A PRIORI KNOWLEDGE
We began with a study of metaphysics.
It seems appropriate to conclude by asking:
How is a priori knowledge possible?
Why?
 Metaphysical knowledge is not based on
empirical evidence.
 But metaphysics deals with questions
about reality.
So, the following naturally arises: can we
really have non-empirical knowledge of the
world?
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A Kantian distinction
Two kinds of judgement:
Analytic(al)
Predicate already
contained in the
subject.
Synthetic
Predicate adds
something to the
subject.
Explains but doesn’t
expand a concept.
Expands on the
subject concept.
Based on law of
contradiction
Requires more than
non-contradiction.
Examples:
Analytic
All bachelors are men.
All bipeds have two legs.
Synthetic
The solar system has 9 planets.
All dogs are loyal.
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Kant: all analytic propositions are a
priori
Kant: all analytic propositions are knowable
a priori because they are based only on the
law of (non-)contradiction:
If X = A & B then:
 ‘All X are A’ is a priori (true, necessary)
 ‘Some X is not A’ is a priori (false, nec.)
E.g.: bachelor = unmarried & man
 ‘All bachelors are unmarried’ is a priori
(true, necessary)
 ‘Some bachelors aren’t men’ is a priori
(false, necessary)
Again: AnalyticA priori
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What about synthetic propositions?
Some are clearly a posteriori; e.g.:
propositions about particular empirical
matters:
‘The Earth’s surface is 70% water’.
 The concept ‘Earth’s surface’ doesn’t
contain ‘is 70% water’.
‘Women have two X-chromosomes’
 The concept ‘woman’ doesn’t contain
‘double X-chromosome’.
Such claims are contingent and can only be
known on the basis of sensory experience.
Call these empirical propositions.
All empirical propositions are a posteriori
But are all synthetic propositions empirical
in this sense?
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Metaphysical judgments
Metaphysical claims are not known or
confirmed by experience. E.g.:
 The future exists
o Can’t experience the future.
 An object that gains a part becomes
a new object
o Our observations underdetermine
this.
 Other possible worlds exist
o They are not connected to our world.
 All events have causes
o Impossible to experience all events.
So:
Metaphysical judgements are a priori.
Key question:
 Are they analytic or synthetic?
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The synthetic a priori: the final category
Kant: metaphysical judgements are not
analytic:
 The concept ‘future’ doesn’t contain
‘real’.
 ‘Object’ doesn’t contain ‘mereological
constancy’
 ‘Possible’ doesn’t contain ‘non-actual
concrete world’.
 ‘Event’ doesn’t contain ‘cause’.
We don’t contradict ourselves if we claim
the future is unreal, or our world is the only
world, etc.
So: metaphysical propositions are
synthetic.
Conclusion: metaphysical propositions are
synthetic a priori.
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How is metaphysics possible?
Kant: the central question of philosophy:
How is synthetic a priori knowledge
possible?
The problem:
 It is easy to see how empirical
propositions are known: use your
senses.
 It is easy to see how analytic
propositions are known: use the law of
(non-) contradiction.
 But metaphysics requires more than
non-contradiction or empirical
observation.
Either synthetic a priori knowledge is
possible, or metaphysics is impossible.
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How is such knowledge possible?
So how could we have knowledge of reality
that is based neither on observation nor the
law of contradiction?
Kant: empiricists and rationalists both
assume that knowledge is a matter of the
mind reflecting/conforming to reality.
 But the mind can’t experience enough to
have metaphysical knowledge:
So, if metaphysical knowledge is possible,
then…
The world must conform to (reflect) the
mind, not the other way around!
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The ‘Copernican’ turn in philosophy
Kant: reality is conditioned by the mind.
 Time is the form of inner intuition.
 Space is the form of outer intuition.
What does this mean?
 The world itself is neither temporal nor
spatial.
 The mind has spatiotemporal structure
(categories).
 The empirical world we experience is
structured by the mind.
In short: the world we experience is spatial
and temporal because:
1. Empirical reality is structured by our
minds.
2. Our minds have space and time ‘built
into’ them (as ‘forms’ of experience or,
as Kant calls it, ‘intuition’).
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More categories
Similarly, the mind is structured by other
categories that form the empirical world:
 Universal causality, moral law, etc.
Does this mean that we each live in our own
worlds?
 After all, what if my mind is structured
differently from your mind?
 If Kant is right, then we live in different
empirical realities.
Kant: the structuring categories are
universal and necessitating. That is:
 They are part of every mind.
 They require that all of empirical reality
conform to them (not just the part you
experience).
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Synthetic a priori knowledge
So, synthetic a priori knowledge is possible
because:
1. Empirical reality is conditioned by the
mind’s universal, necessary
categories.
2. We have direct access to our minds,
so we can use pure reason, not the
senses, to uncover the structure of
reality.
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General and particular
Note that the mental categories determine a
general structure of reality, such as:
 All objects are spatially related to each
other.
 All events are temporal related to each
other.
 All events have a cause.
The categories do not determine particular
matters of fact, such as:
 John is to the left of Sally right now.
 WW II ended in 1945.
 John’s cat has yellow fur.
The former can be learned by pure reason;
that latter require empirical investigation.
 Put another way: metaphysical
propositions are not empirical
propositions (even though both are
synthetic).
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Objection
This is implausible; why not just reject
synthetic a priori knowledge?
Kant: Claims of math, geometry and pure
(mathematical) science are synthetic a
priori.
 Can’t reject these!
Example: 7 + 5 = 12.
Kant: the concept ‘add 5 to 7’ does not
contain the concept ‘12’
 You can think of the first without the
second.
