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Philosophy 190: Seminar on Kant
Spring, 2015
Prof. Peter Hadreas
Course website:
http://oucampus.sjsu.edu/people/peter.hadreas/courses/Ka
nt/index.html
NOTE: The Guyer and Wood translation of
the Critique of Pure Reason – the text we’re
using -- can be accessed online at
http://strangebeautiful.com/lmu/readings/ka
nt-first-critique-cambridge.pdf
Introduction to the Second
Edition of the Critique of Pure
Reason (1787), pp. 136-152.
Very Short Historical
Review
of the a prioria posteriori distinction
In Metaphysics, Book V, Chapter 11,
Aristotle itemizes five senses of prior: two
in respect of knowledge, in respect of
nature and substance, and one in respect
of attributes per se.
Scholasticism
dominated medieval
universities in Europe
from about 1100 to
1700. Picture on the
right is a 14th-century
fresco of a university
lecture.
In the Scholastic tradition,, i. e. the medieval appropriation of
Aristotle, the terms literally mean "from what is prior" and
"from what is posterior." In the Scholastic tradition these terms
meant either: a) A is prior to B in nature only if A could not
exist without B; or, b) A is prior to B in knowledge only if we
cannot know A without knowing B.
The a priori - a posteriori
distinction as it was taught in
Kant’s day.
In the Leibnizian-Wolff system which was the philosophy
"of the Schools" in Kant's day, a priori and a posteriori were
define according to causal relations: "When the mind
reasons from causes to effect, the demonstration is called a
priori; when from effects to causes, the demonstration is
called a posteriori.”
It was this usage which Hume criticizes in the Treatise of
Human Nature, Book I. (1739). It follows from Hume's
analysis of causation that if there is no necessary connection
between cause and effect, the distinction between a priori
and a posteriori falls apart.
Introduction to the Second Edition of the
Critique of Pure Reason (1787), pp. 136-152.
“In the sequel therefore we will understand by a priori
cognitions not those that occur independently of this
or that experience, but rather those that occur
absolutely independently of all experience. Opposed to
them are empirical cognitions, or those that are
possible only a posteriori, i.e., through experience.
Among a priori cognitions, however, those are called
pure with which nothing empirical is intermixed.
Thus, e.g., the proposition "Every alteration has its
cause" is an a priori proposition, only not pure, since
alteration is a concept that can be drawn only from
experience.” (p. 117)
Introduction to the Second Edition of the
Critique of Pure Reason (1787), pp. 136-152.
“First, then, if a proposition is thought along with its necessity,
it is an a priori judgment; if it is, moreover, also not derived
from any proposition except one that in turn is valid as a
necessary proposition, then it is absolutely a priori. Second:
Experience never gives its judgments true or strict but only
assumed and comparative universality (through induction), so
properly it must be said: as far as we have yet perceived, there
is no exception to this or that rule. Thus if a judgment is
thought in strict universality, i.e., in such a way that no
exception at all is allowed to be possible, then it is not derived
from experience, but is rather valid absolutely a priori.”
Introduction to the Second Edition of the
Critique of Pure Reason (1787), pp. 136-152.
So necessary conditions of a all priori judgments are
that they are necessary and universal.
Using Kant’s examples: “Every body has a cause” is a
priori. “All bodies are heavy” is not a priori.
In these examples Kant’s transcendental method is already at
work. “Gradually remove from your experiential concept of a
body everything this is empirical in it – the color, the hardness,
or softness, even the impenetrability – there still remains the
space that was occupied by the body (which has now entirely
disappeared), and you cannot leave that out.” (p. 138)
Introduction to the Second Edition of the
Critique of Pure Reason (1787), pp. 136-152.
“All prime numbers greater than two are odd.”
An priori judgment. It necessary and universal.
“All U. S. Presidents are male.” Not a priori. True, but
neither necessary nor strictly universal. There
could be a U. S. President who is not male. There may
be in 2017. It is an a posteriori judgment.
Introduction to the Second Edition of the
Critique of Pure Reason (1787), pp. 136-152.
