[hist-analytic] Discussion of Aune's ETK, Chapter Two: Modus Ponens/Tollens
Baynesr at comcast.net
Baynesr at comcast.net
Tue Oct 27 17:42:22 EDT 2009
Bruce believes he has found a “clear case” of modus tollens,
which might have a counter instance. Since this one of the
stronger claims he makes that the “laws” of logic may be
invalid, let’s have a look. Here is his example:
If it rained yesterday, it did not rain hard (yesterday)
It did rain hard (yesterday)
Therefore, it did not rain yesterday.
He offers little reason for believing that it may be invalid.
He notes that it is a case worth discussing in the journals,
but I don’t find this very convincing. (p. 59). His second
argument is that an “intuitive glimpse” should not suffice
to assure “sober” minded people will accept it.
What we must not lose sight of is that just because a sentence
contains ‘if’ that does not justify regarding it as a conditional.
A good example is the concessive clause. So consider the
If I lose I don’t care
Therefore I won’t lose.
This is hardly a refutation of logic as we know it. Notice
that if I hold to the first sentence, as a concessive, then
I won’t deny the concession by asserting the second premise
although I could; but then it’s not a concessive. The example
Bruce gives is not exactly a concessive, but I think it is
close, and regardless is not a conditional in the first
premise. Let’s look a bit closer at the peculiar semantics
of this alleged counterexample.
If it didn’t rain yesterday, then it, clearly, did not rain
hard. So the falsity of the antecedent entails the truth of
the consequent. In fact, whether the antecedent is true or
false, the consequent is entailed.
This makes it a theorem of logic. I don't think it's theorem
of logic, however. I restate the argument.
1. If it rained yesterday, it did not rain hard (yesterday)
2. It did rain hard (yesterday)
3. Therefore, it did not rain yesterday
Next consider the following description of it:
1'. P -> q (first premise)
But if it didn't rain yesterday, niether was it the case that
it rained hard. That is, if it didn't rain, it didn't rain hard;
that much is certain, if not analytic. But this gives us
2. ~p -> q
(‘If it didn’t rain yesterday, then it didn’t rain
/therefore (from (1') and (2) it follows that:
pv~p. -> q
Now it looks like it's a theorem of logic: It follows from
logical prinicples, alone! But it is not a logical truth that
it didn't rain hard yesterday.
In any case, MT is safe! But just in case you doubt this,
forget the argument I just gave.Instead, go back to
the original argument. Take a look at the first
premise: ‘If it rained yesterday, it did not rain hard
(yesterday)’ A close look, now, reveals the problems with MT
may arise from a misunderstanding of the syntax, not logic, of
this sentence. I'm not sure, but it's worth examining .
The sentence, to me, looks syntactically ambiguous. If it is,
then the problem may be that ‘not’ does not modify the main
verb but may be read as modifying the adverb, ‘hard’. The
sense of the sentence might then be stated, albeit, more
‘If it rained yesterday, it rained not hard’.
This isn’t as bad as it looks at first since the following is
grammatical: ‘If it rained yesterday, it rained not hard at all’.
The point is that the second premise, ‘It did rain hard yesterday’
would not be the negation of ‘It did not rain hard yesterday’. Now I
don’t wish to make as much of this as what I said before. The
case Bruce mentions is grammatically fascinating but logically
uninteresting in my opinion. There are other cases. E.g.
1 If he knows, he’s not telling
2. He’s telling
3. Therefore, he does not know.
But if he is telling then why would I assert the conditional etc?
When it is pointed out that he is telling, I do not infer that he
doesn’t know. I infer that ‘If he knows he is not telling’ is false.
If someone says I am denying a conditional and so must affirm the
antecedent and deny the consequent, I am incredulous. Why? Simple.
It was never a conditional to begin with.
Suppose someone says ‘It rained five minutes ago’. I look at the
ground and it is dry and the sun is out. I say, ‘If it did rain,
it didn’t rain hard’. But suppose the sidewalks were superheated,
unknown to me. Someone points out that the sidewalks were
superheated and, so, ‘It did rain hard’ is true. Do I conclude that
it didn’t rain five minutes ago because now I know it rained hard
five minutes ago? No. Do I conclude the premise was false? Yes! Do
I concede that it was a conditional and, therefore, Modus Tollens
is an invalid inference form? Not to mention that aside from being
wrong I’ve condradicted myself? Of course not. Why not? Answer: it
was never a logical conditional in the first place.
