Re: Merry Xmas, Logic Hounds!
- From: "Tron" <tronfuru@xxxxxxxxxx>
- Date: Wed, 7 Jan 2009 01:55:17 +0100
Hi,
"Eigendeeg66" <inti_bv@xxxxxxx> skrev i melding
news:83e39376-16be-4604-a246-9a71551bb9fb@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
On 28 dec 2008, 23:19, herbzet <herb...@xxxxxxxxx> wrote:
Tron wrote:gggggg marry xmass best wishes to
Hi,
"herbzet" skrev:
...
Hmmm...
T: - People don't understand the material conditional...
H: - No! People _don't understand_ the material conditional!
T: - ...although it is of course valid...
H: - No! It is valid, of course!
....etc.
LOL! I see that I've convinced you of my position!
So I'll just snip that part where we agree in this sort of disagreeing
way.....
as the trained logician will not discriminate between
truth proper and the "T" of the truth table (sa Schopenhauer and
Frege
pointed out, the truth of any such implication is provisional,
depending
on later confirmation of the actual truth of the premises the
implication
conjoins).
Nonsense. An implication with false premises is true if the conclusion
follows from the premises. An implication with false premises is false
if the conclusion does not follow from the premises.
I think this exchange highlights how the problem under discussion arises
from the difference in perspective, right there.
What I said is TRUE, goddammit. Read it again.
There is a _language product_, the sentence "IF A then B", which is
interpreted differently by the layman and by the trained logician.
The layman *hardly ever* interprets it as a material conditional. On
the rare occasion that he does, the context is strongly involved.
The trained logician *often* interprets it as a matierial conditional,
and sometimes feels a little uneasy about that (more on this below).
On my
analysis, the layman and the logician differ in their interpretation of
words like "true" also.
That may be. I'll admit to not grasping what you're getting at here,
but I *can* say that in some contexts the logician uses "true" to mean
"logically true" or "necessarily true" and in other contexts he means
just ordinary Aristotelian "corresponds-with-reality true".
What you are saying above, is the logician's interpretation of "If A
than
B".
IOW., "...is true.." in your sense = "returns T in the truth table for
its
truth functional value"
No, unless you mean "returns T in *every* row of the truth-table ..."
where this your use is a terminus technicus of logic, and does not
necessarily correspond to any everyday use of "true".
I don' think that's the case.
Example: "If George Bush is an eye-doctor, then George Bush is an
oculist."
We'll agree (I hope) that this is a valid argument. We'll agree (of
course)
that it is an unsound argument. But is this compound sentence true or
false?
I submit that the layman will say that the sentence is a true sentence,
and not because it has a false antecedent. I would hope that a logician
would say it's true, too.
Does someone say that as an argument it is an enthymeme?
OK -- "If all eye-doctors are oculists, and George Bush is an eye-doctor,
then George Bush is an oculist."
That is true.
Valid, unsound, true.
Don't you agree?
Frege's point is that the truth of "If A then B" goes for the _validity_
of
the conclusions, i.e. the correct use of rules of inference, but this
does
not extend to the soundness of the implication as a whole. This requires
true premises.
I agree with both sentences. Are we disagreeing by agreeing again?
This is a semantic problem.
Er, ... what's the problem, now?
So in short one might perhaps say that logicians look to syntax, laymen
to
semantics to find the rules for establishing the truth of "If A the B".
That's because logicians sometimes don't see the forest because there's
too many trees in the way.
Implication as the layman understands it is analytical. Semantics
is sufficient to analyze an argument. Understanding the language
is sufficient. Rules of inference are a convenience for complicated
cases.
A computer need not understand what "eye-doctor" or "oculist" means,
but a computer can be programmed to understand enough of the language
(like "all", "are", "is a", "and" "If-then", some grammar) to verify
the validity/truth of the second argument.
Even a layman need not know what "opthamologist" means to recognize
the validity/truth of an argument which uses "opthamologist" instead
of "eye-doctor" in the second argument.
If Schopenhauer and/or Frege said anything different, then they're
wrong.
Of course they said something different, although that doesn't
necessarily
imply that they contradict what you say above....
We can stick with Frege, as he seems to be barely relevant to the 20.
century, still (I mention Schopi to illustrate that certain logical
principles were known even before the new developments of the late 19.
and
early 20. century).
