kripke 1972).
3. The Necessary/Contingent Distinction

A necessary proposition is one the truth value of which remains
constant across all possible worlds. Thus a necessarily true
proposition is one that is true in every possible world, and a
necessarily false proposition is one that is false in every possible
world. By contrast, the truth value of contingent propositions is not
fixed across all possible worlds: for any contingent proposition,
there is at least one possible world in which it is true and at least
one possible world in which it is false.

The necessary/contingent distinction is closely related to the a
priori/a posteriori distinction. It is reasonable to expect, for
instance, that if a given claim is necessary, it must be knowable only
a priori. Sense experience can tell us only about the actual world and
hence about what is the case; it can say nothing about what must or
must not be the case. Contingent claims, on the other hand, would seem
to be knowable only a posteriori, since it is unclear how pure thought
or reason could tell us anything about the actual world as compared to
other possible worlds.

While closely related, these distinctions are not equivalent. The
necessary/contingent distinction is metaphysical: it concerns the
modal status of propositions. As such, it is clearly distinct from the
a priori/a posteriori distinction, which is epistemological.
Therefore, even if the two distinctions were to coincide, they would
not be identical.

But there are also reasons for thinking that they do not coincide.
Some philosophers have argued that there are contingent a priori
truths (Kripke 1972; Kitcher 1980b). An example of such a truth is the
proposition that the standard meter bar in Paris is one meter long.
This claim appears to be knowable a priori since the bar in question
defines the length of a meter. And yet it also seems that there are
possible worlds in which this claim would be false (e.g., worlds in
which the meter bar is damaged or exposed to extreme heat). Comparable
arguments have been offered in defense of the claim that there are
necessary a posteriori truths. Take, for example, the proposition that
water is H2O (ibid.). It is conceivable that this proposition is true
across all possible worlds, that is, that in every possible world,
water has the molecular structure H2O. But it also appears that this
proposition could only be known by empirical means and hence that it
is a posteriori. Philosophers disagree about what to make of cases of
this sort, but if the above interpretation of them is correct, a
proposition's being a priori does not guarantee that it is necessary,
nor does a proposition's being a posteriori guarantee that it is
contingent.

Finally, on the grounds already discussed, there is no obvious reason
to deny that certain necessary and certain contingent claims might be
unknowable in the relevant sense. If indeed such propositions exist,
then the analytic does not coincide with the necessary, nor the
synthetic with the contingent.
4. The Relevant Sense of "Experience"

In Section 1 above, it was noted that a posteriori justification is
said to derive from experience and a priori justification to be
independent of experience. To further clarify this distinction, more
must be said about the relevant sense of "experience".

There is no widely accepted specific characterization of the kind of
experience in question. Philosophers instead have had more to say
about how not to characterize it. There is broad agreement, for
instance, that experience should not be equated with sensory
experience, as this would exclude from the sources of a posteriori
justification such things as memory and introspection. (It would also
exclude, were they to exist, cognitive phenomena like clairvoyance and
mental telepathy.) Such exclusions are problematic because most cases
of memorial and introspective justification resemble paradigm cases of
sensory justification more than they resemble paradigm cases of a
priori justification. It would be a mistake, however, to characterize
experience so broadly as to include any kind of conscious mental
phenomenon or process; even paradigm cases of a priori justification
involve experience in this sense. This is suggested by the notion of
rational insight, which many philosophers have given a central role in
their accounts of a priori justification. These philosophers describe
a priori justification as involving a kind of rational "seeing" or
perception of the truth or necessity of a priori claims.

There is, however, at least one apparent difference between a priori
and a posteriori justification that might be used to delineate the
relevant conception of experience (see, e.g., BonJour 1998). In the
clearest instances of a posteriori justification, the objects of
cognition are features of the actual world which may or may not be
present in other possible worlds. Moreover, the relation between these
objects and the cognitive states in question is presumably causal. But
neither of these conditions would appear to be satisfied in the
clearest instances of a priori justification. In such cases, the
objects of cognition would appear (at least at first glance) to be
abstract entities existing across all possible worlds (e.g.,
properties and relations). Further, it is unclear how the relation
between these objects and the cognitive states in question could be
causal. While these differences may seem to point to an adequate basis
for characterizing the relevant conception of experience, such a
characterization would, as a matter of principle, rule out the
possibility of contingent a priori and necessary a posteriori
propositions. But since many philosophers have thought that such
propositions do exist (or at least might exist), an alternative or
revised characterization remains desirable.