A very notorious example of a mathematical claim that was
thought to be a priori but was finally determined not to be:
Euclid’s Fifth Postulate:
“If a line segment intersects two straight lines
forming two interior angles on the same side that
sum to less than two right angles, then the two lines,
if extended indefinitely, meet on that side on which
the angles sum to less than two right angles.”
Introduction to the Second Edition of the
Critique of Pure Reason (1787), pp. 136152.
On the difference between pure and empirical cognition.
[Kant Exposes Epistemological Fallacy #1
”There is no doubt whatever that all our cognition begins with
experience; for how else should the cognitive faculty be awakened
into exercise if not through objects that stimulate our senses and
in part themselves produce representations, in part bring the
activity of our understanding into motion to compare these, to
connect or separate them, and thus to work up the raw material
of sensible impressions into a cognition of objects that is called
experience?” (p. 136) [continues]
Introduction to the Second Edition of the
Critique of Pure Reason (1787), pp. 136-152.
Kant Exposes Epistemological Fallacy #1
“As far as time is concerned, then, no cognition in us precedes
experience, and with experience every cognition begins.
But although all our cognition commences with experience, yet
it does not on that account all arise from experience.1 For it
could well be that even our experiential cognition is a composite
of that which we receive through impressions and that which
our own cognitive faculty (merely prompted by sensible
impressions) provides out of itself, which addition we cannot
distinguish from that fundamental material until long practice
has made us attentive to it and skilled in separating
it out.” (p. 136)
Introduction to the Second Edition of the
Critique of Pure Reason (1787), pp. 136-152.
Fundamental epistemological fallacy #1.
“But although all our cognition commences with experience,
yet it does not on that account all arise from experience.” (p.
136)
This fallacy is directed particularly at empiricists.
Introduction to the Second Edition of the
Critique of Pure Reason (1787), pp. 136-152.
Kant Exposes Epistemological Fallacy #2
The Extension of a priori reasoning beyond sensory experience.
The fallacy is particularly directed at the rationalists,
especially Leibniz, Wolff, and when applied to non-ethical
issues, Plato.
“Captivated by such a proof of the power of reason, the drive
for expansion sees no bounds. The light dove, in free flight
cutting through the air the resistance of which it feels, could
get the idea that it could do even better in airless space.
Likewise, Plato abandoned the world of the senses because it
set such narrow limits for the understanding, and dared to go
beyond it on the wings of the ideas, in the empty space of pure
understanding.” (p. 140.)
Kant’s Use of a priori is multi-faceted.
Kant applies the notion of a priori 1) to
knowledge, 2) judgments, 3) concepts, 4)
‘principles,' and 5) a faculty of a priori
knowledge.1
1. CPR B4: Necessity and strict universality are thus sure criteria of a priori knowledge,
and are inseparable from one another.
CPR B4: "it is easy to show that there actually are in human knowledge judgments which
are necessary and in the strictest sense universal, and which are therefore pure a priori
judgments'.
CPR B5: it is possible to show that pure a priori principles are indispensable for the
possibility of experience, and so to prove their existence a priori. For when could
experience derive its certainty, if all the rules, according to which it proceeds, were always
themselves empirical, and therefore contingent.
CPR B5): Such a priori origin is manifest in certain concepts, no less than judgment."
[Kant gives the example that a corporeal body implies a space which it occupies.]
CPR B6: "Owing, therefore to the necessity with which this concept of substance forces
itself upon us, we have no option save to admit that it has its seat in our faculty of a priori
knowledge." (See also B4: 'a faculty of a priori knowledge.'
Kant’s Introduction of the
‘analytic’/ ‘synthetic Distinction
The distinction between 'analytic' and 'synthetic' judgments
was developed by Kant himself and developed especially out of
his criticism of the Leibniz-Wolffian school. Leibniz treated all
judgments as analytic.
