Re: A implies I
- From: "Owen" <owenholden@xxxxxxxxxx>
- Date: 22 Oct 2006 09:41:46 -0700
George Dance wrote:
Owen wrote:
George Dance wrote:
There's precedent for interpreting all of the A, E, I, and O
propositions as true only when their subject terms exist (or, in the
jargon, as having "Existential Import"). Lukaciewicz proposed just that
interpretation of syllogistic logic roughly 70 years ago. However,
that gives one a 3-valued logic rather than a 2-valued one - in the
case where there are no cars on the street, all propositions about
'cars on the street' would be neither true nor false, but meaningless.
(Lukasiewicz was in fact a pioneer of 3-valued logic; I don't know the
historical relationship between his work on that [...] and his interpretation of Aristotle's system, but the logical
connection is clear.)
Why do you believe that Lukaciewicz's three valued logic has any
relevance to the Syllogistic??
"In the twentieth century Lukasiewicz also developed a version of
syllogistic that depends explicitly on the absence of empty terms; he
attributed the system to Aristotle, thus helping to foster the
tradition according to which the ancients were unaware of empty terms."
Lukasiewicz, J. [...] 1951 Aristotle's Syllogistic, Clarendon Press,
Oxford.
In L's syllogistic, all propositions had existential import; they were
not true when their subject terms were empty. But they weren't false,
either; because in that case their contradictories would be true, and
those weren't true, either. So,in some cases, some propositions are
neither true nor false; which invalidates the Law of Excluded Middle.
What is it that you think is logically clear between Aristotle and
Lukaciewicz???
If the propositions are neither true nor false when their subject terms
are empty, they have to have some other truth value. Interpreting that
as "I" for indeterminate, using Lukaciewicz's 3-valued truth tables,
means that all the relations of the Square are valid, whether or not
their subject terms are empty:
A and O are contradictories. (If "All F are G" has the value P, then
"Not all F are G" has the value ~P, and vice versa).
I and E are contradictories.
A and E are contraries. (("All F are G") & ("No F are G")) is never
true).
I and O are subcontraries. (("Some F are G") & ("Not all F are G")) is
never false.)
A implies I. (If "All F are G" and "Some F are G" are Indeterminate,
("All F are G") -> "Some F are G") is true.
O implies E.
Lukasiewicz also wrote that: All (F are F) is valid and Some (F are F)
is valid.
Note that with your interpretation ...both of these assertions are not
valid...
"All F are G: Ex(Fx & Gx) & ~Ex(Fx & ~ Gx)
Some F are G: Ex(Fx & Gx)
No F are G: ~Ex(Fx & Gx)
Not all F are G: ~ExFx(Fx & Gx) v Ex(Fx & ~Gx)
That preserves contradiction -
O=~A
E=~I
- and both contrariety and subcontrariety as well:
~(A & E)
(I v O) "
whereas, both of these assertions are valid in my interpretation.
"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.
O=~A
E=~I"
I would not be surprised if we are both wrong.
I recall a conversation with Ken Pledger about this point some time
ago.
I have not yet worked out your interpretation for the 24 valid
syllogistic forms.
I hope to work on it to-day, and will let you know what I find.
.
- References:
- A implies I
- From: William of Ockham
- Re: A implies I
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- Re: A implies I
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- Re: A implies I
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- Re: A implies I
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- Re: A implies I
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- Re: A implies I
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- Re: A implies I
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- Re: A implies I
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