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!wORKS CITED 

Copi, Irving M. Introduction to t9,~c. 5th 
edn., Macmillan, New York; : 

Fohr, Samuel D. "The Deductive-Inductive 
Distinction." ILN, ii.2 (April 1980), 
5-8. -

Govier, Trudy. "More on Deductive and Induc-
tive Arguments." ILN, ii.3 (.June 198Q1, 
7-8. -

liitchcock, David. "Deductive and Inductive: 
Types o£ validity, Not Types of Argu-
ment." ~, ii.3 LJune 19801, 9-10. 

Weddle, Perry. "Inductive, Deductive." ~, 
iLl (November 19791, 1-5.-0 

discussion 
note 

Proofs and Begging 
the Question 

Milton H. Snoeyenbos 
Georgia State University 

Logicians utilize two distinct conceptions 
of proof. On the one hand, there is a formal 
or syntactic concept: given a formal theory 
T consisting of formulas, well-formed formu-
las (~fs), axioms and inference rules, a 
proof, in T is a sequence of wfs such that 
for each wf in the sequence either it is an 
~iom of T or it is a direct consequence of 
some of the preceding wfs by virtue of one of 
~e inference rules. On the other hand, a 
distinct concept, often used in natural lan-
~age contexts, is that an argument consti-
tutes a proof2 of the truth of its conclusion 
if it is vall.d, has true premises, and is not 
question-begging. 

13 

While the fo~er concept is not controver-
sial, "proof2" is sometimes thought to be 
problematic. James Tomberlin considers the 
following substitution instances of disjunc-
tive syllogism: (lql : NQvP, Q/P and CA21: 
~PvR, NR/*P, where Q=New York is in the U.S.A., 
P=tne mind-body identity theory is correct, 
R=Moscow is in the U.S.A.l Tomberlin asserts 
that neither argument begs a question since 
both are instances of disjunctive syllogism. 
The second premise of each argument is true. 
Furthermore, either the, first premise of Al 
or the first premise of A2 is true, since 
« NQVP)v( ""PvR) is a theorem of proposi-
tional logic. It follows that either Al or 
A2 constitutes a proof2 of its conclusion. 
Yet Tomberlin rightly notes that since the 
truth or falsity of the identity theory could 
not be decided by appeal to either argument, 
neither can be said to prove? its conclusion. 
He concludes that the analysl.s of "proof2" in 
terms of validity, true premises and the 
absence of question-begging must be incorrect. 

Tomberlin(s rejection of the standard anal-
ys;:!.s of "proo f2" follows only if we accept 
the claim that neither Al nor A2 begs the 
iss:ue. He appears to have a formalist con-
ception of begging the question, for his 
claim that Al and A2 do not beq any questions 
rests on his claim that both are instances 
of disjuncti.ve syllogism. But thls overlooks 
the often voiced claim that question-begging 
is a non-formal £allacy. From the formal 
point of view an argument such as rJ,/fX. is a 
perfectly acceptable proofl of its conclusion • 
However, even if ct is true, from a non-formal, 
say, an epistemic, point of view, the premise 
could not be said to constitute a proof2 of 
the conclusion, for to know the premise is 
true we. must know that the conclusion is 
true, i.e., the argument begs the issue. 

Let us say, then, that an argument begs the 
question if and only if in order to know that 
some member of its premise set is true we 
must know that its conclusion is true. On 
this conception of question-begging do Al and 
A2 beg any questions? In either case we can 
know the second premise is true without 
knowing the conclusion is true. But, in con-
sidering the first premise, "knowing that (I¥ 
or ~) is true" is ambiguous. In some cases 
I may know that (<<-orIS) is true and know 
which disjunct is true; in other cases I may 
know that (ct or f3) is true yet not know which 
disjunct is true, as with (S or ~S) where S 
is any controversial proposition. If we 
consider Al in its actual epistemic context, 
we know that~Q is false. Hence, to know 
that (""'Q or P) is true we must know that P 
is true. Since P is the conclusion to be 
established, Al begs the issue. If we con-
sider A2 in its actual epistemic context, 
then, since we know R is false, to know that 
( ..... p or R) is true we must know that AlP is 
true. Since""'p is the conclusion to be 
established, A2 begs the issue. It follows 
that neither Al nor A2 constitutes a "proof2" 
of its conclusion, for both beg the question. 
As a result, Tomberlin's counterexample does 
not demonstrate the unacceptability of the 
st'andard analysis of "proof2." 

NOTE 
lJames. E. Tomberlin, "On Proofs," Inter-

national LOiic Review, vol. VII, no.-r---
(December, 76>-, pp. 233-35. *