[hist-analytic] Response to Danny Frederick

Danny Frederick danny.frederick at tiscali.co.uk
Tue Sep 1 07:33:06 EDT 2009


Hi Bruce,

 

Unfortunately, the fine weather didn't hold up as expected. Our weather has
become Popperian: it sets out to refute whatever forecast the meteorological
office gives; and it usually succeeds. So I have now read your chapter 2 and
Appendices 2 and 3. I have also, prompted by your protests, re-read your
chapter 3; though it seems to me that I fully understood it the first time.
I admit that my previous summary of your position, in four bullet-points,
was crude; but in the criticisms I raised I took account of the relevant
aspects of your view that I did not state in the bullet points. I agree,
though, that I could have spelt this out better, and I try to do that in
this message. I think your responses to my criticisms (I reproduce your
email below) miss the point. In this message I will rebut your responses one
by one, though I will change the order for expository convenience.

 

 

You say: 'if the class of such statements [i.e., those that may be
substituted for the schematic letters of propositional logic] 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.'
You expand: '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.'

 

My response: There are two problems with this approach. The first is that it
is ad hoc: it amounts to saying that classical logic is necessarily true for
all those propositions for which it is necessarily true. It thus ceases to
talk about necessary truth or validity and talks instead about the things
which make the theory true, if indeed there are any such things. Imagine a
Newtonian physicist who, in response to the objection that the precession of
the perihelion of Mercury is inconsistent with his theory, replied that
Newtonian theory only applies to Newtonian worlds, and thus applies only to
those planets whose motions actually conform to the theory; and, therefore,
the actual motions of the planet Mercury do not refute the theory because
the theory was never talking about non-Newtonian objects. He would rightly
be a laughing stock: he would be ejected from the company of scientists and
have to find a new home amongst astrologers, Marxists or other
pseudo-scientific humbugs. A classical logician who responds in the way you
recommend should, I suggest, be treated in the same way. He has given up on
truth and consoles himself with his own little fantasy world in which
everything runs according to the rules he lays down. If logic is to be taken
seriously, it must be a theory of validity, not just a description of what
validity would be in a particular theorist's fictional world.

 

The second problem with the approach is that there is no guarantee that his
restricted theory actually applies to anything at all: it might be
inconsistent. For there can be no way of proving that any logical theory, or
any other theory, is consistent, as I pointed out last time. But you raise
an objection to this.

 

 

You say: '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.'

 

My response: The rules used in the consistency proof are the same apart from
the fact that they are metalinguistic. We have a choice here. We can
acknowledge the object-language/meta-language distinction but say that,
despite this, the underlying rules of inference are the same. In this case
we have a circularity: the proof of the consistency of the object-language
system uses rules of inference of that system. Or, we can insist that the
rules are different, in which case the consistency proof uses a different
logic that has not been shown to be consistent, which leads us to a vicious
infinite regress. We are out of the frying pan, but into the fire. Either
way the question of consistency is begged: we assume the consistency of some
logical system without proof. There can be no way around this.

 

 

You say: '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.'

 

My response: Referentially transparent contexts are those in which
co-designative terms can be swapped salva veritate; and opaque contexts are
those in which this is not so (Quine, 'Word and Object,' section 30). Until
Kripke's 'puzzle about belief' it was (I think generally) assumed that
synonyms could be swapped salva veritate in any context, including opaque
ones. Kripke's puzzle and related work by others, which impugns this, raises
a problem for you. For, your conventional account is not just an account of
logical truth but is also an account of how we know logical truth. Your
conventions are supposed to explain not just why it is true that p, but also
why any 'alert and attentive speaker' will know that it is true that p; and
'know that' creates an opaque context. You need inter-substitutivity of
synonyms in opaque contexts.

 

 

You say: '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.'

 

My response: The word 'bank' is straightforwardly ambiguous. I do not know
of even a philosopher who denies this ambiguity (though there probably is
one). It is not at all clear that the word 'all' when used as a quantifier
is ambiguous. If two logicians disagree about whether 'all' has existential
import, they are disagreeing about what arguments containing 'all' are
logically valid. This disagreement presupposes their linguistic competence
in the use of the word 'all.' It is not the case that one of them has a poor
command of the language. It is also not the case that one or both of them is
simply proposing a new definition for the word 'all.' A grasp of the meaning
of 'all' does not settle the question of what inferences containing it are
valid; and to assume that it does settle it in favour of your preferred
system of logic is simply dogmatic.

 

 

You go on: '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.'

