Re: Goodbye,Descartes
 

Is this the same logical construct.

"No circle is a sqaure."
"All square-circles are square."
-------------------------------
"Some square-circles are not square."

Re: Goodbye,Descartes
 

[ QUOTE ]
Is this the same logical construct.

"No circle is a sqaure."
"All square-circles are square."
-------------------------------
"Some square-circles are not square."

[/ QUOTE ]

Devlin's construction contains only 2 named entities..."Unicorns" and "horned animals".
Yours uses 3. and to use his structure it would be...
"No circle is a square."
"All squares are circles."
-------------------------------
"Some squares are not circles."

( but his 'circle' changes in meaning from one premise to the next... or it does for me).
Maybe his comments will help when I get home,

thanks, luckyme

Re: Goodbye,Descartes
 

Doug, here's the Aristotle syllogism Devlin was working from -

No councillors are bankers.
All bankers are atheletes.
Some atheletes are not councillors.

Seems valid to me.
But if the 2nd premises 'bankers' meant 'lazy salespeople' then I don't see anything useful coming out of it.

He gives the form -
PeM
MaS

But when dealing with 'animals' as the M they are not the same M in both premises. So it's not really M in the second premise, and you end up with nonsense.

Devlins explanation --
" In the case of Aristotles original list of syllogisms , they are all valid provided they are applied to real things like atheletes, bankers and councillors. You only run into trouble when you apply some of them to things that do not exist, such as unicorns."

Oh, pooh. You only run into trouble when you use the same symbol/name for two different entities in the same syllogism. It has nothing to do with real/unreal.

hope that helps, luckyme

Re: Goodbye,Descartes
 

I remember this problem in my intro to philo class. The proof let me gloss over it, with something about the 1st premise being faulty. Such as how does Descartes know if no horned animal is a unicorn? But anyways…


The premises are contradictory. You can't say p and not-p at the same time. The author chooses a bad example to illustrate his point about imaginary objects. As far as I can tell here is what he did.


No Bankers are athletes
All Athletes are Bankers
Some Bankers are not Bankers.

It seems pretty stupid of him not to point that out instead of the mumbo jumbo about imaginary objects. Also why does he say, Some unicorns aren’t horned animals, shouldn’t it be Some horned animals aren’t horned animals?

I'm actually having trouble figuring out if imaginary objects work fine or not

No triangle is a square-circle.
All square-circles are square.
Some squares aren't triangular.

No square is a square-circle.
All square-circles are square.
Some squares aren't square.

I see what you are saying about the different uses, I just think there is a better way of saying it. In Devlins defense I don't think he said that the use of imaginary objects was the underlying cause, just that that is when we are app to run into trouble. And the reason why we run into trouble is what you are getting at, but I can't really verbalize it well. I think you and Devlin agree. The use of imaginary object lets us define horned animals using different criteria. But he appears to be saying we only and always will run into the problem when we use imaginary objects.

So I offer of this proof that God is not imaginary,

The “PeM MaS Some S are not P” syllogism is invalid at least sometimes when one uses an imaginary object as M.
All syllogisms of that type using God for M are valid.
God is not imaginary

I think you are on to something that cause is not the imaginary nature of the object but more so the criteria’s being used to define that imaginary object are being used in two different ways. So that the syllogism isn’t in correct from. Of course an ill-formed syllogism will cause you to run into problems. Duh Descretes.

Re: Goodbye,Descartes
 

if a mind requires this thread to get warmed up to do some real work, it needs a complete overhaul--or a proper burial..................b

Re: Goodbye,Descartes
 

Well, I don't really understand the problem, or the author's claim, or anything else for that matter. But perhaps the most charitable interpretation is this: Aristotelian logic is sound, only assuming that one cannot quantify over the empty set. If one can quanitfy over the empty set, then you get apparently sound arguments with false conclusions.

Or maybe that's not what the author had in mind at all. I haven't read the book.

Re: Goodbye,Descartes
 

There's no equivication in the way this argument is intended to be interpreted. Nothing in the premise "All unicorns are horned animals.", is meant to refer to anything 'conceptual', but to actual 'corporal' animals. It's not meant to be true in the context of this argument because of our concept of a "unicorn" says that they have a horn and so fit in our concept of "horned animals". It is meant to be true in the context of this argument because there are no unicorns (we're talking real, 'corporeal' animals here), and so trivially, they are all horned animals.

Any sentence of the form "All x are y" are true when there are no x's. Because this sentence is contradictory to "Some x are not y", and if there are no x's, this sentence will be false for any y. So since it is not the case that "Some unicorns are not horned animals" (since there are no unicorns, and so no unicorns that are not horned animals), it must be the case that "All unicorns are horned animals". Of course by the same logic, it is also the case that "All unicorns are non-horned animals".

This may not fit perfectly with our intuitive understanding of sentences of the form "All x are y", since in the real world, we often assume that this implies that "Some x are y". And this what the original syllogism assumes, and why it fails. The weirdness comes in from talking about predicates which aren't satisfied by anything (things that aren't real), and the argument is just an illustration of why Aristotle's reasoning doesn't work with such predicates. It's just not designed to talk about such things. And this won't be a problem for a lot of things, since we normally wouldn't talk about something that didn't exist. But there are times when we want to talk about things we don't know exist without assuming that these things exist (mathematical objects, God, etc.) and this guy is just pointing out that Aristotilean logic won't work for this stuff.

I hope that made some sense. This has some page has some a better explanation for why Aristotle's reasoning doesn't work if you can't follow mine. Through section 1.2 The Argument Against the Traditional Square, is relevent, I didn't read further than that.

Re: Goodbye,Descartes
 

So, if Lucktard is correct,

No logic is contradictory
All Aristotlian logic regarding unknown or non existences is contradictory
-------------------------------
Some Goodbye, Descartes' pages are not bad reads.

Maybe I'll read it too.