Re: Merry Xmas, Logic Hounds!



Tron wrote:

Hi,

"herbzet" <herbzet@xxxxxxxxx> skrev i melding
news:495CD6A7.F598C84E@xxxxxxxxxxxx
....

I'll have to reeducate myself on the above; pending.

See http://en.wikipedia.org/wiki/Paradoxes_of_material_implication

Hi, sorry not to have replied yet; I fell very ill Friday night
(while typing a reply to this!) -- I'm just getting well enough
to post again.

But more soon.

--
hz



Wikiing around, there are a lot of pages on problems with implication.
I've been imprecise again - the paradoxes you quoted are technical ones,
inside of logic, so to speak.
I was adressing the discrepancy between OL and Logic - which of course also
touch on technical matters.
However, I find both "my" problem and "my" solution mentioned:

http://en.wikipedia.org/wiki/Entailment

"....The use of the operator is stipulated by logicians, and, as a result,
can yield some unexpected truths. For example, any material conditional
statement with a false antecedent is true. So the statement "2 is odd
implies Paris is in America" is true. Similarly, any material conditional
with a true consequent is true. So the statement, "If pigs fly, then Paris
is in France" is true.
These unexpected truths arise because speakers of English (and other natural
languages) are tempted to equivocate between the material conditional and
the indicative conditional, or other conditional statements, like the
counterfactual conditional and the material biconditional. This temptation
can be lessened by reading conditional statements without using the words
"if" and "then". The most common way to do this is to read A ? B as "it is
not the case that A and/or it is the case that B" or, more simply, "A is
false and/or B is true". (This equivalent statement is captured in logical
notation by , using negation and disjunction.)..."

http://en.wikipedia.org/wiki/Indicative_conditional states:

"...One problem is that the material conditional allows implications to be
true even when the antecedent is irrelevant to the consequent. For example,
it's commonly accepted that the sun is made of gas, on one hand, and that 3
is a prime number, on the other. The standard definition of implication
allows us to conclude that, since the sun is made of gas, 3 is a prime
number. This is arguably synonymous to the following: the sun's being made
of gas makes 3 be a prime number. Many people intuitively think that this is
false, because the sun and the number three simply have nothing to do with
one another..."

I
USES OF "TRUE"
...
- Combined: Soundness (non-contradictory and correspondent)

Not necessarily -- in a sound argument the premises might all
be *analytic* truths, and so also the conclusion.

OK. So soundness is a wider concept:
Non-contradictory, and correspondent synthetically, and again
non-contradictory analytically?

A sound argument *might* have contingently true (extralogical) premises,
but the truth of the inference itself is (imo) analytic (intralogical).

Agreed.

Can we agree on some word conventions, for the present purpose?
We need one for truth-functional truth, and I'm not sure if you would be
happy with merely "valid"?

I am distinctly unhappy with the choice of "valid". Valid arguments,
in herbspeak, are true and NOT ... TRUTH ... FUNCTIONAL. They are
/analytic truths/.

I need to look up "truth functional", or ask you for a short refresher.

Contingent truths. Synthetic truths. (Analytic truths are facts too,
imo,
do you not agree?)

Yes.

And I think "soundness" still works for the combination.

Please note my objection to this characterization of "soundess" above.

Duly noted.

...

II
Intra-logical vs. extra-logical logical operators
.......

Instructive.
In my version, the focus is on the empirical fact of GB being an oculist
or
not, in your version, the focus is on the "logical fact" that the
implication is valid/truth-functionally true (?), L-true, or not.
Totally different truth conditions and proof methods.

But the question here is what did Frege mean?

I'll need to dig up my photocopy of "Begriffsschrift".
I don't have the KS with the Jourdain quote to hand; still the property ofg
the Uni Library, alas.

Does either interpretation
make more sense in the original German?

Could it be as simple as:
" 'If A, then B' is true "
as opposed to
"If A is true, then B is true"?
(Leaving aside the issues of the redundancy of adding "... is true" to any
asserting proposition.)
Still not quite there..... No, I'm looking for an expression for
".....causes...." or "....makes..." that will obviate the need to use "if -
then" in the description of two phenomena that we would want to connect in a
causal relationship. With that in hand, I would _prohibit_ using "if -
then" in place of this new operator. This might actually help with e.g.
Gettier problems, the question of justifed true belief.

And more importantly, is herbzet right where Frege is wrong?

