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is, whether experience produces the idea by means of the understanding
or of the imagination; whether we are determin ’ d by reason to make the
transition, or by a certain association of perceptions. If reason determin ’ d us,
it wou ’ d proceed upon that principle, that instances, of which we have had
no experience must resemble those, of which we have had experience, and
that the course of nature continues always uniformly the same. In order
therefore to clear up this matter, let us consider all the arguments, upon which
such a proposition may suppos ’ d to be founded ’ and as these must be deriv ’ d
either from knowledge or probability, let us cast our eye on each of these
degrees of evidence, and see whether they afford any just conclusion of this
nature. (Hume, 1.3.6.3, 1.3.6.4)
P1. When the mind makes what appears to be a necessary transition from
a present impression, or a memory of an impression, to a given idea, we
call that transition “ cause and effect. ” The question is, on what is this
seemingly necessary transition founded? Of what is it a function: understanding
(i.e., reason) or the imagination?
P2. If reason does determine us to make these causal transitions, then this
reasoning must proceed upon the principle that instances (e.g., particular
associations of any two objects) that occurred in the past will continue
to occur as such in the future (the principle of uniformity).
P3. If causal necessity is a function of reason, where that reason is based
on the principle of uniformity, then the principle of uniformity must,
in some fashion or other, be justifi ed ; it too must be “ founded ” on
Hume and the Problem of Induction 179
reason. In symbolic form, this reads (N ⊃ P) ⊃ J, where ‘ N ’ stands for
causal necessity is a function of reason, ‘ P ’ stands for a principle of
uniformity, and ‘ J ’ stands for “ the principle of uniformity is justifi ed by
reason. ”
P4. There are only two kinds of reason that may justify a principle, including
the principle of uniformity: (a) “ knowledge ” (demonstrative reasoning)
or (b) “ probable ” reasoning.
P5. Assume that the principle of uniformity is justifi ed by demonstrative
reasoning.
P6. If the principle of uniformity is justifi ed by demonstrative reasoning – in
other words, it is an instance of demonstrative reasoning – then the
principle of uniformity cannot be imagined otherwise.
P7. We can imagine that nature will not continue uniformly in the future,
while simultaneously imagining that nature has always continued the
same in the past, without contradicting ourselves.
C1. The principle of uniformity is not proved; that is, justifi ed by demonstrative
reasoning ( modus tollens , P6, P7).
P8. The principle of uniformity is justifi ed by probable reasoning (assumption
for reductio ).
P9. Probable reasoning is actually causal reasoning, since both are cases
where we are automatically led to think of an idea in virtue of experiencing
an impression or remembering an impression.
P10. If the reasoning at hand is an instance of causal reasoning, then such
reasoning is justifi ed by the principle of uniformity.
C2. Probable reasoning is justifi ed by the principle of uniformity ( modus
ponens , P9, P10).
C3. The principle of uniformity is justifi ed by probable reasoning (i.e.,
causal reasoning) and justifi es probable reasoning (i.e., causal reasoning)
(conjunction, P7, C2).
C4. The principle of uniformity is not justifi ed by probable reason
( reductio , P7 – C3).
C5. The principle of uniformity is not justifi ed by either demonstrative
or probable reasoning (conjunction C1, C4).
P11. If the principle of uniformity is not justifi ed by either demonstrative
or probable reasoning, then we must reject the claim that the principle
of uniformity is justifi ed by reason.
C6. We must reject the claim that the principle of uniformity is justifi ed
by reason ( modus ponens , C5, P11).
P12. If we must reject the claim that the principle of uniformity is justifi ed
by reason, then we must reject the claim that the necessity that seems to
accompany causal relations is a function of reason.
C7. We must reject the claim that the necessity that seems to accompany
causal relations is a function of reason ( modus ponens , P12, C6).
46
Argument by Analogy in Thales
and Anaximenes
Giannis Stamatellos
Aristotle . On the Heavens , translated by W. K. C. Guthrie. Cambridge, MA :
Harvard University Press , 1939 .
Barnes , Jonathan . The Presocratic Philosophers . London : Routledge , 1979 .
Diels , Hermann . Die Fragmente der Vorsokratiker , 6th edn. , revised with
additions and index by W. Kranz . Berlin : Weidmann , 1951 – 52 . (DK)
Kirk , Geoffrey Stephen , John Earl Raven , and Malcolm Schofi eld . The
Presocratic Philosophers . Cambridge, UK : Cambridge University Press ,
1983 .
Lloyd , Geoffrey Ernest Richard . Polarity and Analogy: Two Types of
Argumentation in Early Greek Thought . Bristol : Bristol Classical Press ,
1992 .
Pachenko , Dmitri . “ Thales and the Origin of Theoretical Reasoning . ”
Confi gurations 3 ( 1993 ): 387 – 484 .
Wright , M. R . The Presocratics . Bristol : Bristol Classical Press , 1985 .
If x is P and Q , and y is P , we infer that y is also Q .
An argument by analogy relies on inductive inference. Arguing by analogy
is arguing that since things are similar or alike in certain respects, they are
similar or alike in others. An analogical argument is based on hypothetical
similarities between distinct cases: in other words, since things are similar
in certain observable or identifi ed cases, they are also similar in some other
unobservable or unidentifi ed cases.
Just the Arguments: 100 of the Most Important Arguments in Western Philosophy,
First Edition. Edited by Michael Bruce and Steven Barbone.
© 2011 Blackwell Publishing Ltd. Published 2011 by Blackwell Publishing Ltd.
Argument by Analogy in Thales and Anaximenes 181
An argument by analogy is not deductively valid. It is considered as a
weak form of argumentation due to the arbitrary presupposition of similarities
between things. However, analogy is not only used in literal cases but
also in cases of metaphor and explanatory purposes. Moreover, an argument

is, whether experience produces the idea by means of the understanding

or of the imagination; whether we are determin ’ d by reason to make the

transition, or by a certain association of perceptions. If reason determin ’ d us,

it wou ’ d proceed upon that principle, that instances, of which we have had

no experience must resemble those, of which we have had experience, and

that the course of nature continues always uniformly the same. In order

therefore to clear up this matter, let us consider all the arguments, upon which

such a proposition may suppos ’ d to be founded ’ and as these must be deriv ’ d

either from knowledge or probability, let us cast our eye on each of these

degrees of evidence, and see whether they afford any just conclusion of this

nature. (Hume, 1.3.6.3, 1.3.6.4)