 

My response: These logicians say that they contradict the principle of
conjunction elimination. And they say they reject it in order to provide an
acceptable account of validity. Their assumption is that logic should give
an account of validity, i.e., actual validity, not just an exposition of the
arbitrary way in which someone likes to talk of validity. They argue that
conjunction elimination is invalid. I am not saying that they are right. I
am just saying that their contentions are substantial. And they should not
be dismissed as merely introducing a novel meaning for an old expression.
There is a paper on connexive logic available here:

 

http://plato.stanford.edu/entries/logic-connexive/

 

 

You say: '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.'

 

My response: Nothing I said should have suggested that it does follow.

 

 

You say: '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?

 

My response: What about a genetically engineered duck? Perhaps Nero's
fiddling and Rome's burning are simultaneous in one co-ordinate system but
not in another. This might not be possible in relativity theory as so far
developed, but who knows what the future holds? In dialetheic logic, some
propositions are such that they true even though their negations are the
case (dialetheic logic permits the truth of some contradictions). Notice
that I am not endorsing any of these claims; I am just pointing out that
some linguistically competent and intelligent people may (or do)
intelligibly make them (so there is no linguistic convention which rules
them out).

 

 

You say: 'If the [example] 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?'

 

My response: I am not sure what conditional you have in mind. Let's just
state the axiom of parallels: through any point not on a given line just one
line parallel to the given line may be drawn. My claim was that the vast
majority of speakers of English who understand the sentence would find its
denial 'odd, puzzling, or paradoxical.' If they are dogmatic, they might
even dismiss the denial as altering the customary meaning of words. But they
would be wrong.

 

 

You say: '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.' 

 

My response: I agree with you. The vast majority of people know nothing of
Einstein's denial of absolute simultaneity. My point was that before
Einstein, almost everyone would have regarded as valid the inference of 'A
is simultaneous with B' from 'B is simultaneous with A.' It would not have
occurred to them to ask whether the co-ordinate system was the same in the
two statements. It is only in the light of relativity that we question the
validity of the inference.

 

In my initial message I said: 'For millennia our linguistic practices
committed us to inferring "A is simultaneous with B" from "B is simultaneous
with A" whether or not the co-ordinate system changed between the two
utterances.' That was very badly expressed: our linguistic practices
committed us to no such thing. What I meant was that, on your view,
according to which the way we use words settles questions of analyticity,
relativity theory would have seemed analytically false, because the denial
of absolute simultaneity would have been just as 'odd, puzzling, or
paradoxical' as the denial of any of your supposed analytic truths.

 

 

You say: '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.'

 

My response: I think this is significantly wrong. From what you say, it
sounds as if you are endorsing the pseudo-scientific manoeuvre criticised
above: Newtonian theory is true of Newtonian worlds, Einsteinian theory is
true of Einsteinian worlds. That abandons science in favour of
self-indulgent fantasy. Perhaps it is more likely that you mean that
Newtonian theory consists of two parts, roughly as follows: a definition of
a Newtonian world as whatever world would make Newton's theory true (where
Newton's theory is itself an implicit definition of the theoretical terms
employed in the theory); and a statement that the actual world is Newtonian.
And similarly for Einsteinian theory. The problem with this is that it
breaks the connection between Newtonian and Einsteinian theory and the
connection of each with our ordinary thought and talk about the world.
Newton and Einstein were talking about simultaneity, the same simultaneity
that pre-Newtonians spoke about. But Newton and Einstein said incompatible
things about it. Their theories are not implicit definitions of otherwise
undefined terms which just happen to be homophonic ('simultaneous,' 'force,'
'mass,' etc.). Einstein's theories grew out of a criticism of Newtonian
theory: he worked with Newtonian concepts and he struggled to solve the
problems that had arisen in Newtonian physics. But his modifications to
pre-existing theory were so significant that the resulting theory was
revolutionary. Still, he would never have come up with it if he had not been
immersed in the theoretical problems and theoretical concepts of Newtonian
theory. When we say he modified the concepts of Newtonian theory all we are
saying is that he rejected some previously accepted fundamental statements
involving those concepts; but this need not commit us to any concept of
analyticity. For related discussion see Popper, 'The Logic of Scientific
Discovery,' sections 17 and 20; Kuhn, 'Second thoughts on Paradigms' and 'A
Function for Thought Experiments,' both in his 'The Essential Tension;' also
even Quine 'Success and Limits of Mathematization' in his 'Theories and
Things.'

 

 

If you still think I am mistaken, please come back with further criticism.

 

Best wishes,

 

Danny

 

  _____  

From: hist-analytic-manager at simplelists.com
[mailto:hist-analytic-manager at simplelists.com] On Behalf Of Bruce Aune
Sent: 28 August 2009 14:41
To: hist-analytic at simplelists.com
Subject: Response to Danny Frederick

 

 

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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