[hist-analytic] Response to Danny Frederick

Bruce Aune aune at philos.umass.edu
Fri Aug 28 09:40:49 EDT 2009



This is my response to Danny Fredrick’s criticism of my account of  
analyticity in my book, An Empiricist Theory of Knowledge.

Danny:

If you are going to criticize someone’s views on a certain topic, you  
ought to have a clear idea of what those views are.  But your  
comments make it plain that you gave my chapter only a swift and  
careless reading. I say this because your principal objections  
completely ignore the central issue I discuss near the beginning of  
my section, “Analyticity, Logic, and Everyday Language,” where I  
raise the question, “How could we possibly know that the schematic  
formulas [the logical “laws”] that are supposed to hold true for all  
statements corresponding to them do not, in fact, have a single  
falsifying instance?” I made it clear that if the class of such  
statements is not restricted in ways I discuss, falsifying instances  
(and therefore inconsistencies) can actually be found. My discussion  
of the appropriate restrictions was a crucial part of my general  
position on logical truths, but you completely ignore it even though  
it explicitly addresses the subject of your principal objections.

Before moving on to comments you make about specific passages in my  
chapter, I must say that some of your criticisms involve logical  
difficulties that render them ineffective.  First, the derivation you  
mention for “All bachelors are unmarried” does not depend on the  
assumption that the substitution of synonyms for synonyms can always  
be made salva veritate. It is well known that there are contexts  
(Quine called them “opaque”) in which such substitutions cannot be  
validly made, but “All bachelors are bachelors” is not one of them.   
In a context like this, which Quine called “referentially  
transparent,” the relevant substitution is known to preserve truth.   
Second, the fact that the vernacular word “all” can, as you say, be  
interpreted differently by different people does not show that a use  
of “all” in a given sense (one rejected by Aristotelians) does not  
yield a logical truth.  If I say “I went to the bank” yesterday,  
meaning I went to a financial institution, I cannot be refuted by the  
observation that some people apply the word (or inscription) “bank”  
to the strip of land running along a river.  For a similar reason,  
logicians who reject a principle of conjunction elimination in favor  
of a different principle do not, strictly speaking, contradict the  
classical principle of conjunction elimination. They provide an  
alternative to it, because their conjunction operator has a different  
meaning, a different semantical interpretation. [I discuss this point  
explicitly in my Appendix 3.] Third, if the meaning of certain  
logical words is associated with an inconsistent system of rules, it  
does not follow that an assertion, “All unmarried men are unmarried,”  
formulated in that system, is not necessarily true.  A system of  
rules is inconsistent if a contradiction is derivable from it, or if  
every formula is derivable from it, but his does not imply that  
nothing derivable from it is true or necessary.  Finally, standard  
consistency proofs are not, in fact, question begging.  A proof that  
the rules R applied to the formulas of a system S do not yield a  
contradiction in S does not presuppose that the rules used in the  
proof do not yield a contradiction in S; in fact, the rules used in  
the proof are metalinguistic, and they apply to an entirely different  
class of formulas. As I emphasize in several places in my book, it is  
an error to suppose that logical rules and principles can be assessed  
independently of their application. If a system allows formulas that,  
owing to vagueness, do not satisfy the principle of bivalence, the  
system will not satisfy the axioms of classical logic.  This failure  
would be owing to the formulas allowed in the system, not the axioms  
themselves.

I now turn to the two places in your comments where you consider  
specific remarks I made in my book.  The first concerns a remark I  
made on p. 62.  The complete remark was “The examples I gave in the  
last paragraph make it obvious that words, phrases, clauses and  
constructions in existing dialects of natural languages [often] have  
implications so vital to the meaning of what they are used to say  
that any alert and attentive speakers of a relevant dialect would  
find it odd, puzzling, or paradoxical to question them.  When this  
condition is satisfied by a word or symbol, it seems to me that a  
sentence of the dialect clearly and unambiguously expressing an  
appropriate implication can reasonably be regarded as analytically  
true for those alert and attentive speakers.”  My examples did not  
concern beliefs people have about various subjects; they concerned  
implications of “words, phrases, clauses and constructions in  
existing dialects of natural languages,” implications that are  
particularly vital to the meaning of these linguistic items.  I am  
utterly confident that anyone who speaks the dialect of English that  
I do would not find them questionable.  Could something be a fake  
duck and at the same time a real one? Could Nero fiddle while Rome  
burned but Rome not burn while he is fiddling?  And could the  
statement, “Lacking an umbrella, she hit him with a shoe” be true  
when the person referred to had an umbrella (in the relevant sense)  
or didn’t hit the relevant other person or animal with a shoe? The  
examples you gave to refute my claim but were too sketchy to prove  
much of anything. If the one about the axiom of parallels is  
transformed into a conditional representing an implication, is it  
reasonable to suppose that anyone would consider it true by virtue of  
meaning? Since Kant, the axiom of parallels (applied to physical  
space) has been a paradigm example of a synthetic truth. Your example  
about simultaneity is equally dubious. Are “the vast majority of  
people” supposed to believe that if a is simultaneous with b in an  
inertial frame A, then b is simultaneous with a in some different  
frame B?  I think not.  If “simultaneous” is understood as a relative  
notion, it does not have the pre-relativistic meaning.  And if that  
pre-relativistic meaning were rejected on scientific purposes, a  
relevant conditional involving it would not then be falsified on  
scientific grounds; it would be viewed as having a false antecedent.   
Nothing would then be considered simultaneous in a pre-relativistic,  
“absolute” sense, and conditionals with false antecedents are  
vacuously true.

As for my remark, “we do in fact identify specific colors in a way  
that assumes indiscernibility as an identity condition for them,” the  
we I was speaking of are people willing to concede (as philosophers  
almost always do) that nothing can have two different determinate  
colors at the same time—colors being understood in an ordinary,  
nontechnical way. If, on reflection, you are not willing to concede  
this, you won’t mean what philosophers usually mean by “determinate  
colors” when they discus the impossibility of a thing having two such  
colors at the same time. And if, to repeat, you attempt to falsify an  
assertion by fixing on unintended meanings of an ingredient word (by  
taking “color” to apply to light of various wavelengths) your  
falsifying attempt will fail because it will involve what can rightly  
be called a fallacy of equivocation.

At the end of my book I include two appendices that disarm other  
objections that you raised against me.  Appendix 2 includes (a) my  
criticism and rejection of Boghossian’s use of the the kind of  
implicit definition that you mentioned (I show that it leads to  
absurdity) and (b) a criticism of the hackneyed claim that  
consistency proofs are circular (they are not). Appendix 3 defends  
the idea that a priori truths can be created by stipulation; it  
explicitly opposes the well-known criticism offered by Paul Horwich,  
who uses Prior’s example of the runabout inference ticket.  I think  
both appendices will show, as indeed my chapters two and three should  
have already, that I don’t need to make use of the little  
bibliography you attached to your comments.  Nothing in your comments  
was new to me, and nothing you said casts doubt on the position I  
actually took in my new book.



Best regards, Bruce 
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