 Therefore, math is synthetic a priori.
Similarly:
 Interior angles of all triangles add to
180o.
 Distinct parallel lines never meet.
 Law of conservation of mass.
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In sum
1. Synthetic a priori knowledge is
possible only if the mind conditions
reality.
2. Math, geometry and theoretical
science provide certain knowledge.
3. They are all synthetic a priori.
Therefore:
4. The mind conditions reality.
5. We can know non-analytic, necessary
truths by analyzing the structure of
human thought (pure reason).
6. Metaphysics is possible.
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Empiricist critique of a priori knowledge
How can the empiricist account for our
knowledge of necessary truths?
 E.g. math and logic.
 These can’t be verified empirically.
 No finite number of observations can
render a universal claim certain.
 E.g. problem of induction.
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Mill’s empiricism
Mill: logical/mathematical claims are
inductions based on many, many
observations.
 So much evidence in their favour that
they seem necessary, but they are not.
Ayer: this is not plausible.
 Of course we learn logic and math
empirically, by being taught.
 But once we understand them, we see
that they are not verified the same way
as empirical claims.
 Any cases that might seem to refute
such claims are better explained as
cases of error.
Examples
 Not, 2 + 2 = 5; rather, I miscounted.
 Not really a Euclidean triangle.
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Analytic/synthetic
Empiricist account of the distinction:
Analytic claim
True in virtue of the
meanings of the
words involved.
Synthetic claim
True in virtue of the
facts of experience
(and meanings).
Ayer: there are no synthetic a priori claims.
 All truths of math and logic are in fact
tautologies, true in virtue of the
meanings of their words.
E.g.:
 Or = one or the other is true.
 Not = p and not-p have opposite truthvalues.
If you know these meanings, you know that
‘p or not-p’ must follow—it is simply what
the meanings add up to.
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Tautologies
Ayer: analytic propositions are rules or
stipulations for how to use our language.
 They tell us how our words relate to
each other; how our language hangs
together.
E.g.: ‘If p implies q, and p is true, then q is
true’.
 This is a rule that guides how to use
your words.
Math and logic are rules we agree upon in
using our language.
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Analyticity and necessity
Analytic truths can be known a priori:
 They make no claims about the world.
 They are only conventions that we adopt
to guide our language.
 As soon as you learn your language,
you know them.
So, there is no possibility of confirming or
denying them in experience.
They are necessary because they guide
your language.
 To violate them is to be guided by them
and also to break them.
 That is a simple contradiction.
 Hence, they are necessary.
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Another example
Stipulation: ‘shmat’ = ‘anything with four
legs’.
 As soon as you know this, you know a
priori that there are no five legged
shmats—tautology.
 But you need to use your senses to
determine whether there are in fact any
shmats.
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Empiricism and metaphysics
Ayer: a priori knowledge of the world is
impossible.
 Necessary, universal claims are all
analytic.
 These only depend on the meanings of
words and are devoid of factual content.
Therefore, metaphysical knowledge is
impossible—at best it is linguistic analysis.
E.g.: ‘all events have a cause’.
 Can’t be verified empirically.
 Not true in virtue of meanings of words
(+ logic/math).
Therefore, it is nonsense.
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The point of a priori knowledge
Ensure empirical claims are consistent.
Determine the implications of factual claims.
Determine the implications of claims that
are too complex for us to see directly.
 E.g. complex mathematical claims are
verified by smaller, a priori steps.
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Math and analyticity
What about Kant’s claim? Isn’t 7 + 5 = 12
synthetic?
Ayer: Kant gives two definitions of analytic:
1. Law of contradiction
2. Can’t think of subject without also
thinking of predicate.
It is true that 7 + 5 = 12 isn’t analytic by #2.
 But that is just a psychological principle,
so it’s irrelevant.
7 + 5 = 12 is analytic by #1:
 Once you know the meanings of ‘7’, ‘5’,
‘12’ and ‘+’, you see that ‘7 + 5’ is
synonymous with ‘12’.
 So, the claim can’t be denied without
violating your definitions.
Same applies to geometry: everything
follows by definition.
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Convention
Ayer: because analytic propositions are
independent of the facts, we could have
chosen different conventions.
 However, whichever conventions we
were to choose, they would form
tautologies and would therefore be
necessary.
In other words, necessity (analyticity) is
relative to a set of linguistic rules.
Do you agree: is it plausible to suppose we
might not have settled on:
 P v ~P?
 2 + 2 = 4?
 etc.?
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Two more objections
First: Isn’t ‘there are no synthetic, a priori
truths’ itself a synthetic a priori claim?
Second: Some logical laws are not based
on the meanings of words.
E.g.: Bivalence: every proposition is either
true or false.
 This doesn’t follow from the meaning of
‘true’ or ‘false’.
 It is a logical principle, not a semantic
one.
 How can the empiricist account for this?
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Important categories to keep distinct
Epistemological
A priori proposition A posteriori prop.
Known independently Known on the basis
of sensory evidence of sensory evidence
Semantic
Analytic prop.
Predicate contained
in subject
Synthetic prop.
Predicate adds to
subject
Metaphysical
Necessary truth
Couldn’t be false
Contingent truth
Might have been
otherwise
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Summary of positions
Kant
All a priori knowledge
is of necessary truths
Some necessary
truths are synthetic
So, we can have
synthetic a priori
knowledge
Metaphysics is
possible
Ayer
All a priori knowledge
is of necessary truths
All necessary truths
are analytic
There is no synthetic
a priori knowledge
Metaphysics is
impossible.
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