P1. When the mind makes what appears to be a necessary transition from

a present impression, or a memory of an impression, to a given idea, we

call that transition “ cause and effect. ” The question is, on what is this

seemingly necessary transition founded? Of what is it a function: understanding

(i.e., reason) or the imagination?

P2. If reason does determine us to make these causal transitions, then this

reasoning must proceed upon the principle that instances (e.g., particular

associations of any two objects) that occurred in the past will continue

to occur as such in the future (the principle of uniformity).

P3. If causal necessity is a function of reason, where that reason is based

on the principle of uniformity, then the principle of uniformity must,

in some fashion or other, be justifi ed ; it too must be “ founded ” on

Hume and the Problem of Induction 179

reason. In symbolic form, this reads (N ⊃ P) ⊃ J, where ‘ N ’ stands for

causal necessity is a function of reason, ‘ P ’ stands for a principle of

uniformity, and ‘ J ’ stands for “ the principle of uniformity is justifi ed by

reason. ”

P4. There are only two kinds of reason that may justify a principle, including

the principle of uniformity: (a) “ knowledge ” (demonstrative reasoning)

or (b) “ probable ” reasoning.

P5. Assume that the principle of uniformity is justifi ed by demonstrative

reasoning.

P6. If the principle of uniformity is justifi ed by demonstrative reasoning – in

other words, it is an instance of demonstrative reasoning – then the

principle of uniformity cannot be imagined otherwise.

P7. We can imagine that nature will not continue uniformly in the future,

while simultaneously imagining that nature has always continued the

same in the past, without contradicting ourselves.

C1. The principle of uniformity is not proved; that is, justifi ed by demonstrative

reasoning ( modus tollens , P6, P7).

P8. The principle of uniformity is justifi ed by probable reasoning (assumption

for reductio ).

P9. Probable reasoning is actually causal reasoning, since both are cases

where we are automatically led to think of an idea in virtue of experiencing

an impression or remembering an impression.

P10. If the reasoning at hand is an instance of causal reasoning, then such

reasoning is justifi ed by the principle of uniformity.

C2. Probable reasoning is justifi ed by the principle of uniformity ( modus

ponens , P9, P10).

C3. The principle of uniformity is justifi ed by probable reasoning (i.e.,

causal reasoning) and justifi es probable reasoning (i.e., causal reasoning)

(conjunction, P7, C2).

C4. The principle of uniformity is not justifi ed by probable reason

( reductio , P7 – C3).

C5. The principle of uniformity is not justifi ed by either demonstrative

or probable reasoning (conjunction C1, C4).

P11. If the principle of uniformity is not justifi ed by either demonstrative

or probable reasoning, then we must reject the claim that the principle

of uniformity is justifi ed by reason.

C6. We must reject the claim that the principle of uniformity is justifi ed

by reason ( modus ponens , C5, P11).

P12. If we must reject the claim that the principle of uniformity is justifi ed

by reason, then we must reject the claim that the necessity that seems to

accompany causal relations is a function of reason.

C7. We must reject the claim that the necessity that seems to accompany

causal relations is a function of reason ( modus ponens , P12, C6).

46

Argument by Analogy in Thales

and Anaximenes

Giannis Stamatellos

Aristotle . On the Heavens , translated by W. K. C. Guthrie. Cambridge, MA :

Harvard University Press , 1939 .

Barnes , Jonathan . The Presocratic Philosophers . London : Routledge , 1979 .

Diels , Hermann . Die Fragmente der Vorsokratiker , 6th edn. , revised with

additions and index by W. Kranz . Berlin : Weidmann , 1951 – 52 . (DK)

Kirk , Geoffrey Stephen , John Earl Raven , and Malcolm Schofi eld . The

Presocratic Philosophers . Cambridge, UK : Cambridge University Press ,

1983 .

Lloyd , Geoffrey Ernest Richard . Polarity and Analogy: Two Types of

Argumentation in Early Greek Thought . Bristol : Bristol Classical Press ,

1992 .

Pachenko , Dmitri . “ Thales and the Origin of Theoretical Reasoning . ”

Confi gurations 3 ( 1993 ): 387 – 484 .

Wright , M. R . The Presocratics . Bristol : Bristol Classical Press , 1985 .

If x is P and Q , and y is P , we infer that y is also Q .

An argument by analogy relies on inductive inference. Arguing by analogy

is arguing that since things are similar or alike in certain respects, they are

similar or alike in others. An analogical argument is based on hypothetical

similarities between distinct cases: in other words, since things are similar

in certain observable or identifi ed cases, they are also similar in some other

unobservable or unidentifi ed cases.

Just the Arguments: 100 of the Most Important Arguments in Western Philosophy,

First Edition. Edited by Michael Bruce and Steven Barbone.

Argument by Analogy in Thales and Anaximenes 181

An argument by analogy is not deductively valid. It is considered as a

weak form of argumentation due to the arbitrary presupposition of similarities

between things. However, analogy is not only used in literal cases but

also in cases of metaphor and explanatory purposes. Moreover, an argument