> POSTULATE 2. If a premise A in the formal inference
> (**) is FALSE,
> then any its consequence B is necessarily FALSE too, or shortly:
> FALSE ==> FALSE (only!). IFF the Aristotle's Logic deductive rules are
> applied correctly.
>
> Why did Great Aristotle's not formulate explicitly such obvious
> Postulate 2? I think the reason is purely psychological:
I have some doubts. I'd suggest that Arsitotle did not
formulate it, because he believed it to be false. Aristotle's
logic is a syllogistic one. Each syllogism has *two* premises.
And a syllogism with a wrom premise can nevertheless render a
true result:
<Example 1>
All Renaissance philosophers where great mathematicians (F)
Cardano was a Renaissance philosopher (T)
Cardano was a great mathematician (T)
</Example 1>
And even syllogisms with two false premises can have a true
result:
<Example 2>
Palatinate philosophers are and were always great mathematicians (F)
Cardano was a Palatinate philosopher (F)
Cardano was a great mathematician (T)
</Example 2>
Besides: I have the impression that when writing about the
impossibility of infinity Aristotle's main focus was on
*physics* and *not* on mathematics. AZ wrote that in Aristotle's
context there was a "very abstract problem as whether the
Infinity is actual or potential": I'd assume that for
Aristotle it was not a "very abstract" problem. It concerns
e.g. the question whether movement is possible at all (remember
the running contest with the turtle ...) ... .
Regards
Heinrich C. Kuhn
+---------------------------------------------------------
| Dr. Heinrich C. Kuhn
| Institut fuer Geistesgeschichte der Renaissance
| Ludwig-Maximilians-Universitaet Muenchen
| D-80539 Muenchen / Ludwigstr. 31/IV
| T.: +49-89-2180 2018, F.: +49-89-2180 2907
| inst. URL: http://www.phil-hum-ren.uni-muenchen.de/
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