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Gábor Forgács, Tihamér Margitay, Zsolt Ziegler
Dept. of Philosophy and the History of Science
1111 Budapest, Egry J. st. 1. E 610.
[email protected], [email protected], [email protected]
www.filozofia.bme.hu
A priori
Standard Distinction
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I.

analytic:







knowable “prior to” experience
independent of sense experience
Kant: "although all our knowledge begins
with experience, it does not follow that it
arises from experience”
necessary:


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
true in virtue of meaning alone. It’s validity
depends solely on the definitions of the
symbols it contains.
Grounded in meaning independently of
matters of fact
Kant: a proposition whose predicate concept
is contained in its subject concept
a priori:

II.
Logically impossible that it is false
Denial of it involves a contradiction
True in all possible world
synthetic:



a posteriori


not analytic. It’s validity is determined by the
facts of experience.
Kant: a proposition whose predicate concept
is not contained in its subject concept
(“empirical”): can only be known “after” (on
the basis of) experience
contingent:



Not necessary
Not true in all possible world
Possible: at least in one possible world it is
true
Epistemology
Tools
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Analytic:
 true in virtue of meaning alone. It’s validity depends solely on the definitions of
the symbols/words it contains.
 Grounded in meaning independently of matters of fact.
Example:
I know analytically that:
 No unmarried man is married
 No bachelor is married


Because
 The word unmarried is defined as not-married
 The word bacherlor is defined as not-married
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Epistemology
Tools
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A priori:
 knowable “prior to” experience or independent of sense experience
 Kant: "although all our knowledge begins with experience, it does not follow
that it arises from experience”
Example:
I know a priori that
 ”7+5=12”
 ”Entities x and y are identical if every predicatre possessed by x is also
possessed by y and vice versa”


Because


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Knowing that ”7+5=12” is true does not require to count on my fingers or I do
not have to meet these guys ”7” and ”5” in order to know their nature.
Knowing that the Leibniz Law is true does not requre to find two identical
objects – that would be, nevetherless, impossible.
Epistemology
Tools
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Necessary:
 Logically impossible that it is false / Denial of it involves a contradiction
 True in all possible world
 Possible Worlds: Every logically conceivable non-contradictory state of affair
Example:
I know it is necessary that:
 A triangle has three sides
 Nothing can be red and green all over


Because:
 It is true for every possible world that if a triangle is exemplified in it, then it has
three sides.
 There is no possible world/ logically conceivable non-contradictory state of
affair in which an object has an all over greem and red surface simultanously
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Epistemology
Problematizing

1.
2.
3.
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Since, they are interchangeable I know analytically/a prioriy/necessarily that:
 No bachelor is married
 ”7+5=12”
 A triangle has three sides
But what about these?
 Water is H2O
 The standard ethalon meter stick in Paris is one meter long
 Every event has a cause / everything that has a beginning has an end
 God exists
Does a priori knowledge pose a problem for empiricism?
 Or a priory knowledge is a genuinely different kind of knowledge?
How do we justify a priori statements?
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Epistemology
Problematizing:
A priori synthetic? A priori contingent?
I.

analytic:








knowable “prior to” experience
independent of sense experience
Kant: "although all our knowledge begins
with experience, it does not follow that it
arises from experience”
necessary:


2015.07.07.
II.

true in virtue of meaning alone. It’s validity
depends solely on the definitions of the
symbols it contains.
Grounded in meaning independently of
matters of fact
Kant: a proposition whose predicate concept
is contained in its subject concept
a priori:
Logically impossible that it is false
Denial of it involves a contradiction
True in all possible world
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synthetic:



a posteriori


not analytic. It’s validity is determined by the
facts of experience.
Kant: a proposition whose predicate concept
is not contained in its subject concept
(“empirical”): can only be known “after” (on
the basis of) experience
contingent:



Not necessary
Not true in all possible world
Possible: at least in one possible world it is
true
Epistemology
Outline
I.
A priori contingent/synthetic?
II.
Deal with the problem of Empiricism and A priori
III.