“In all judgments in which the relation of a subject to the
predicate is . . . 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, though to be sure it stands in connection
with it. In the first case I call the judgment analytic, in the
second synthetic.” (p. 141) [continued]
Kant’s Introduction of the
‘analytic’/ ‘synthetic Distinction
“Analytic judgments (affirmative ones) are thus those in which
the connection of the predicate is thought through identity, but
those in which this connection is thought without identity are
to be called synthetic judgments. One could also call the
former judgments of clarification, and the latter judgments of
amplification since through the predicate the former
do not add anything to the concept of the subject, but only
break it up by means of analysis into its component concepts,
which were already thought in it (though confusedly); while
the latter, on the contrary, add to the concept of the subject a
predicate that was not thought in it at all, and could not have
been extracted from it through any analysis.” (p. 141)
[continued]
Kant’s Introduction of the
‘analytic’/ ‘synthetic Distinction
[continued from previous slide] “E.g., if I say: "All bodies
are extended," then this is an analytic judgment. For I do
not need to go beyond the concept that I combine with the
body in order to find that extension is connected with it, but
rather I need only to analyze that concept, i.e., become
conscious of the manifold that I always think in it, in order
to encounter this predicate therein; it is therefore an
analytic judgment. On the contrary, if I say: "All bodies are
heavy," then the predicate is something entirely different
from that which I think in the mere concept of a body in
general. The addition of such a predicate thus yields a
synthetic judgment.” (p. 141) [continues}
Kant’s Introduction of the
‘analytic’/ ‘synthetic Distinction
[continued from previous slide] “Judgments of
experience, as such, are all synthetic. For it would be
absurd to ground an analytic judgment on experience,
since I do not need to go beyond my concept at all in
order to formulate the judgment, and therefore need no
testimony from experience for that.” (p. 142)
The Key Question of Division One of
the CPR:
How are synthetic a priori judgments
possible?
Kant’s allows a few intuitively obvious mathematical
truths to be analytic. His examples:
“To be sure, a few principles that the geometers
presuppose are actually analytic and rest on the principle
of contradiction; but they also only serve, as identical
propositions, for the chain of method and not as
principles, e.g., a = a, the whole is equal to itself, or (a +
b) > a, i.e., the whole is greater than its part. And yet
even these, although they are valid in accordance with
mere concepts, are admitted in mathematics
only because they can be exhibited in intuition.” (p. 145)
But all but the most intuitively
obvious true proposition of
mathematics and science are
synthetic a priori judgments.
Even 7 + 5 = 12 is synthetic a priori. “The arithmetical
proposition is therefore always synthetic; one becomes all the
more distinctly aware of that if one takes somewhat larger
numbers, for it is then clear that, twist and turn our concepts
as we will, without getting help from intuition we could never
find the sum by means of the mere analysis of our concepts.”
(p. 144)
All but the most intuitively obvious
true propositions of mathematics and
science are
synthetic a priori judgments.
“A straight line is the shortest distance between two points” is
synthetic a priori.
“That the straight line between two points is the shortest is a
synthetic proposition. For my concept of the straight contains
nothing of quantity, but only a quality. The concept of the
shortest is therefore entirely additional to it, and cannot be
extracted out of the concept of the straight line by any
analysis. Help must here be gotten from intuition, by means of
which alone the synthesis is possible.” (p. 145)
A definition of ‘straight line’ relies on concepts
outside of those contained in ‘straight’ and ‘line’
themselves.
Some definitions of straight line.
1. Plato, Parmenides 137 E. And the straight, again, is that of
which the middle is in the nearest line between the two
extremes."
2. Euclid, Elements, Book One, Definition #4: "A straight line is
a line which lies evenly with the points on itself.”
3. Archimedes (c. 225 B. C.), On the Sphere and the Cylinder,
Book I, Assumptions, "Of all lines which have the same
extremities the straight line is the least."
4. Carl Friedrich Gauss, (1777 –1855). "The line in which lie all
points that, during the revolution of a body (or part of space)
about two fixed points, maintain their position unchanged is
called a straight line."
Kant’s Examples of Synthetic A Priori Judgments
from Physical Sciences
“Natural science (Physica) contains within itself synthetic a
priori judgments as principles. I will adduce only a couple of
propositions as examples, such as the proposition that in all
alterations of the corporeal world the quantity of matter remains
unaltered, [the law of the conservation of mass]1 or that in all
communication of motion effect and counter-effect must always
be equal.2 In both of these not only the necessity, thus their a
priori origin, but also that they are synthetic propositions is
clear.” (p. 145)
1. Mass conservation was discovered in chemical reactions by
Antoine Lavoisier in the late 18th century. This law
contributed to the progress from alchemy to the modern
natural science of chemistry.