All that can be said with much confidence, then, is that an adequate
definition of "experience" must be broad enough to include things like
introspection and memory, yet sufficiently narrow that putative
paradigm instances of a priori justification can indeed be said to be
independent of experience.
5. The Relevant Sense of "Independent"

It is also important to examine in more detail the way in which a
priori justification is thought to be independent of experience. Here
again the standard characterizations are typically negative. There are
at least two ways in which a priori justification is often said not to
be independent of experience.

The first begins with the observation that before one can be a priori
justified in believing a given claim, one must understand that claim.
The reasoning for this is that for many a priori claims experience is
required to possess the concepts necessary to understand them (Kant
1781). Consider again the claim that if something is red all over then
it is not green all over. To understand this proposition, I must have
the concepts of red and green, which in turn requires my having had
prior visual experiences of these colors.

It would be a mistake, however, to conclude from this that the
justification in question is not essentially independent of
experience. My actual reason for thinking that the relevant claim is
true does not emerge from experience, but rather from pure thought or
rational reflection, or from simply thinking about the properties and
relations in question. Moreover, the very notion of epistemic
justification presupposes that of understanding. In considering
whether a person has an epistemic reason to support one of her
beliefs, it is simply taken for granted that she understands the
believed proposition. Therefore, at most, experience is sometimes a
precondition for a priori justification.

Second, many contemporary philosophers accept that a priori
justification depends on experience in the negative sense that
experience can sometimes undermine or even defeat such justification.
This counters the opinions of many historical philosophers who took
the position that a priori justification is infallible. Most
contemporary philosophers deny such infallibility, but the
infallibility of a priori justification does not in itself entail that
such justification can be undermined by experience. It is possible
that a priori justification is fallible, but that we never, in any
particular case, have reason to think it has been undermined by
experience. Further, the fallibility of a priori justification is
consistent with the possibility that only other instances of a priori
justification can undermine or defeat it.

Nonetheless, there would appear to be straightforward cases in which a
priori justification might be undermined or overridden by experience.
Suppose, for instance, that I am preparing my tax return and add up
several numbers in my head. I do this carefully and arrive at a
certain sum. Presumably, my belief about this sum is justified and
justified a priori. If, however, I decide to check my addition with a
calculator and arrive at a different sum, I am quite likely to revise
my belief about the original sum and assume that I erred in my initial
calculation. It seems clear that my revised belief would be justified
and that this justification would be a posteriori, since it is by
experience that I am acquainted with what the calculator reads and
with the fact that it is a reliable instrument. This is apparently a
case in which a priori justification is corrected, and indeed
defeated, by experience.

It is important, however, not to overstate the dependence of a priori
justification on experience in cases like this, since the initial,
positive justification in question is wholly a priori. My original
belief in the relevant sum, for example, was based entirely on my
mental calculations. It "depended" on experience only in the sense
that it was possible for experience to undermine or defeat it. This
relation of negative dependence between a priori justification and
experience casts little doubt on the view that a priori justification
is essentially independent of experience.
6. Positive Characterizations of the A Priori

A priori justification has thus far been defined, negatively, as
justification that is independent of experience and, positively, as
justification that depends on pure thought or reason. More needs to be
said, however, about the positive characterization, both because as it
stands it remains less epistemically illuminating than it might and
because it is not the only positive characterization available.

How, then, might reason or rational reflection by itself lead a person
to think that a particular proposition is true? Traditionally, the
most common response to this question has been to appeal to the notion
of rational insight. Several historical philosophers (e.g., Descartes
1641; Kant 1781) as well as some contemporary philosophers (e.g.,
BonJour 1998) have argued that a priori justification should be
understood as involving a kind of rational "seeing" or grasping of the
truth or necessity of the proposition in question. Consider, for
instance, the claim that if Ted is taller than Sandy and Sandy is
taller than Louise, then Ted is taller than Louise. Once I consider
the meaning of the relevant terms, I seem able to see, in a direct and
purely rational way, that if the conjunctive antecedent of this
conditional is true, then the conclusion must also be true. According
to the traditional conception of a priori justification, my apparent
insight into the necessity of this claim justifies my belief in it.
Its seeming to me in this clear, immediate, and purely rational way
that the claim must be true provides me with a compelling reason for
thinking that it is true. Therefore, the following more positive
account of a priori justification may be advanced: one is a priori
justified in believing a certain claim if one has rational insight
into the truth or necessity of that claim.

While phenomenologically plausible and epistemically more illuminating
than the previous characterizations, this account of a priori
justification is not without difficulties. It would seem, for
instance, to require that the objects of rational insight be eternal,
abstract, Platonistic entities existing in all possible worlds. If
this is the case, however, it becomes very difficult to know what the
relation between these entities and our minds might amount to in cases
of genuine rational insight (presumably it would not be causal) and
whether our minds could reasonably be thought to stand in such a
relation (Benacerraf 1973). As a result of this and related concerns,
many contemporary philosophers have either denied that there is any a
priori justification, or have attempted to offer an account of a
priori justification that does not appeal to rational insight.

