Re: A implies I


Owen wrote:
George Dance wrote:
Owen wrote:
George Dance wrote:
Owen wrote:

Of course you did.

You made expicit reference to 'your' point of view, as though 'your
point of view
had some sort of importance, and My point of view did not.

Well, excuse me. Let me go back and give your 'point of view' another
look:

I believe, we can interpret Syllogistic logic in terms of Predicate
logic if we define the categorical propositions of Aristotle this way:

A...All F are G: ( ExFx & ExGx) -> Ax(Fx -> Gx)
I....Some F are G: (ExFx & ExGx) -> Ex(Fx & Gx).

In which case, (All F are G) -> (Some F are G), is valid.


My conclusion: No, Your 'point of view' does not have any importance,
because it doesn't even 'work' (your term) for contradiction. Let me
spell that out formally:

1. The E and I propositions are contradictories.
2. Of either of a pair of contradictories, one is true and one is false
at all times.
3. Therefore, of any pair of E and I propositions, one is true and one
is false at all times. (1,2)
4. Therefore, of any pair of E and I propopositions, one is true and
one is false when their subject term is empty. (3)
5. The E proposition "No F are G" is interpreted as x(Fx -> ~Gx), which
is true when there are no F's.
6. The I proposition "Some F are G" is interpreted as (ExFx & ExGx) ->
Ex(Fx & Gx), which
is true when there are no F's.
7. Therefore, when there are no F's, the E and I propositions are both
true.
8. Which contradicts 4.

Who the hell do you think you are??

Evidently someone who's thought about the subject a bit more than you.
If you want to offer a sensible interpretation - sorry, a 'point of
view' - of Aristotle's system, it had better be one that 'works' for
all the syllogisms and all the traditional relations of the Square.
Yours had better work for contradiction or it's not even a plausible
interpretation of syllogistic logic.

You have made many claims without foundation, and, here you go again,
what the hell??

Here's a claim: Your above 'point of view' is not a plausible
interpretation of syllogistic logic; and your assertion of it was
thoughtless. My 'foundation' for that claim is the above argument.

So it's your move. Which false premise of my argument do you reject?
Do you deny Aristotle's principle of contradictories? Do you deny that
the E and I propositions are contradictories? Do you re-interpret "No
F is G" as *false*
when there are no F's? Or (heaven forbid!) do you consider the
possibility that your interpretation of the I proposition just might be
mistaken?

You said that L's threee valued logic was interpretable within
Aristotle's Syllogictic.

No, I said (to someone else, BTW) that Lukasiewicz's interpretation of
Aristotle's syllogistic implied three-valued logic.; > Why, you cannot
supply logical evidence for that any mor than you can
supply logical evidence for the restr of your nonsense!!

Oh, you want another argument? Well, here it is:

1. In L's interpretation of Aristotle's syllogistic, none of the A, E,
I, and O propositions are true when their subject terms are empty.
2. Therefore, "All F are G" is not true when their are no F. (1)
3. "All F are G" and "Some F are not G" are contradictories.
4. Assume that "All F are G" is false when there are no F.
5. Then "Some F are not G" is true when there are no F.
6. Which contradicts 1.
7. Therefore "All F are G" is not false when there are no F. (4-6)
8. Therefore, in L's interpretation of Aristotle's syllogistic, "All F
are G" is neither true nor false when there are no F. (2,7)

OTOH, since the contradictory of a meaningless proposition is also
meaningless, a 3-valued interpretation does preserve contradiction.

Give me a break?!?

I will give you a 'break' from reading my 'point of view' again, since
you have no comments; but I am leaving in the link:

Been there, done that; please see "Testing Validity in FOPL-A":
http://tinyurl.com/y2v5qv

.

Relevant Pages

  • Re: A implies I
    ... propositions as true only when their subject terms exist (or, ... interpretation of syllogistic logic roughly 70 years ago. ... tradition according to which the ancients were unaware of empty terms." ... A and O are contradictories. ...
    (sci.logic)
  • Re: A implies I
    ... propositions as true only when their subject terms exist (or, ... interpretation of syllogistic logic roughly 70 years ago. ... tradition according to which the ancients were unaware of empty terms." ... A and O are contradictories. ...
    (sci.logic)
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