# The Limits of Aristotle?



## RamistThomist (Jul 4, 2004)

I was reading from Copi and Cohen, Introduction to Logic, 11 edition, and notice that they seem to give up on categorical propositions. Now, if I read it right, they seem to agree that categorical propositions with respect to the square of opposition have some value but must &quot;be abandoned, and a more mdoern interpretation employed.&quot; The title of the section is &quot;Existential Import and the Interpretation of Categorical Propositions.&quot;

Here is their line of argument:

A proposition is said to have existential import if it typically uttered to assert the existence of objects of some kind.

We begin with I and O propositions. Thus the I proposition &quot;Some soldiers are heroes&quot; says that there exists at least one soldier who is a hero. And the O proposition, &quot;Some dogs are not companions&quot; says that there exists at least one dog that is not a companion. These particular propositions assert that the classes designated by their subject terms are not empty. Wherein lies the problem? The problem arises from the consequences of that fact, which are very awkward. It is given that an I proposition follows validly from its corresponding A proposition by sublalternation. That is, from &quot;All spiders are eight legged&quot; we infer that some spiders are eight-legged. The same inference can be made from an E proposition to an O proposition.

But if I and O propositions have existential import, and they follow validly from their corresponding A and E propositions, then A and E propositions must also have existential import. Thus, according to these authors, the problem arises. We know that A and O propositions, on the traditional square of opposition, are contradictories. &quot;All Danes speak English&quot; is contradicted by &quot;Some Danes do not speak English.&quot; Contradictories cannot both be true, since one of the pair must be false, and vice-versa. But [i:0511a2f273]if[/i:0511a2f273] corresponding A and O propositions do have existential import, as we concluded in the paragraph just above, then both contradictores could be false! To illustrate: The A proposition, &quot;All inhabitants of Mars are Blond&quot; and its corresponding O propositions &quot;Some inhabitants of Mars are not blond&quot; are contradictories; if they have existential import, that is, if we interpret them as asserting that there are inhabitants of Mars--then both of these propositions are false if Mars has no inhabitants. And of course, we know that Mars has no inhabitants; the class of its inhabitants is empty, so both of the propositions given in the example are false. But if they could both be false, then they could not be contradictories!

This is the authors' argument so far. Paul, this is where I want you to help me. The authors then ask what could be done to save the traditional square of opposition. They postulate reviving it via a [i:0511a2f273]presupposition[/i:0511a2f273]. Would their following argument have anything to do with transcendentals?

To illustrate: Some complex questions are properly answered &quot;yes&quot; or &quot;no&quot; only if the answer to a prior question has been presupposed. &quot;Did you spend the money you stole?&quot; can be reasonably answered yes or no only if the presupposition that you stole some money be granted. Now, to rescue the Square of Opposition, we might insist that all propoisiotns--that is, the four standard form propositions--presuppose (in the sense indicated above) that the classes to which they refer, do have members, are not empty. In this way, the Square is saved, but at a high price. To do this we must pay by making the blanket supposition that all classes designated by our terms do have members, are not empty.

Well, why not do just that? (Here is where the authors propose the abandonment of Aristotelian logic)

1)This rescue preserves the traditional relations among A,E,I, and O propositions, but only at the cost of reducing their power to formulate assertions that we may need to formulate later. If we invariably presuppose that the class designated has members, we will never be able to formulate the proposition that denies that it has members!

2)Even ordinary usage of language is not complete accord with this blanket supposition. SOmetimes what we say does not suppose tha tthere are members in the class we are talking about.

3) In science we often wish to reason without making any presuppositions(!!!!!!!!) about existence.

Upon these objections, the authors conclude Aristotelian logic outdated.

My questions: are they right? 
Knowing that at least one of them was an unbeliever, what is the effect of this on transcendentals?


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## RamistThomist (Jul 5, 2004)

Yes, that helps. I knew #3 would make you raise some eyebrows. I took a logic class last semester and at the same time was reading Bahnsen. When I got to that part of the textbook I wrote in the margins, &quot;But that is impossible!&quot; (science without presuppositions). 

thanks again


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## Civbert (May 30, 2006)

The author's problem was in insisting that the I and O forms imply the existence of at least one member. And the example in natural prose was given. But the problem with the example was in equivocation, not that they can both be false. They can not be both false using terms in the same sense. They impose a supposition on traditional logic that isn't the case. Aristotelian logic still works because it does not makes any suppositions about existence that the modern logic has construed. The problem was not one of "transcendentals" so much as mixing metaphysical issues into the logic. Aristotelian logic is not concerned with existence. Existence is just another potential predicate - that should not be assumed in any of the forms. The authors "solution" was a strawman made to be blown over.

Consider the mars example. Both propositions can not be false, but how do you know which is false? It's not enough to say, there are no men on mars. You have to take the proposition "No men are mars men" and then show how that makes "all mars men are blond men" is false. What's the syllogism that proves that both "all mars men are blonds" and "some men on mars are not blond" are false? The authors just assert that it proves it, but have not given the argument. That's because the argument is not evident.


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## Civbert (May 31, 2006)

The author's problem was in insisting that the I and O forms imply the existence of at least one member. And the example in natural prose was given. But the problem with the example was in equivocation, not that they can both be false. They can not be both false using terms in the same sense. They impose a supposition on traditional logic that isn't the case. Aristotelian logic still works because it does not makes any suppositions about existence that the modern logic has construed. The problem was not one of "transcendentals" so much as mixing metaphysical issues into the logic. Aristotelian logic is not concerned with existence. Existence is just another potential predicate - that should not be assumed in any of the forms. The authors "solution" was a strawman made to be blown over.

Consider the mars example. Both propositions can not be false, but how do you know which is false? It's not enough to say, there are no men on mars. You have to take the proposition "No men are mars men" and then show how that makes "all mars men are blond men" is false. What's the syllogism that proves that both "all mars men are blonds" and "some men on mars are not blond" are false? The authors just assert that it proves it, but have not given the argument. That's because the argument is not evident.


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