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be no demonstration. (1006a, 8 – 10)
Here is an abridged version of Aristotle ’ s implicit reductio ad infi nitum
argument:
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.
Aristotle and the Argument to End All Arguments 199
P1. For any p , if p is a proposition, then reasons can be given for/
against p .
P2. p is a proposition.
C1. Reasons can be given for/against P ( modus ponens , P1, P2).
P3. q and r are reasons for/against p .
P4. If q and r are propositions, then reasons can be given for/against q
and r .
P5. q is a proposition.
C2. Reasons can be given for/against q ( modus ponens , P1, P5).
P6. s and t are reasons for/against q .
P7. If s and t are propositions, then reasons can be given for/against s
and t .
P8. s is a proposition.
C3. Reasons can be given for/against s ( modus ponens P1, P8).
P9. u and v are reasons for/against s .
P10. If u and v are propositions, then reasons can be given for/against u
and v .
P11. u is a proposition.
C4. Reasons can be given for/against u ( modus ponens , P1, 11).
And so on, ad infi nitum (omitting r , t , and v for the sake of brevity).
If we demand reasons for/against every proposition, in other words, we
will be stuck in an endless process of justifi cation, unable to assert anything
at all. As the philosopher of logic and mathematics Charles Parsons put it,
“ The buck has to stop somewhere. ”
This argument does not, of course, prevent us from giving reasons for
many, indeed most, propositions. And even where we cannot give reasons
for a proposition, it does not follow that we are therefore unjustifi ed in
believing it. Some propositions may be self - evident – known intuitively, as
“ evident without proof or reasoning, ” to quote Webster ’ s Ninth . That is
how Aristotle viewed the logical law of noncontradiction and how others
have treated moral rules like promise keeping. The American Declaration
of Independence famously begins: “ We hold these truths to be
self - evident. ”
Then, too, while the buck has to stop somewhere, it need not always
stop in the same place. We can assume the truth of a proposition merely
conditionally, for the sake of argument. We can even assume that p is true
for one argument and false for another. As the economic theorist Milton
Friedman notes in his Essays in Positive Economics , “ there is no inconsistency
in regarding the same fi rm as if it were a perfect competitor for one
problem, and a monopolist for another, just as there is none in regarding
the same chalk mark as a Euclidean line for one problem, a Euclidean
surface for a second, and a Euclidean solid for a third ” (36).
200 Toni Vogel Carey
It is important, though, to know what proposition(s) one is taking as
given. People are often unaware of their underlying premises or think them
too obvious to mention. But marriages, friendships, and political alliances
can come to a bad end simply because of unarticulated disagreements about
where the buck stops.
We hold some truths to be more self - evident than others, not only for
the sake of argument, but without qualifi cation. Scientists operate on the
assumption that whatever laws hold for the universe today will continue to
hold tomorrow. And that the buck has to stop somewhere is even more
foundational than this principle of induction. Philosophers have traditionally
supposed there are some necessary truths; that is, propositions that
could not, in any possible world, be false. If so, the Aristotelian argument
we are considering is one of these.
On the other hand, in “ Two Dogmas of Empiricism, ” the philosopher
W. V. Quine put forward the idea that so - called necessary truths are merely
those propositions we would be most reluctant to give up (#44). For many,
the existence and benevolence of God is a belief to keep when all else fails.
For Quine, though, no statement, not even a law of logic, is “ immune to
revision. ”
The argument we are considering is important because it shows that
there are limitations to what reasoning can accomplish, which goes against
our cherished belief that the exercise of reason can, in principle, settle all
disputes. If the buck has to stop somewhere, then even in logic the ultimate
appeal is not to reason, deductive or inductive, but to something closer to
intuition. Aristotle had no trouble accepting this; nor, for that matter, did
Einstein. But John Stuart Mill and others have made ‘ intuition ’ a term of
ill repute – notwithstanding Mill ’ s assertion in A System of Logic that
“ truths known by intuition are the original premises from which all others
are inferred ” ( § 4).
The trouble with intuition is that people are often loath to brook any
challenge, however well taken, to their entrenched intuitive beliefs, making
further discussion pointless, if not impossible; and this can lead to toxic
forms of fanaticism. That one bases a belief on intuition does nothing to
guarantee its truth. But fallible, and even dangerous, as intuitive beliefs can
be, it does not follow that intuition should simply be discredited. As George
Bealer notes in his entry on “ Intuition ” in the Supplement to the Encyclopedia
of Philosophy , perception too is fallible (even dangerous at times), but no
one thinks we should therefore discount it. On the contrary, it is a truism
that “ seeing is believing. ”
Valid logical inference is safe, while the appeal to intuition carries some
risk. But what Aristotle ’ s argument shows is that valid logical inference
itself rests on propositions (axioms) whose truth we accept intuitively; that
is perforce where the buck stops.
Part IV
Ethics
51
Justice Brings Happiness in
Plato ’ s Republic
Joshua I. Weinstein
Plato . Republic , translated by G. M. A. Grube and C. D. C. Reeve.

be no demonstration. (1006a, 8 – 10)

Here is an abridged version of Aristotle ’ s implicit reductio ad infi nitum

argument:

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

First Edition. Edited by Michael Bruce and Steven Barbone.