2. Newton’s Third Law of Motion.
Kant’s Examples of Synthetic A Priori Judgments
from Metaphysics
“In metaphysics, even if one regards it as a science that has
thus far merely been sought but is nevertheless indispensable
because of the nature of human reason, synthetic a priori
cognitions are supposed to be contained, and it is not
concerned merely with analyzing concepts that we make of
things a priori and thereby clarifying them analytically, but we
want to amplify our cognition a priori; to this end we must
make use of such principles that add something to the given
concepts that was not contained in them, and through
synthetic a priori judgments go so far beyond that experience
itself cannot follow us that far, e.g., in the proposition "The
world must have a first beginning," and others besides, and
thus metaphysics, at least as far as its end is concerned,
consists of purely synthetic a priori propositions.” (pp. 145-6)
Will the CPR be an ‘Organon’ or a ‘Canon’?
VII. Section VII of 'The Introduction’, “The Idea and Division
of a Special Science, under the Title 'Critique of Pure
Reason'"
(p. 149, B 24-5) "An organon of pure reason would be the sum
total of those principles in accordance with which all modes of
pure a priori knowledge can be acquired and actually brought
about.” . . . . .
(p. 150, B26.) “Such a critique is accordingly a preparation, if
possible, for an organon, and, if this cannot be accomplished,
then at least for a canon, in accordance with with which the
complete system of philosophy of pure reason, whether it is to
consist in the amplification or the mere limitation of its of its
cognition, can at least some day be established both
analytically and synthetically.”
Main Historical Developments
Since Kant Which Have Set
Out to
Establish New Foundation the
Synthetic A Priori Issue.
Gottlob Frege
1848 – 26 July 1925)
Frege, Gottlob, The
Foundations of
Arithmetic, 1884, pp.
3ff.
“Philosophical motives have prompted me to enquiries of this
kind. The answers to the questions raised about the nature of
arithmetical truths -- are they a priori or a posteriori?
synthetic or analytic? -- must lie in this same direction. For
even though the concepts concerned may themselves belong to
philosophy, yet, as I believe, no decision on these questions can
be reached without assistance from mathematics -- though this
depends on the sense in which we understand them.”
Frege, Gottlob, The
Foundations of
Arithmetic, 1884, pp.
3ff.
”It not uncommonly happens that we first discover the
content of a proposition, and only later give the rigorous proof
of it, on other and more difficult lines; and often this same
proof also reveals more precisely the conditions restricting the
validity of the original proposition. In general therefore, the
question of how we arrive at the content of a judgment should
be kept distinct from the other question. Whence do we derive
the justification for its assertion?”
Frege, Gottlob, The
Foundations of
Arithmetic, 1884, pp.
3ff.
“Now distinctions between a priori and a posteriori, synthetic
and analytic, concern, as I see it,1 not the content of the
judgment, but the justification for making the judgment.”
1. By this I do not, of course, mean to assign a new sense to
these terms, but only to state accurately what earlier writers,
Kant in particular, have meant by them.
Frege, Gottlob, The
Foundations of
Arithmetic, 1884, pp.
3ff.
This means that the question is removed from the sphere of
psychology, and assigned, if the truth concerned is a
mathematical one, to the sphere of mathematics. The problem
becomes, in fact, that of finding the proof of the proposition,
and of following it up right back to the primitive truths. If, in
carrying out this process, we come only on general logical laws
and on definitions, then the truth is an analytic one, bearing in
mind that we must take account also of all propositions upon
which the admissibility of any of the definitions depends.
Frege, Gottlob, The Foundations
of Arithmetic, 1884, pp. 3ff.