Hume, Kant, Mill, Ayer,

Metaphysical and Epistemological Conception of Analycity

‘Tonk dilemma’
Justifyability of aprioricity

IV.
BonJour, Plantinga, Goldman/Peacocke
Two dimensional semantics about necessity

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Frege, Carnap, Kripke, Chalmers
Epistemology
I. A priori contingent/synthetic?
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A prioriy synthetic
It should be prior to/independent of sense experience and
i. Its validity is determined by the facts of experience.
ii. A proposition whose predicate concept is not contained in its subject
concept

‘Nothing can be both a cow and a horse at the same time’

Is it part of the meaning of “is a cow” that it excludes being a horse?
– If so, this example is analytic and again not what we’re after.

But, knowing the meaning of “cow” perfectly well does not involve having heard of
horses.

If the meaning of “is a cow” included all these exclusions, no one could learn it,
especially given that the other words would contain their own exclusions. So, the
proposition that ‘nothing is both a cow and a horse’ is non-analytic
Ayer: Does it mean that cognitive capacity is involved in definition of a priori synthetic?
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Epistemology
I. A priori contingent/synthetic?
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A prioriy contingent
It should be prior to/independent of sense experience and
i. Not true in all possible world

‘The standard ethalon meter stick in Paris is one meter long’
It will be discused in IV. two dimensional semantics
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Epistemology
II. Problem of Empiricism and A priori
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The empiricist must deal with the truths of logic and mathematics in one of the two
following ways:
i.
he must say either that they are not necessary truths, in which case he must account
for the universal conviction that they are; or
ii.
he must say that they have no factual content, and then he must explain how a
proposition which is empty of all factual content can be true and useful and surprising
i.Not
necessary
truths!
J. S. Mill
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ii.No
factual
content!
David Hume
Epistemology
II. Hume and Kant

Hume’s Fork: “Tautologies” and factual claims



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The a priori: mathematics and logic
Factual claims: science and everything else
Kant: ‘In all judgments in which the relation of a subject to the predicate is
thought … this relation is possible in two different ways. Either the predicate B
belongs to the subject A as something that is (covertly) contained in this concept
A; or B lies entirely outside the concept A… In the first case, I call the judgment
analytic, in the second synthetic…I merely draw out the predicate in accordance
with the principle of contradiction, and can thereby at the same time become
conscious of the necessity of the judgment’



Analytic sentences are true in virtue of language alone
They’re a priori (knowable independent of experience) because they’re empty of
factual content.
They’re necessary because we don’t allow them to be false, e.g.
– if the angles of a figure don’t add up to 180 degrees we don’t count it as a Euclidean
triangle.
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Epistemology
II. Objection and Answer
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
Objection: If all the assertions which mathematics puts forward can be derived
from one another by formal logic, mathematicians cannot amount to anything
more than an immense tautology…Can we really allow that these theorems
which fill so many books serve no other purpose than to say in a roundabout
fashion A = A?

There is a sense in which analytic propositions do give us new knowledge. They
call attention to linguistic usages, of which we might otherwise not be conscious
and they reveal unsuspected implications in our assertions and beliefs.

The business of philosophy is analysis: to elicit those features linguistic usage
and reveal entailment relations
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Epistemology
II. A priori: only about lingustic usage?
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Hypothesis: v(B) > v(S)
1. entailment: v(B) > v(B+S) > v(S)
2. entailment: v(B+S) > v(B) > v(S)
Concluion: v(B+S) = v(B) = v(S)

Hypotheis is false

Know without any
reference to experience
Task:

How is that possible?
(Agree or Disagree)
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Epistemology
II. Mill
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J. S. Mill's radical empiricist alternative:
 Maths and logic are inductive generalisations
Argument against Mill
 If mathematical propositions are inductive generalisations, it's possible to have
refuting instances

Take a putative refuting instance: count 5 pairs and get 9.

