[FOM] "Leibniz's Law"

Dean Buckner Dean.Buckner at btopenworld.com
Sat Jun 7 13:53:14 EDT 2003

(Putting the scare quotes because Leibniz Law is strictly different from
what we have been discussing here - as Richard noted).

Richard Heck writes

>There are two quite different questions ...(i) Do we have any reason
>to suppose that Leibniz's Law is unrestrictedly valid?
>(ii) How are we to distinguish the contexts in which it is valid from those
in >which it is not? The answers to these questions are: (i) Not much, so
far as > I can see; and (ii) Uhh...that's quite a hard question,

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.

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.

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 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).

4.  Richard writes
>It is not an unreasonable proposal, for example, that Leibniz's Law
>always fails to be logically valid when the term in question falls
>within a finite clause that occurs as an argument (that is, roughly,
>within that-clauses).

So we all agree.  And it is not an unreasonable proposal that this is
because, in the case of "Alice hates Bob", you are asserting a relation
between Alice and Bob, not between "Alice hates -" and Bob.  Whereas in the
case of "Alice thinks  Bob is an oaf", there is no reason at all to think
the rule holds, since no obvious relation is being asserted.  Unless of
course you think there is a relation is between "Alice thinks -- is an oaf"
and Bob (as many logicians unconsciously hold).

5.  Richard:
>Plenty of interesting work has been and is being done on this [problem],
>both in logic and in semantics

Some very silly work in my view.  Frege's explanation was that a proper name
means something different within a "that" clause than outside.  It refers to
its own meaning, if you like.  Philosophers don't believe that sort of thing
any more, (& neither do I b.t.w.) and some very odd views have emerged,
including the idea that we can believe and disbelieve the same proposition.

For example, if Shakespeare really is Bacon, some philosophers think we all
believe that Bacon is Macbeth.  Without knowing it.  Except of course we do
know it, since (according to them) we can substitute the same proposition in
any that-clause, and since (if Bacon = Shakespeare) the proposition that
Shakespeare wrote Macbeth = that Bacon wrote Macbeth.

"There are different ways of grasping and believing a single proposition. A
rational speaker could believe a proposition in one of these ways, without
believing that proposition in another way. In fact, a rational person could
believe a proposition in one way, while believing its negation in a suitably
different way."  (David Braun, "Understanding Belief Reports",
Philosophical Review, October 1998)

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.

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?  It's something you contrast
with "opinion".

Dean Buckner

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