“If, however, it is impossible to give the proof without making
use of truths which are not of a general logical nature, but
belong to the sphere of some special science, then the
proposition is a synthetic one. For a truth to be a posteriori, it
must be impossible to construct a proof of it without including
an appeal to facts, i. e., to truths which cannot be proved and
are not general, since they contain assertions about particular
objects. But, if on the contrary, its proof can be derived
exclusively from general laws, which themselves neither need
nor admit of proof, then the truth is a priori.”
Frege, Gottlob, The Foundations
of Arithmetic, 1884, pp. 3ff.
Thus Frege opens up the notion of ‘analytic’ to
include all those truths that may be inferred logically
from given principles. This would undo Kant’s notion
of synthetic a priori. For a judgment to be a priori it
must only qualify as analytic and this means that it
can be derived logically from accepted first
principles.
Principia Mathematica
Bertrand Russell (18721970) and A.N. Whitehead
(1861-1947)
Frege’s concept of ‘analytic’ had a great influence on
the foundations of so-called ‘analytic philosophy.’ In
fact it motivated Russell and Whitehead to attempt to
found all of mathematics upon logical principles. In
1903, the book had the more modest English title.
Principles of Mathematics. In 1910-1913 Russell and
Whitehead attempted to accomplish the derivation or
at least show how to do it. The three-volume magnum
opus took on the weightier title Principia
Mathematica.
Kurt Godel’s Incompleteness Proof
(1931)
But Russell’s and Whitehead’s painstaking effort to
found mathematics on logic, which involved many
years of their lives, turned out to be in vain. The
Göttigen mathematician, Hilbert, was dedicated to
clarifying the foundations of geometry. He challenged
mathematicians to prove rigorously that Russell and
Whitehead ha succeeded. The question was finally
settled in 1931 when Kurt Gödel, in a revolutionary
theorem – the Incompleteness Proof– proved that in a
mathematical theory of sufficient complexity – such
as number theory – there must be a theorem that
cannot be proven true or false.
Willard Van Orman Quine
(1908 –2000)
Quine Attacks the Analytic/
Synthetic Distinction in a Three
Main Ways in Different
Developments of His Thought
In “Two Dogmas of Empiricism” a highly influential chapter
in his book From a Logical Point of View, reprinted by
Harvard University Press in 1980, Quine suggests a weaker
argument that there is a gray area between analytic and
synthetic statements, so we cannot always tell whether a
statement is analytic or synthetic. Consider the claim that the
heights of a group of males or females will follow the
frequencies described by a normal distribution, or bell curve.
Is this analytic or synthetic?
Quine Attacks the Analytic/ Synthetic
Distinction in a Three Main Ways in
Different Developments of His Thought
Quine’s most influential and complex attempt to undermine the
notion of analyticity turns on pressing the point that, at least in
its Kantian expression, analyticity is semantic. Kant had said
that a statement is analytic if the predicate is contained in the
subject and Kant meant the meaning (semantic value) of the
judgment. In Word and Object, (1960) Quine argues for ‘radical
indeterminacy.’ The is a thought experiment which leads to the
conclusion that as long as we are dealing only with the meaning
(semantic value) of objects, and not their extension, we can
never be certain about a translation from one language to
another. Consequently the underpinnings of ‘analyticity’ are
undone, because they are semantic (intentional) and not
extensional.
Quine Attacks the Analytic/ Synthetic
Distinction in a Three Main Ways in
Different Developments of His Thought
Kantian Graham Bird answers Quine on this attempt to undo
the groundwork of ‘analyticity’ through the thought –
experiment of the radical indeterminacy of
translation:
“It is quite possible then to distinguish the philosophical
argument from the practice that allows it. . . . We can simply
allow the analytic/synthetic distinction to be used in practice
independently of the philosophical argument, just as we may
still use the resources of a current, perhaps inadequate,
semantic theory to separate analytic from synthetic judgments
or truths.”1
1. Bird,. Graham, The Revolutionary Kant, (Chicago/La Salle, IL.: Open
Court, 2006), p. 61
Quine Attacks the Analytic/ Synthetic
Distinction in a Three Main Ways in
Different Developments of His Thought
Third, sometimes Quine attacks the ‘analytic/synthetic
distinction by saying that if there are enough strong theories
which lead us to believe in their truth, we will give up even the
most basic analytic judgments, such as the Law of Excluded
Middle. We do something like this in attempting to find a model
for features of quanta. It would seem that quanta have the
property to be and not to be at the same place at the same time.