I'm interested in the history of logic and math. So at some
point we'll need to hear more about Schopi's logic. As history. ;)
They both qualify the truth of the MI
I wonder what exactly you mean by "the truth of the MI". (Perhaps
this is the source of our divergence (if we actually do diverge).)
In Lewis and Langford's "Symbolic Logic" they say that their formal
system of strict implication "asserts" this or that formula, by which
they mean that certain formulae are theorems of the system. This locution
confused me for awhile, since my understanding of the word "assertion"
led me to think that an "assertion" of the system was just a wff in
the language of strict implication -- a wff that might be a theorem,
or refutable, or undecidable in the system.
Is it possible here that by "the truth of the MI" you mean "the truth
of the *valid* MI" in a mannar analagous to Lewis and Langford's
"assertion"?
They both qualify the truth of the MI
to say that it is hypothetically true
on the basis of rules of inference, and that it may be "semantically"
true
provided the premises are true;
i.e., "sound"
but this cannot be demonstrated by the MI
returning a truth value on the basis of rules of inference; hence,
semantically, the truth of the MI is provisional.
Meaning, we can't decide on the basis of the validity of a valid MI
that its premises are true? And hence the truth of the valid MI is
provisional?
Here's how I use the words:
This is a true MI: "The Empire State Building is in Paris -> George Bush
is an oculist"
It's true because it has a false antecedent, and a material implication
with a false antecedent is true.
This is a false implication: "'The Empire State Building is in Paris'
implies that George Bush is an oculist."
It's false because the consequent does not follow from the antecedent.
This is ambiguous: "If the Empire State Building is in Paris, then
George Bush is an oculist."
It's ambiguous because the "if-then" locution may be taken as
material implication or as ordinary implication. Context
will usually settle the matter.
Is it possible that you have misunderstood certain passages?
Like this one, where Frege writes of the MI?
"Mere hypotheses cannot be used as premises. I can, indeed, investigate
what
results from the supposition that A is true without having recognized
the
truth of A; but the result will the contain the condition "if A is
true"."
(Frege, "Anmerkungen zu Jourdain."/"Notes on Jourdain"/, Kleinere
Schriften
p. 336. )
It appears here that "result" in its second occurance refers to the
conclusion of the argument from A, rather than the argument itself ??
This seems dubious on the face of it to me; changing A and B to future
contingent propositions might complicate the analysis significantly.
Semantically, yes; but wrt. RoI? I can't see why.
Hypothetical propositions are not "here and now" statements.
Perhaps you are correct here. I don't want to think about
Aristotle's sea-battle till we agree on the nature of inferences
in the indicative (or declarative) mode. Horse before cart.
Well, give me some time to get used to the idea, anyway.
And besides, as I have mentioned, the respective truth values of A and
B have very little to do with the matter of the truth-value of the
implication "If A then B".
They do, in some contexts; see above.
Yeesh, where above? You mean when the context is that "If A then B"
is interpreted as a material conditional? You can't mean that, that's
too easy. In what *other* context do the respective truth values of A
and B have a lot to do with the truth value of the implication "If A then
B"?
Do you mean in the context where "If A then B" is taken as meaning
"A causes B"?
The concept of causation, as intereresting as that may be
scientifically
and philosophically, is not the relation of logical implication with
which I'm concerned. Whatever the foundation for the truth of the
proposition "A causes B", that's not what I'm talking about.
Oh pardon me.
A natual mistake, think nothing of it.
It is, however, what I'm talking about.
It goes to the various uses of "true", which differ between OL and
logic.
Of course there is no "difference" if you only want to look at one side
of
the comparison.
But where's the fun in that? The use of MI in logic has been undisputed
nigh
on hundred years now,
hasn't it?
Hardly. It's just the standard -- there's a lot of bad conscience
about it. In the Lewis and Langford book referred to above, the
whole motivation to invent the modal systems S1 thru S5 was to
replace MI with something that represents OL implication better:
Strict Implication. This is not a subtle interpretation on my part,
it's all over the book.
The invention of relevance logics is another disputation of the pre-
eminence of material
implication:http://en.wikipedia.org/wiki/Relevance_logic,
the modern seminal work being Belknap and Anderson's "Entailment:
The Logic of Relevevance and Necessity" [1975] -- (which I haven't
read, btw, huge doorstop of a book).
If you really want I can find a boatload of books and papers critical
of MI.
You want to talk about causality (between things) and implication
(between
...
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Let's go dutch.
For every line you snip, I'll snip one, too.
T
.
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