Well, Frege has been proven wrong before, but by minds far sharper than
mine,
so I'll waive my umpire position on this one. Provisionally.

/Moved up:/

This would require a double meaning of -->,
one as "If...then.." and one as ".... causes...".

No, we just adopt a new symbol to denote the new relation.
Then we prove that the two relatations, differently symbolized,
are, or are not, isomorphic to one another.

And how, when, why and wherefore is "...causes..." a logical operator?

Well, we make it an operator, axiomatize it, and fight about whether its
a "logical" operator later.

OK.... this is more your field than mine.
At the moment, I fail to see the utility.
This would be either....
1) a better modelling of OL on implication,
2) a new shorthand for problems so far not described
3) a way of making explicit the "...causes..." part of a proof in order to
ensure that all required steps in the proof are included,
4) it would help invent new rules of inference, or find a new field of
application for old ones, that would actually help solve problems of causal
inferences in a fastr, easier, smarter, less fault-prone way...?

I could see possibilites for 1, which is my original premise.
2 and 3 might also be candidates.
The problem with 4 is the one I described in my previous post - the actual
heavy duty work will be to establish a domain of existents and above all
their properties. OTOH one might say that this is what (ontologically)
realist (epistemologically) empirical natural philosophy, AKA natural
science, AKA science, is actually doing at the moment; although there is not
so much hard work involved in stating its two basic premises: "Reality
exists" and "Reality is as we see it".

....

Standardly it is assumed that the "universe of discourse" contains
at least one object (though it is NOT assumed that any given
predicate has at least one object in its extension; that is,
for any given predicate F, Ex(Fx) can be false).

This and any similar assumptions will be the field of contention in any
"causal logic", then.

The same goes
for any newfangled HerbzeTronic Causality Logic with a "--C-->" operator
(for "if...then..." = "....causes...."). At least in this direct,
primitive
version the whole problem of truth-finding is shifted almost completely
outside of logic (and may as such be of little interest to logicians).
The
relevance logic guys in your wiki link seemed to have been able to
construct
some intra-logical justification for their work, which is would be
required
here too; I fear, however, that it is beyond my means.

So this avenue is perhaps blocked.

I get about 2000 hits for "logic of causation" at google. Perhaps
some of the spadework has already been done.

http://www.springerlink.com/content/v283280j78686v46/

seems a candidate.
Note, though, that here, as in other places, reality is simply assumed
(whether they choose to call it "situations", a semantic or whatever), or
simply assert it ex cathedra without further ado ("...causation can be
directly observed, in lab or field: it is simply one of many contextually
embedded configurations ...", from
http://homepages.wmich.edu/~mscriven/THELO5GICOFCAUSALINVE.doc . The latter
argues extensively from the genesis of our concepts of causation without
spending a second thought on the difference between genetic description on
the one hand, and justification on the other).
So my caveat holds, I think.

T
.

Relevant Pages

  • Re: Merry Xmas, Logic Hounds!
    ... truth proper and the "T" of the truth table (sa Schopenhauer and Frege ... pointed out, the truth of any such implication is provisional, depending ... An implication with false premises is true if the conclusion ... as it ordinarily occurs in natural language, ...
    (sci.logic)
  • Re: Merry Xmas, Logic Hounds!
    ... truth proper and the "T" of the truth table (sa Schopenhauer and ... pointed out, the truth of any such implication is provisional, ... follows from the premises. ... The invention of relevance logics is another disputation of the pre- ...
    (sci.logic)
  • Re: Merry Xmas, Logic Hounds!
    ... truth proper and the "T" of the truth table (sa Schopenhauer and Frege ... pointed out, the truth of any such implication is provisional, ... An implication with false premises is true if the conclusion ... be at least one George Bush who is an oculist, ...
    (sci.logic)
  • Re: Merry Xmas, Logic Hounds!
    ... truth proper and the "T" of the truth table (sa Schopenhauer and Frege ... pointed out, the truth of any such implication is provisional, ... An implication with false premises is true if the conclusion ... The invention of relevance logics is another disputation of the pre- ...
    (sci.logic)
  • Re: Merry Xmas, Logic Hounds!
    ... truth proper and the "T" of the truth table (sa Schopenhauer and Frege ... on later confirmation of the actual truth of the premises the implication ... follows from the premises. ... The invention of relevance logics is another disputation of the pre- ...
    (sci.logic)