So, the predictive value of quantum theory (presumably
synthetic truths) trumps analytic truth of the Law of Excluded
Middle. This is sometimes called the epistemic vulnerability of
analytic truths.
1. adapted from Bird,. Graham, The Revolutionary Kant, (Chicago/La Salle,
IL.: Open Court, 2006), p. 61.
Quine Attacks the Analytic/ Synthetic
Distinction in a Three Main Ways in
Different Developments of His Thought
Graham Bird answers Quine on the epistemic vulnerability of
analytic truths.
“For Quine even logical truths, and those elsewhere classified as
analytic, are vulnerable to and can be replaced in the light of,
such recalcitrant experience. Even if this is true, however, what
it shows is that both analytic and synthetic truths have one such
feature, epistemic vulnerability, in common. But even if they
cannot be discriminated on that basis it does not follow that
there is no other way of distinguishing them.”1
1. Bird,. Graham, The Revolutionary Kant, (Chicago/La Salle, IL.: Open
Court, 2006), pp. 61-2.
Edmund Husserl
1859-1938
Husserl’s approach is to stay with meaning.
All extension can be derived from intensions
for Husserl. Husserl focuses particularly on
the a priori which he finds in objects and
states of affairs as well as judgments. He coins
the term eidos for the essence of a thing. It
has elements of necessity and universality – as
given to consciousness.
From, Husserl, Ideas I, Section 20, (1913):
“When it is actually natural science that speaks, we listen
gladly and as disciples. But it is not always natural science
that speaks when natural scientists are speaking; and it
assuredly is not when they are talking about "philosophy of
Nature" and "epistemology as a natural science.”
[continues]
[continued] “And, above all, it is not natural
science that speaks when they try to make us
believe that general truisms such as all axioms
express (propositions such as "a + 1 = 1 + a", "a
judgment cannot be colored", "of only two
qualitatively different tones, one is lower and the
other higher", "a perception is, in itself, a
perception of something") are indeed expressions
of experiential matters of fact; whereas we know
with full insight that propositions such as those
give explicative expression to data of eidetic
intuition.”
“But this very situation makes it clear to us that the
"positivists" sometimes confuse the cardinal differences among
kinds of intuition and sometimes indeed see them in contrast
but, bound by their prejudices, will to accept only a single one
of them as valid or even as existent. (Husserl 1913, section 20)”
from “Philosophy as Rigorous Science”, (Husserl
1965, pp. 90-91)
“The spell of the naturalistic point of view...has
blocked the road to a great science unparalleled in
its fecundity... The spell of inborn naturalism also
consists in the fact that it makes it so difficult for
all of us to see "essences", or "ideas" -- or rather,
since in fact we do, so to speak, constantly see
them, for us to let them have the peculiar value
which is theirs instead of absurdly naturalizing
them. Intuiting essences conceals no more
difficulties or "mystical" secrets than does
perception.”
Slides #1, 3, 4, 5, Portrait of Immanuel Kant in mid-life:
http://www.lancaster.ac.uk/users/philosophy/courses/100/Kant003.jpg
Slide # 15 , bust of Aristotle:
http://en.wikipedia.org/wiki/Aristotle#mediaviewer/File:Aristotle_Altemp
s_Inv8575.jpg
Slide #16, image of a 14th century University lecture:
http://upload.wikimedia.org/wikipedia/commons/f/fc/Laurentius_de_Volt
olina_001.jpg
Slide #29, photograph of Gottlob Frege:
https://www.google.com/search?q=frege&biw=
slide #36: photograsph of Russel and Whitehead:
http://www.storyofmathematics.com/20th_russell.html
Slide #38: Photograph of Willard Van Orman Quine:
http://www.bing.com/images/search?q=picture+of+willard+van+orman+
quine&qpvt
Side #44, photograph of Edmund Husserl:
http://www.husserlpage.com/