Accounts of the latter sort come in several varieties. One variety
retains the traditional conception of a priori justification requiring
the possession of epistemic reasons arrived at on the basis of pure
thought or reason, but then claims that such justification is limited
to trivial or analytic propositions and therefore does not require an
appeal to rational insight (Ayer 1946). A priori justification
understood in this way is thought to avoid an appeal to rational
insight. The grounds for this claim are that an explanation can be
offered of how a person might "see" in a purely rational way that, for
example, the predicate concept of a given proposition is contained in
the subject concept without attributing to that person anything like
an ability to grasp the necessary character of reality. A priori
justification is thereby allegedly accounted for in a metaphysically
innocuous way.

But views of this kind typically face at least one of two serious
objections (BonJour 1998). First, they are difficult to reconcile with
what are intuitively the full range of a priori claims. While many a
priori claims are analytic, some appear not to be, for instance, the
principle of transitivity, the red-green incompatibility case
discussed above, as well as several other logical, mathematical,
philosophical, and perhaps even moral claims. It is possible, of
course, to construe the notion of the analytic so broadly that it
apparently does cover such claims, and some accounts of a priori
justification have done just this. But this leads immediately to a
second and equally troubling objection, namely, that if the claims in
question are to be regarded as analytic, it is doubtful that the truth
of all analytic claims can be grasped in the absence of anything like
rational insight or intuition. Seeing the truth of the claim that
seven plus five equals twelve, for instance, does not amount to
grasping the definitions of the relevant terms, nor seeing that one
concept contains another. Rather, it seems to involve something more
substantial and positive, something like an intuitive grasping of the
fact that if seven is added to five, the resulting sum must be –
cannot possibly fail to be – twelve. But this of course sounds
precisely like what the traditional view says is involved with the
occurrence of rational insight.

A second alternative to the traditional conception of a priori
justification emerges from a general account of epistemic
justification that shifts the focus away from the possession of
epistemic reasons and onto concepts like epistemic reasonability or
responsibility. While presumably closely related to the possession of
epistemic reasons, the latter concepts – for reasons discussed below –
should not simply be equated with it. On accounts of this sort, one is
epistemically justified in believing a given claim if doing so is
epistemically reasonable or responsible (e.g., is not in violation of
any of one's epistemic duties).

This model of epistemic justification per se opens the door to an
alternative account of a priori justification. It is sometimes argued
that belief in many of the principles or propositions that are
typically thought to be a priori (e.g., the law of noncontradiction)
is in part constitutive of rational thought and discourse. This claim
is made on the grounds that without such belief, rational thought and
discourse would be impossible. If this argument is compelling, then
quite apart from whether we do or even could have any epistemic
reasons in support of the claims in question, it would seem we are not
violating any epistemic duties, nor behaving in an epistemically
unreasonable way, by believing them. Again, the possession of such
beliefs is thought to be indispensable to any kind of rational thought
or discourse. This yields an account of a priori justification
according to which a given claim is justified if belief in it is
rationally indispensable in the relevant sense (see, e.g., Boghossian
2000; a view of this sort is also gestured at in Wittgenstein 1969).

While views like this manage to avoid an appeal to the notion of
rational insight, they contain at least two serious problems. First,
they seem unable to account for the full range of claims ordinarily
regarded as a priori. There are arguably a number of a priori
mathematical and philosophical claims, for instance, such that belief
in them (or in any of the more general claims they might instantiate)
is not a necessary condition for rational thought or discourse.
Second, these accounts of a priori justification appear susceptible to
a serious form of skepticism, for there is no obvious connection
between a belief's being necessary for rational activity and its being
true, or likely to be true. Consequently, it seems possible on such a
view that a person might be a priori justified in thinking that the
belief in question is true and yet have no reason to support it. In
fact, given the epistemically foundational character of the beliefs in
question, it may be impossible (once an appeal to a priori insight is
ruled out) for a person to have any (noncircular) reasons for thinking
that any of these beliefs are true. Views of this sort, therefore,
appear to have deep skeptical implications.

A third alternative conception of a priori justification shifts the
focus toward yet another aspect of cognition. According to externalist
accounts of epistemic justification, one can be justified in believing
a given claim without having cognitive access to, or awareness of, the
factors which ground this justification. Such factors can be
"external" to one's subjective or first-person perspective.
(Externalist accounts of justification obviously contrast sharply with
accounts of justification that require the possession of epistemic
reasons, since the possession of such reasons is a matter of having
cognitive access to justifying grounds.) The most popular form of
externalism is reliabilism. In broad terms, reliabilists hold that the
epistemic justification or warrant for a given belief depends on how,
or by what means, this belief was formed. More specifically, they ask
whether it was formed by way of a reliable or truth-conducive process
or faculty. Thus, according to reliabilist accounts of a priori
justification, a person is a priori justified in believing a given
claim if this belief was formed by a reliable, nonempirical or
nonexperiential belief-forming process or faculty.

