A Crash Course in Formal Logic Pt 5c: Squares of Opposition

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[@clintonwilcox4690]

Thanks so much for this. I teach a logic class to homeschool students, but the textbook I use approaches it from an Aristotelian perspective, though it does mention Boolean logic in the section on the square of opposition, but didn't go into detail about it. This was very informative. Though I am curious, if the I and O statements have existential import, then why is the subcontrariety relationship still considered logically undetermined? And why are contradictory statements still seen as logically determined, even though you're moving from a statement without existential import to a statement with existential import?

[@PhilHelper]

Excellent! Knowing both approaches will help with the jump to quantified logic...at least I think it does.

[@PhilHelper]

It's not too big of an issue. He just insists that if one wants to help themselves to the extra premise "cellphones exist" that they have to add it to their premises. Then it's a deduction from two premises instead of one and no longer an "immediate inference." Consider another example. "All unicorns are one-horned animals." It has the same form as "All cellphones are wireless devices." Aristotle avoids unicorns by denying the proposition. Boole limits what can be deduced from it.

[@sushmitamukherjee2215]

Though other people are dismissing the Boolean Claim, it is very interesting. The Three Step Checklist avoids any fallacies!

[@kelseycollette7980]

What are the differences between the Boolean and Aristotelian Venn diagrams can be used to explain the differences between the Modern and the Traditional the squares of opposition?

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[@Crypt0n1an]

PhilHelper I need your help in clarifying the following for me; Consider the proposition, X exists. If I were to claim that this is false would that mean that I am indirectly claiming that X does not exist is true? Am i obliged to accept that X does not exist is a true statement if i claim that x exists is false. Can i simultaneously claim that X exists and X does not exist are both false? Thank you for your great videos, your help with this would be much appreciated.

[@pckeller7400]

Thanks so much for the course that i never took but wanted to.

[@PhilHelper]

You're welcome. I'll try to come up with videos with sample problems to work through...

[@crossgearedviking1559]

So Aristotle's only conflict with Boole is not wanting to deal with hypothetical ideas? How does this relate to there being a "hole" in his logic system? Why does it matter? Seems to be a rather trivial difference.

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Sound goes away sometimes.

[@devindavidson8274]

This is the kind of thing that kills one's interest in academic logic. The wizards example at the end is a perfect demonstration of the absurdity of the entire subject of this video. No X are Y, therefore it's false that all X are Y. This is an obviously valid statement. It doesn't matter if X or Y exist, that's a question of truth of the conclusion, not validity. And the idea that the statement "all cats are animals, therefore some cats are animals" isn't valid is equally absurd. If all X are Y, then some X are Y. It doesn't matter if they do or don't exist, and neither the statement "all x are y" nor "some x are y" in themselves make the claim that X or Y exist. If you want to claim that X or Y exist, you need that as an additional premise. Boole's way of thinking seems completely arbitrary, and Aristotle's demonstrates a lack of understanding of hypothetical situations. I'm a little annoyed that I wasted 20 minutes watching this nonsense after the preceding videos, which were all valuable.

[@PhilHelper]

Devin Davidson Well, I suppose I have to defend both Boole and Aristotle.You say "Aristotle's (method) demonstrates a lack of understanding of hypothetical situations." Rather, Aristotle assumes that "All X are Y" carries with it the assumption that Xs exist. He would have real trouble with a seemingly true tautology like "All unicorns are unicorns" or "All unicorns have one horn." The problem (see video 1) is that Aristotle holds both to the correspondence theory of truth (truths require truth makers) and denies that categories exist when the are empty (so no unicorns existing=no abstract category of unicorns=no truth maker for the propositions in question). Plato didn't have this problem. Nor did Boole (a Platonist here). Categories such as unicorns may exist abstractly. The empty category exists and is the truth maker. But...and this is important...this requires Boole to give up the inference from "All X are Y" to "Xs exist" and consequently the inference from "All X are Y" to "Some X is a Y."Please try hard to wrestle with this point. Boole laid the foundations for computer science and rules for quantified logic (which is Boolean, not Aristotelian). It will be hard to go far in either discipline if you think these developments to be an "absurdity."

[@devindavidson8274]

>Aristotle assumes that "All X are Y" carries with it the assumption that Xs exist. Yeah, it doesn't though. There's no reason to believe that such a statement carries such an assumption. I guess Boole would agree on that point. >and consequently the inference from "All X are Y" to "Some X is a Y." Why? If all X are Y, even if Xs don't exist, that still means some X are Y, because if there are any X, they are necessarily Y. I think the problem here is that Boole is assuming "some X are Y" implies the existence of X, which it doesn't. "Some wizards are powerful" doesn't imply that wizards exist. We can very easily discuss an entirely fictional scenario with logic, nothing in the scenario has to be real. None of the words we use even need to exist in english, if we define them clearly ourselves.

[@devindavidson8274]

In other words, the word "some" doesn't imply existence. That seems to me to be an arbitrary assumption with no rational basis. Existence of a subject is not even relevant to the validity of an argument, it's only relevant to the truth of the conclusion. Why would you then assume that something must exist just based on the phrasing of the argument? It's like mixing up validity vs. soundness.

[@PhilHelper]

Devin Davidson You are correct on the point that Boole agrees with you that "All X are Y" does not imply existence. But there is a problem with your statement "I think the problem here is that Boole is assuming "some X are Y" implies the existence of X, which it doesn't." On both Boole and Aristotle's view, "Some X are Y" means "Something is an X and a Y." On your reading, "Some X are Y" means "Some X, if it had existed, would have been a Y." In other words, your logic has as much trouble dealing with actual objects (since you cannot derive an existence claim as a conclusion using your logic) as Aristotle's had with dealing with merely possible objects. In short, you are extending logic to deal with merely possible objects...possibly existing (or hypothetical) Xs or subjects. Modal logic, the logic of possibilities, deals with that. As logic developed after Boole, it was able to handle both actual and possible truths and objects...quantified modal logic...I'll cover that in videos later. For now, If Necessarily all Wizards are powerful and Possibly (or hypothetically) Wizards exists, then the conclusion follows that Possibly powerful things exist. Whether they actually exist does not follow. Aristotles logic only deals with actual objects...he needs them as truth-makers for propositions involving "All" or "Some." Boole is a Platonist...Categories for him actually exist, contra Aristotle, regardless of whether members actually exist and these categories are the truth-makers for "All" statements with non-existing subjects. But what is such a category? Spooky, some think, a purely abstract thing. Watch out for logics that deal with merely hypothetical objects too...If statements involving these objects are true then (according to the correspondence theory of truth) there has to be a truth-maker for them as well. Thus, using such a logic will seemingly require an worldview involving merely possible objects...W.V.O. Quine, a famous logician, snarked at such a theory..."How many merely possible fat men are now stuck in that doorway?" he would say.

[@DevinDTV]

PhilHelper >your logic has as much trouble dealing with actual objects (since you cannot derive an existence claim as a conclusion using your logic) How is this a problem? I don't want to assume something exists based on a statement like "some x are y". >you are extending logic to deal with merely possible objects All objects are "merely possible". We don't actually know that anything exists, in the widest scope, without any assumptions. Things only exist if we say that they exist in the premises.

[@crossgearedviking1559]

Seems like Boole is overthinking the whole thing. We know that cellphones exist. I'm holding one in my hand right now! Why is this an issue for him?

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