If the angles of a figure don’t add up to 180 degrees we don’t count it as a
Euclidean triangle.
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Epistemology
II. Ayer - Devoid of factual content
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
Empirical justification is inductive

No Empirical justification can support necessary truths

Ayer (& moderate empiricists): analytic truths give no information about the
world, but reveal linguistic usage of it
‘Either some ants are parasitic or none are’

If one knows what is the function of the words ‘either’, ‘or’, and ‘not’, then one
can see that any proposition of the form ‘Either p is true or p is not true’ is valid,
independently of experience.
What does ‘see’ mean here?
→The explanation of knowledge of logical truths is not further explained
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
1. On what depends the truth of a priori statements?

2. How do we grasp it? (Ch. III.)
Epistemology
II.Metaphysical and epistemological
conception of analyticity
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Mathematics and logic statements are analytic

Their truth depends on the meaning of words ('metaphysical' conception of
analyticity)

We can know whether they are true or false just by knowing the meaning of
words ('epistemological' conception of analyticity)
Critique of the metaphysical conception


“Isn't it in general true that for any statement S,

S is true iff for some p, S means that p and p?
How could the mere fact that S means that p make it the case that S is true?
Doesn't it also have to be the case that p?” (Paul Boghossian “Analyticity reconsidered”)
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
Metaphyical conception but epistemological

Ayer? → by knowing the meaning of ‘either’, ‘or’, ‘not’, (logic connectives) the validity
of ‘either p is true or p is not true’ can be known.
Epistemology
II. The ‘tonk’ dilemma
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
By knowing the meaning of ‘either’, ‘or’, ‘not’, (logic connectives) the validity of
‘either p is true or p is not true’ can be known.

Standard Locic Connectives: ‘&’, ‘V’, ‘→’, ‘↔’
e.g: ‘&’




p&q → q;
p&q → p;
p, q → p&q
- we mean by '&' whatever makes these schemas valid
Problem: “tonk”. Define Tonk [۞ - “tonkjunct”] as the following connective,
From any ψ to be derived from any φ:





p → p۞q;
p۞q → q
By knowing the meaning of “tonkjunct” the valifity of ‘If Zsolt is a philosopher,
then you are a BIV’ can be known.
Absurd! Why is it absurd? ‘I see it as absurd’ – and here we are again: ‘see’…
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Epistemology
III. Justifyability of aprioricity
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How can we explain a priori justification – how can we ‘see’?

Task:

How cognitive studies want to give an account for understanding mathematical and
logical statements?

How economists account for the phenomena that mathematics can work in
calculating the movements of the market?
– Both A and B groups work independently
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Epistemology
III. Justifyability of aprioricity
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How can we explain a priori justification – how can we ‘see’?
I.
II.

a person might have an intuition that the proposition is true based on understanding
the concepts involved
she might have an intuition that based on her inability to think of counterexamples to
those claims / intuition on → inconceivability of PW → Necessary falsity of the claim
BonJour: non-inferential grasp, apprehension, or “seeing” that some proposition is
necessarily true. these appearances are not propositional, they are unlike beliefs and
more like perceptual sensations.
(J) S's belief that p is likely to be true, if S has a rational intuition that necessarily p,
(i) after, considering p with a reasonable degree of care (careful understanding: p)
(ii) having at least an approximate understanding of the concept of necessity” and
(iii) S is neither dogmatic nor biased regarding p.
BUT the PROBLEM: If the justificatory force of rational insights requires that a premise like
(J) be justified, then it begs the question.
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Epistemology
III. Justifyability of aprioricity
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How can we explain a priori justification – how can we ‘see’?
I.
II.
a person might have an intuition that the proposition is true based on understanding
the concepts involved
she might have an intuition that based on her inability to think of counterexamples to
those claims / intuition on → inconceivability of PW → Necessary falsity of the claim
•
Plantinga: analyzes that “seeing” in terms of immediately believing, and being
convinced, that a proposition is necessary – ‘an indescribable mental state’
•
Goldman/Peacocke:concept possession guarantees reliably (ikelihood) that these sorts
of intuition are based on concept possession. To possess a concept, you must be
reliable in your judgments involving application of that concept to hypothetical cases.
•
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Reliability, however, does not guarantee justification (as we have learnt from Gabor)
Epistemology
My questions - Tasks
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
Suppose, we are hard-wired for the logic that we have - hypothesis

