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 Post subject: Aristotelian Logic Question
PostPosted: Wed Apr 17, 2019 8:31 am 
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I'd like some help with conditional validity, because I think some points made in modern logic are leaving me missing Aristotle's point. I think I have a really good grasp on categorical syllogisms generally, on the moods, on valid forms, on the rules for validity, etc. I know that there are fifteen unconditionally valid mood/figure combinations and nine conditionally valid ones for a total of twenty-four.

It's those last nine that get me. Let me illustrate with an AAI-1, which is, of course, a conditionally valid syllogism. Here's one that's valid:

1. All dragons are fire-breathers
2. All lizards are dragons
3. Therefore, some lizards are fire-breathers

So Aristotle says this is conditionally valid if the subject, lizards, exists. And they do, so it's valid. Now let's invert the major and minor premise:

1. All lizards are dragons
2. All dragons are fire-breathers
3. Therefore, some dragons are fire-breathers

And this is supposed to be invalid because dragons don't exist.

So I have lots of problems with this. The first is that I think I'm getting hung up on my objection to the first syllogism insofar as a modern logician would say it's valid but not sound, and I feel like I've read that's not language Aristotle would like. The second premise in the first example is just false, so while it might be valid in the modern sense, Aristotle might say the entire thing is false/invalid/unsound/whatever. And maybe that's part of what is making this hard for me, because I'm not seeing a very intuitive example of how all this is helpful.

That gets to my second problem. I get that deriving an I-type statement from two A-types (assuming the proper figure) is easy. After all, AAA-1 is unconditionally valid. And since if A is true, I must be true, then if AAA is true, then how much more AAI. But . . . in that case . . . why does it matter at all? What's the point in deriving an I type statement in the conclusion when you could just derive an A type statement? The logic itself seems to demand an A and seems to let us derive an I only because it warrants an A.

Third, the whole idea of a condition seems not to be a matter of form but on the existence of the term in question (S, P, or M). But now this isn't a matter of logical form but rather with a secondary question that a modern logician might speak of in terms of soundness. Now if we're going to assess an argument's soundness, why is this particular area of soundness (say, in the question of an AAI-1, then existence of S) particularly special to warrant this being called conditionally valid?

Does anybody have an intuitive example of this? Because every example I come up with for any and all of the forms (AAI-1, EAO-1, AEO-2, EAO-2, AAI-3, EAO-3, AEO-4, EAO-4, and AAI-4 -- and yes, I've written out examples for myself of every single one of those) just seems entirely superfluous.

Help?

edit:

Actually, I came up with one example I felt like I intuitively grasp. It was this one of an AAI-4:

1. All medicines have side effects
2. Everything with side effects should be used cautiously
3. Some things that should be used cautiously are medicines

But interestingly, if I change the first to an I it is unconditionally valid:


1. Some medicines have side effects
2. Everything with side effects should be used cautiously
3. Some things that should be used cautiously are medicines

And I intuitively get both . . . so . . . wuh?

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Indeed, the Lord Jesus, when He prayed to the Father, "that all may be one. . . as we are one" (John 17:21-22) opened up vistas closed to human reason, for He implied a certain likeness between the union of the divine Persons, and the unity of God's sons in truth and charity. This likeness reveals that man, who is the only creature on earth which God willed for itself, cannot fully find himself except through a sincere gift of himself. ~ Pope Paul VI, Gaudium et Spes 24.3


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 Post subject: Re: Aristotelian Logic Question
PostPosted: Wed Apr 17, 2019 8:43 am 
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theJack wrote:
I'd like some help with conditional validity, because I think some points made in modern logic are leaving me missing Aristotle's point. I think I have a really good grasp on categorical syllogisms generally, on the moods, on valid forms, on the rules for validity, etc. I know that there are fifteen unconditionally valid mood/figure combinations and nine conditionally valid ones for a total of twenty-four.

It's those last nine that get me. Let me illustrate with an AAI-1, which is, of course, a conditionally valid syllogism. Here's one that's valid:

1. All dragons are fire-breathers
2. All lizards are dragons
3. Therefore, some lizards are fire-breathers

So Aristotle says this is conditionally valid if the subject, lizards, exists. And they do, so it's valid.


I'm not much of a philosopher, so maybe I'm completely missing this, but this entire premise seems wrong.

If all dragons are fire-breathers, and all lizards are dragons, then all lizards are fire breathers. You can't have a lizard that isn't a fire-breather, since all lizards are dragons, and all dragons breathe fire. If a lizard isn't a fire breather, then that negates either point 1 or point 2. Either all lizards aren't dragons, or all dragons don't breathe fire.

Quote:
Now let's invert the major and minor premise:

1. All lizards are dragons
2. All dragons are fire-breathers
3. Therefore, some dragons are fire-breathers

And this is supposed to be invalid because dragons don't exist.



This one makes no sense at all. 3 completely negates 2. Also, statement 1 is completely unnecessary.

Unless, in all these cases, "some" doesn't mean "some but not all". I suppose that could be the case.

Kinda like the Mitch Hedberg joke:

"I used to do drugs. I still do. But I used to, too."

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 Post subject: Re: Aristotelian Logic Question
PostPosted: Wed Apr 17, 2019 9:03 am 
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You're getting at some of my problem, BK! In logic, there are what are called A and I type statements (also E and O). A type statements are in the form "all X are Y." I type statements are in the form "Some X are Y." So part of my confusion here is that AAI type statements (so long as they are in what is called the first figure) are necessarily true. Let me modify the classic example to illustrate your (and our) point:

    Example 1
    All humans are mortal
    All the citizens of Athens are humans
    Therefore, all the citizens of Athens are a mortal

That logically follows. It's in the AAA-1 mood/figure combo, which Aristotle rightly demonstrates is valid. And the premises are true, so this is sound. But the AAI (which is called a conditionally valid argument) would look like this:

    Example 1'
    All humans are mortal
    All the citizens of Athens are humans
    Therefore, some the citizens of Athens are a mortal

And fine. Some of the citizens are mortal. But that's because ALL the citizens are mortal. Aristotle thinks this is important because it is valid on the condition that the subject of the conclusion (in this case, the citizens of Athens) really exist. I am failing to see how that's relevant. Let's take another example.

    Example 2
    All humans are mortal
    All the citizens of Atlantis are humans
    Therefore, some the citizens of Atlantis are a mortal

Aristotle would say this is conditionally INVALID because the subject, the citizens of Atlantis, don't actually exist. But why is this invalid but the AAA form of the same argument valid? In this case:

    Example 2'
    All humans are mortal
    All the citizens of Atlantis are humans
    Therefore, all the citizens of Atlantis are a mortal

In this latter case, the subject still doesn't exist, but now Aristotle says this is valid (though still not sound). And that's where I'm confused. I don't really get the point. It seems to me we can just ignore the conditionally valid mood/figure combinations all the way around as they don't tell us anything the unconditional forms don't already tell us. My hope is that someone will help me fill in the gaps in my thinking here.

_________________
Indeed, the Lord Jesus, when He prayed to the Father, "that all may be one. . . as we are one" (John 17:21-22) opened up vistas closed to human reason, for He implied a certain likeness between the union of the divine Persons, and the unity of God's sons in truth and charity. This likeness reveals that man, who is the only creature on earth which God willed for itself, cannot fully find himself except through a sincere gift of himself. ~ Pope Paul VI, Gaudium et Spes 24.3


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