[FOM] Re: "Leibniz's Law"

Richard Heck heck at fas.harvard.edu
Sat Jun 7 16:22:10 EDT 2003

> 1.  Depends on what we mean by the "law".  I meant
>     (x) (y) [R(a, x) & x=y --> R(a,y) ]
> which is unrestrictedly valid.

That depends upon whether you mean it schematically, or whether you mean
"R" to be a higher-order variable. If you mean the latter, then I will
agree that it is valid, unrestrictedly, but then the question arises
what instances of comprehension you accept, and the standard examples
suggest that comprehension does not hold in all cases. But if you mean
the former, then it is not unrestrictedly valid, and there is no reason
to suppose it is or should be. So I do not see what the problem is.

> 2.  Another version runs: We can substitute names for the same thing in any
> formula, salva veritate.  Which is far from obvious, as the examples show.

No one, so far as I know, has ever held this view. Even Scott Soames
(say), who holds otherwise counter-intuitive views about substitution,
does not hold this insane view, since even he would acknowledge that
substitution fails in
	The Fridge was so-called because of his size
(modified of course from Quine's original example).

> 3.  The connection between the two, which makes it difficult, is that we can
> interpret  R as the relation that holds between a predicate "...x..." and an
> object A, when "...A..." is true. 

If by "predicate", you mean, in effect, sentence-with-a-hole-in-it,
then, once again, the standard examples give us reason to deny that, in
every such case, *there is* any relation holding between the predicate
and the object to which "A" refers when "...A..." is true. (Forgive the
sloppiness about use and mention.) It does not follow that there is no
such relation in *some* or even *most* cases. It just follows that there
isn't such a relation in every case.

> If there really is such a relation (which I would question) then we
> ought to be able to substitute names for the same
> thing, salva veritate.  If they are names for the same thing, then the
> predicate is asserted of the same thing.  The same relation R holds, and so
> the same truth-value holds.  (I don't see how you escape this).

If, in a particular case, "...a..." can be analyzed as "R('...x...',A)",
then certainly substitution must hold. But, as noted above, there is no
reason to suppose that the analysis in terms of "R" is always available
(that is, that it would be correct).

> An enormous amount of work has gone into explaining that-clauses in belief
> reports.  If a tenth of the work had gone to looking at the same type of
> clause in "S says that --", "There is evidence that --", "it has been
> discoverd that --", "it has been proved that --", such theories as Braun's
> would have become extinct pretty rapidly.

Most people who work on this problem take themselves to be focused upon
that-clauses in general, not on belief-reports in particular. Anyone who
is familiar with the literature knows as much.

> 6.  On Richard's view that , "probable" expresses an epistemic (sometimes
> called "subjective") conception.  How about "There is
> objective/empirical/mathematical evidence that ....".  You will still get
> substitution failure, however objective the evidence. In fact, all evidence
> is objective, isn't it?

No, not in the relevant sense. The point is that the notion of
"evidence", and so the notion of what the evidence supports, is an
epistemological one. Evidence is always the evidence that someone has.
Hence there is no reason to be surprised if "There is evidence that p"
creates an opaque context. Indeed, as I suggested earlier, there is
reason to suppose that "that p" creates an opaque context, all by
itself, in which case it doesn't much matter what verb you put in front
of it. In any event, the distinction between subjective and objective
probability is well established.

Richard Heck

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