But, with a different brain structure we would have a different logic
– There is nothing prescriptive in our logic
– E.T would find the tonk connective naturally true

If our brains perform logic (inductively → contingently), how logic is
possible to be deductive and necessary?
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Epistemology
VI. Bypass: Philosophy of Language

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Frege: the extension of an expression does not determine its
cognitive significance
Clark Kent = Superman
Clark Kent = Clark Kent
‘Hesperus’ = ‘Phosporus’
‘Hespherus’ = ‘Hespherus’
Cognitively Significant
Cognitively not Significant

We need an aspect of meaning that is tied constitutively to
cognitive significance: sense.

Fregean Thesis: ‘A’ and ‘B’ have the same sense iff ‘A=B is
cognitively significant.
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Epistemology
VI. Carnap on Intension


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Carnap: Expressions have intensions, capturing their extensions
across possible tates of affairs.

Intension = function from possibilities to extensions

Intension can play the role of sense.
Carnapian Thesis: ‘A’, ‘B’ have the same intension iff ‘A=B’ is
necessary.
From the Carnapian Thesis:

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Apriroicity defines identity: it is necessary that if ‘A’ and ‘B’ have
the same intension, then they are identical.
Epistemology
VI. Carnap & Kant → Frege

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Carnapian Thesis: ‘A’, ‘B’ have the same intension iff ‘A=B’ is
necessary.
From the Carnapian Thesis: It is necessary that if ‘A’ and ‘B’ have the same intension, then
they are identical.
&

Kantian Thesis: P is necessary iff P is a priori


Neo-Fregean Thesis: ‘A’, ‘B’ have the same intension iff ‘A=B’ is
a priori.
From the Neo-Freagen Thesis: It is a priori that if ‘A’ and ‘B’ have the same intension, then
they are identical: from the pure notion of A(cows) B(not-horse) should be known - Ayer
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Epistemology
IV. Kripke
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Kripkean Thesis: P is necessary  P is a priori.


Nec (water=H2O)
~A priori (water=H2O)

~Nec (Hesperus=evening star)
A priori (Hesperus=evening star)

Nec (I am Zsolt Ziegler)
~A priori (I am Zsolt Ziegler)
Denies Kantian thesis:

–
P is necessary iff P is a priori
Denies Neo-Fregean Thesis:

–
‘A’, ‘B’ have the same intension iff ‘A=B’ is a priori
Carnapian thesis is retained

–
‘A’, ‘B’ have the same intension iff ‘A=B’ is necessary.
Names, natural kind terms, indexicals are rigid designators

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Pick out actual extension at all possibilities
Epistemology
IV. Two-Dimensional Semantics
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Core idea of 2-D semantics: There are two sorts of dependence
of extension on possible states of the world, and so two sorts of
intension.