In the next section, there is a list of entries of, purportedly
intuitive truths, more specifically truths “known by rational insight.”
(p. 60). Dismissed from consideration is ‘A square is a rectangle’.
It is dismissed because it is thought to be true by definition. That
much seems clear enough, but I’m not positive. Now what about
‘red is a color’. Why does Bruce think this is true by definition?
Why does he think this? He says it is “clear that ‘red’ refers to
a certain color. Now no one is arguing that it is not clear. But
the question is whether its clarity is owing to “rational insight.”
No reason is given for thinking otherwise. Suppose we run to the
dictionary, as Bruce does in the case of the first example. Ok.
The dictionary says red is color. But suppose I am the sort of
fellow who doesn’t trust dictionaries because they have too many
philosophers doing the definitions. What do I have to check the
dictionary against? If I say ‘A tree is not a color’, what reason
do I have for thinking this is true. It isn’t contingent (let’s
suppose). So how can I be certain? I go to the dictionary and look
up ‘tree’ and ‘color’. Nothing rules the sentence out as false. So
is this analytic? Clearly, a tree is not a bush. Now it may be that
all I need to know this is to know language, but language is a tricky
thing and someone might argue that it may turn out that a tree is a
color. Essences are involved. Is the concept ‘not a color’ included
in the concept of the subject? How do we know? It seems unreasonable
to suppose otherwise. It is because of rational insight that we are
justified in claiming a sentence is analytic and, so, certain definiens
are used to define certain terms. What other appeal is there? Certainly,
not the dictionary; many of these differ and some are dead wrong, and
they are all written by people who depend on ‘rational insight’.
The rationalist finds admissible a question of this sort: What must the
world be like in order that it make sense. If making sense requires a
rational mind, then the rationalist becomes an idealist. Moving on to
properties, I have another point where we don’t’ see eye to eye.
Bruce says that the concept red has “built into it the idea that
“To be the way it looks a red object must look red when viewed in a
good light by an observer with a good eye for colors.” Well, to begin
with I don’t believe that all this “goodness” is built in to the *concept*.
For one who is to say what is “good light” depends on what kind of
light we have when what we see as red is actually red. But what kind
of light is this? First we have to know that THIS is red, then we set
a standard for excellence of vision, light etc. But knowing what this
is presupposes an occasion where we know that what we are seeing is
red. We can’t say light good for seeing red is derived from what is
good for seeing blue etc. Eventually we have to fess up to the problem.
And, even if we buy into this ad hoc device for avoiding sense data or
some equivalent we then must distinguish concepts and properties,
criteria and concepts etc. This is very much a mess and can’t be done
as expeditiously as Bruce seems to think. So when Moore says that we
are acquainted with the simple property red he isn’t talking about he
concept; he is talking about a property that is the object of acquaintance.
Anyway, this business about standard lighting is aping similar
ideas in science, e.g. standard temperature and pressure. The problem
is that we can’t set the standard without knowing what it should be.
This is not, like ‘meter’, an arbitrary matter. So in my opinion
the idea that red as a property/concept has all this “built in” is a
convenient ad hoc device for avoiding rather than addressing the
philosophical problems. As Broad says, the standard does not come out
of the night trailing in a blaze of glory! I wish philosophy were all
that simple; it is not. Sellars bought into this in his criticism of Broad,
but here I think Wilfred is just wrong.
Once we accept a difference, as we should, between concepts and properties
then Aune complaints about “discreteness” become significantly weaker.
Kant was right on this, but that is a long story.
Bruce seems to believe that all colors can be perceived. I’m not so sure
that this is justified without certain physicalistic arguments I’m not
prepared to accept unqualifiedly. Why can’t there be a mix of red in green
in an object even though our eyes can’t perceive them, unless we assume
that color is a secondary property? Even it colors are secondary properties,
the eye may a poor instrument for becoming aware of all colors. A
visitor from Mongo may see such things, nothing Bruce says rules it out
as far as I can see.
I'm going to digress a bit. Before moving on in Bruce's book, I want to take
a look at Putnam (1956-57) cited in a footnote. It's not a recent article, but it
is very much worth reading, or rereading. Let me take another look at this
over the next few days. Bruce cites it (p. 68) but there is more to it than can
fit in a small footnote. The artifcle is "Reds, Greens, and Logical Analysis,"
in Philosophical Review. LXV 1956 pp. 206-217. This is the main one; there
is the one in 1957, which is a reply to Pap. Let's take a closer look, eh?
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