Reliabilist accounts of a priori justification face at least two of
the difficulties mentioned above in connection with the other
nontraditional accounts of a priori justification. First, they seem to
allow that a person might be a priori justified in believing a given
claim without having any reason for thinking that the claim is true. A
person might form a belief in a reliable and nonempirical way, yet
have no epistemic reason to support it. Accounts of this sort are
therefore also susceptible to a serious form of skepticism. A second
problem is that, contrary to the claims of some reliabilists (e.g.,
Bealer 1999), it is difficult to see how accounts of this sort can
avoid appealing to something like the notion of rational insight.
There are at least two levels at which this is so. First, the
reliabilist must provide a more specific characterization of the
cognitive processes or faculties that generate a priori justification.
It is not enough simply to claim that these processes or faculties are
nonempirical or nonexperiential. This in turn will require a more
detailed account of the phenomenology associated with the operation of
these processes or faculties. But what would a more detailed account
of this phenomenology look like if it did not, in some way, refer to
what traditional accounts of a priori justification characterize as
rational insight? After all, reliable nonempirical methods of belief
formation differ from those that are unreliable, such as sheer
guesswork or paranoia, precisely because they involve a reasonable
appearance of truth or logical necessity. And it is just this kind of
intuitive appearance that is said to be characteristic of rational
insight. Thus it appears that in working out some of the details of
her account, the reliabilist will be forced to invoke at least the
appearance of rational insight. Second, the reliabilist is obliged to
shed some light on why the kind of nonempirical cognitive process or
faculty in question is reliable. But here again it is difficult to
know how to avoid an appeal to rational insight. How else could a
given nonempirical cognitive process or faculty lead reliably to the
formation of true beliefs if not by virtue of its involving a kind of
rational access to the truth or necessity of these beliefs? It is far
from clear to what else the reliabilist might plausibly appeal in
order to explain the reliability of the relevant kind of process or
faculty.

It appears, then, that the most viable reliabilist accounts of a
priori justification will, like traditional accounts, make use of the
notion of rational insight. Some reliabilist views (e.g., Plantinga
1993) do precisely this by claiming, for instance, that one is a
priori justified in believing a given claim if this belief was
produced by the faculty of reason, the operation of which involves
rational insight into the truth or necessity of the claim in question.
The plausibility of a reliabilist account of this sort, vis-à-vis a
traditional account, ultimately depends, of course, on the
plausibility of the externalist commitment that drives it.
7. References and Further Reading

* Audi, Robert. 1999. "Self-Evidence," Philosophical Perspectives,
vol. 13, ed. James E. Tomberlin (Oxford: Blackwell), pp. 205-28.
* Ayer, A.J. 1946. "The A Priori," in Language, Truth and Logic,
2nd ed. (New York: Dover), pp. 71-87.
* Bealer, George. 1999. "The A Priori," in The Blackwell Guide to
Epistemology, eds. John Greco and Ernest Sosa (Oxford: Blackwell), pp.
243-70.
* Benacerraf, Paul. 1973. "Mathematical Truth," The Journal of
Philosophy 19: 661-79.
* Boghossian, Paul. 2000. "Knowledge of Logic," in New Essays on
the A Priori (Oxford: Oxford University Press), pp. 229-54.
* BonJour, Laurence. 1998. In Defense of Pure Reason (Cambridge:
Cambridge University Press).
* Casullo, Albert. 1992. "A priori/a posteriori," in A Companion
to Epistemology, eds. Jonathan Dancy and Ernest Sosa (Oxford:
Blackwell), pp. 1-3.
* Descartes, René. 1641. Meditations on First Philosophy, 3rd ed.,
trans. D.A. Cress (Indianapolis: Hackett Publishing Company, 1993).
* Hamlyn, D.W. 1967. "A Priori and A Posteriori," in The
Encyclopedia of Philosophy, vol. 1, ed. Paul Edwards (New York:
Macmillan Publishing Company & The Free Press), pp. 140-44.
* Kant, Immanuel. 1781. Critique of Pure Reason, trans. N.K. Smith
(London: Macmillan, 1929).
* Kitcher, Philip. 1980a. "A Priori Knowledge," Philosophical
Review 89: 3-23.
* Kitcher, Philip. 1980b. "A Priority and Necessity," Australasian
Journal of Philosophy 58: 89-101.
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