First dimension: Extension in possibilities considered as actual
(‘context of utterance’)
–

Second dimension: Extension in possibilities considered as
counterfactual (‘circumstance of evaluation’)
–
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The very thing itself!
The reference-fixer: according to which the object can be
picked out in possible worlds
Epistemology
Examples
E.g. ‘I’




2-intension picks out ZsZ in all worlds
1-intension picks out speaker/center in all worlds
‘I’ and ‘ZsZ’ have same 2-intension, different 1-intension
–
It is secoondarily necessary that ‘I am ZsZ’
–
It is primarily possible that ‘a speaker says I’
E.g. ‘Hesperus’




2-intension picks out Venus in all worlds
1-intension picks out evening star in all/many worlds
‘Hesperus’ & ‘Phosphorus’ have same 2-intension, different 1-intension
–
It is secoondarily necessary that ‘H is Ph’
–
It is primarily possible that ‘the evening star is the Moon’
E.g. ‘water’




2015.07.07.
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2-intension (the very thing) picks out H2O in all worlds (Earth, Twin Earth)
1-intension (transparent, odorless) picks out H2O in Earth, XYZ in Twin Earth
‘water’ & ‘H2O’ have same 2-intension, different 1-intension
–
It is secoondarily necessary that ‘water is H2O’
–
It is primarily possible that ‘water is XYZ’
Epistemology
Necessary A posteriori and Contingent A priori
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‘Water is H2O’ – Necessary A posteriori
 It is 2-necessary: in every possible world where ‘this/our’ water is exemplified it
is necessarily H2O
 It is 1-contingent: it is not necessary that in every possible world (water)
odorless-drinkable-tranparent-liquid is exemplified
 You can justify it only empirically/a posteriori - The notion of Water does not
imply H2O
‘The standard meter stick in Paris is one meter long’ – Contingent A priori
 It is 2-contingent: it is not necessary that ‘this/our’ standard meter stick is
exemplified in all possible worlds.
 It is 1-necessary: in every possible world where there is a stick ‘called standard
meter stick’ is one meter long
 Because of the definition of ‘meter’ so can be known a priori
‘
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Epistemology
End(?)

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…
2015.07.07.
Epistemology
If you are smart enough
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“A priori reasoning from PQTI, puts one in a position to know all about the physical
composition, the phenomenal appearance, the spatial structure and dynamic
behavior of macro physical system, along facts about their relation to oneself
and their distribution to know all ordinary macro physical truth S about such
systems, as long as one possesses the concepts involved in S.” (Chalmers
2002: p. 179)
i.
Primary Intension can be know a priori
ii.
S is a priori iff S has a necessary 1-intension
2015.07.07.
Epistemology
paper: prove it is false or not
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Superman does not exist in the actual world. But let us primarily conceive a comic possible world where
Superman exists, call it marvel universe. Moreover, “Superman” and “Clark Kent” are proper names,
and according to Kripke, they are rigid designators and primary intension of them is necessary.
Hereby, the assertion “Superman is Clark Kent” is a metaphysical necessity. The marvel universe is
a metaphysically possible centered world satisfying the primary intensions of “Superman” and “Clark
Kent”. More precisely, the secondary intension of Superman (in the marvel universe) picks out Clark
Kent and Superman in every possible world (where he is exemplified). Now, suppose that Lex Luthor
(the greatest genius enemy of Superman) has a limitless cognitive power (like an ideal reasoner).
Furthermore, he also knows PQTI of the marvel universe – since PQTI is speaker relative. According
to Chalmers, by limitless reasoning and PQTI in his armchair Lex Luthor would know a priory that
“Clark Kent is Superman” (and it is metaphysically necessary).
Chalmers' strategy is that a complete qualitative description of a world, which is epistemically complete,
can built up any epistemic possible scenario. This PQTI, which is absolutely epistemic, allows
identity statements formed by proper names such as “Superman is Clark Kent” or “(twin-) water is
XYZ”. Naturally, in the actual world there is no such thing as Superman. However, the assertion
“Superman is Clark Kent” is metaphysically necessary in that epistemic word that is 1-conceived. Viz.
the secondary intension of Superman picks out that very (Clark Kent) object in every possible world.
Of course, it is possible that Zsolt Ziegler (me) is superman, but it is an epistemic possibility. It is 1conveivable that in the actual world I have those (reference fixing) superman properties.
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Epistemology