Aristotle and the Argument to End All Arguments 199

P1. For any p , if p is a proposition, then reasons can be given for/

against p .

P2. p is a proposition.

C1. Reasons can be given for/against P ( modus ponens , P1, P2).

P3. q and r are reasons for/against p .

P4. If q and r are propositions, then reasons can be given for/against q

and r .

P5. q is a proposition.

C2. Reasons can be given for/against q ( modus ponens , P1, P5).

P6. s and t are reasons for/against q .

P7. If s and t are propositions, then reasons can be given for/against s

and t .

P8. s is a proposition.

C3. Reasons can be given for/against s ( modus ponens P1, P8).

P9. u and v are reasons for/against s .

P10. If u and v are propositions, then reasons can be given for/against u

and v .

P11. u is a proposition.

C4. Reasons can be given for/against u ( modus ponens , P1, 11).

And so on, ad infi nitum (omitting r , t , and v for the sake of brevity).

If we demand reasons for/against every proposition, in other words, we

will be stuck in an endless process of justifi cation, unable to assert anything

at all. As the philosopher of logic and mathematics Charles Parsons put it,

“ The buck has to stop somewhere. ”

This argument does not, of course, prevent us from giving reasons for

many, indeed most, propositions. And even where we cannot give reasons

for a proposition, it does not follow that we are therefore unjustifi ed in

believing it. Some propositions may be self - evident – known intuitively, as

“ evident without proof or reasoning, ” to quote Webster ’ s Ninth . That is

how Aristotle viewed the logical law of noncontradiction and how others

have treated moral rules like promise keeping. The American Declaration

of Independence famously begins: “ We hold these truths to be

self - evident. ”

Then, too, while the buck has to stop somewhere, it need not always

stop in the same place. We can assume the truth of a proposition merely

conditionally, for the sake of argument. We can even assume that p is true

for one argument and false for another. As the economic theorist Milton

Friedman notes in his Essays in Positive Economics , “ there is no inconsistency

in regarding the same fi rm as if it were a perfect competitor for one

problem, and a monopolist for another, just as there is none in regarding

the same chalk mark as a Euclidean line for one problem, a Euclidean

surface for a second, and a Euclidean solid for a third ” (36).

200 Toni Vogel Carey

It is important, though, to know what proposition(s) one is taking as

given. People are often unaware of their underlying premises or think them

too obvious to mention. But marriages, friendships, and political alliances

can come to a bad end simply because of unarticulated disagreements about

where the buck stops.

We hold some truths to be more self - evident than others, not only for

the sake of argument, but without qualifi cation. Scientists operate on the

assumption that whatever laws hold for the universe today will continue to

hold tomorrow. And that the buck has to stop somewhere is even more

foundational than this principle of induction. Philosophers have traditionally

supposed there are some necessary truths; that is, propositions that

could not, in any possible world, be false. If so, the Aristotelian argument

we are considering is one of these.

On the other hand, in “ Two Dogmas of Empiricism, ” the philosopher

W. V. Quine put forward the idea that so - called necessary truths are merely

those propositions we would be most reluctant to give up (#44). For many,

the existence and benevolence of God is a belief to keep when all else fails.

For Quine, though, no statement, not even a law of logic, is “ immune to

revision. ”

The argument we are considering is important because it shows that

there are limitations to what reasoning can accomplish, which goes against

our cherished belief that the exercise of reason can, in principle, settle all

disputes. If the buck has to stop somewhere, then even in logic the ultimate

appeal is not to reason, deductive or inductive, but to something closer to

intuition. Aristotle had no trouble accepting this; nor, for that matter, did

Einstein. But John Stuart Mill and others have made ‘ intuition ’ a term of

ill repute – notwithstanding Mill ’ s assertion in A System of Logic that

“ truths known by intuition are the original premises from which all others

are inferred ” ( § 4).

The trouble with intuition is that people are often loath to brook any

challenge, however well taken, to their entrenched intuitive beliefs, making

further discussion pointless, if not impossible; and this can lead to toxic

forms of fanaticism. That one bases a belief on intuition does nothing to

guarantee its truth. But fallible, and even dangerous, as intuitive beliefs can

be, it does not follow that intuition should simply be discredited. As George

Bealer notes in his entry on “ Intuition ” in the Supplement to the Encyclopedia

of Philosophy , perception too is fallible (even dangerous at times), but no

one thinks we should therefore discount it. On the contrary, it is a truism

that “ seeing is believing. ”

Valid logical inference is safe, while the appeal to intuition carries some

risk. But what Aristotle ’ s argument shows is that valid logical inference

itself rests on propositions (axioms) whose truth we accept intuitively; that

is perforce where the buck stops.

Part IV

Ethics

51

Justice Brings Happiness in

Plato ’ s Republic

Joshua I. Weinstein

Plato . Republic , translated by G. M. A. Grube and C. D. C. Reeve.