Talk:Square of opposition

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i want to know more about the rules and examples of subaltern opposition.

== Rewrite How do I do tables? Dbuckner 07:42, 1 August 2006 (UTC)

Does Aristotle even define the subaltern in De Interpretatione? I can't find it. You might define it as truth of one implies the other but not vice verse, or falsity of one implies falsity of the other but not vice versa, or make both requirements. These 3 definitions will all be equivalent in the traditional square, but will diverge for statements that cannot be put into standard form, and I can't find which def is used. Maybe this is a later Aristotelian twiddle. Likewise, I always portray the traditional square with subaltern lines with arrows for the truth goes up and falsity goes down parts of the subaltern inferences. Bmorton3 15:26, 3 August 2006 (UTC)

Good point. I checked and I think you are right (though always much harder to establish someone didn't say something than conversely). I will alter it at some point. Clearly the subaltern relation follows from contrariety and contradiction).

Brian: I don't suppose you would be interested in getting this one in shape for FAC? Or has the other thing put you off? Dbuckner 18:44, 6 August 2006 (UTC)

It's short, and not very "pressing," let's get it to GA, and then see how any of the FA stuff works out. See my comments on well-written vs well-edited at the guideline for reviewers site. I suspect I lack the skills required to push an article from GA to FA, and am instead interested in trying to get stuff to GA. Look at Nature (philosophy) and Naturalism (philosophy) those sites are much higher traffic, more pressing and badly need work jsut to get to GA. Bmorton3 15:55, 7 August 2006 (UTC)

I used to have a great list of like half a dozen different medieval compromises on existential import, but I can't find it. So I can't reference the "lots of compromises" claims, but not I ws thinking much earlier than Keynes. Also Spade asserts that Aristotle has no term for subaltern, is it Porphyrian maybe? Bmorton3 20:41, 3 August 2006 (UTC)

Boethius explicitly calls it that in his commentary. Dbuckner 18:45, 6 August 2006 (UTC)

My pre-Spade notes claim a modified Aristotelian position of all propositions have EI in subject only (which ditches conversion) in the early middle ages (but who? I don't know), Only affirmitive statements have EI in some late middle age texts (damn who?), and Boole and Ferre's positions. For what it is worth, Spade argues that Aristotle is committed to EI on all terms, not from his discussion of O forms, but from the very head of Prior Analytics where he says our aim is only to explore demonstration and demostrative science, look also at the posterior analytics "We suppose ourselves to possess unqualified scientific knowledge of a thing." The Demonstrative is only for knowledge of things, not of that which is not (although of course there are other mannners of knowing, and non-demonstrative forms of argumentation). But again lots of what the medievals get is coming from Theophrastus, Porphyry, Alexander Aphrodisias, etc. Bmorton3 21:03, 3 August 2006 (UTC)

Uhm some of my edit got squashed, if you allow EI on A and I but not on E and O, subcontriety fails as does half of subalternation, and there might be other problems too. Bmorton3 19:10, 5 September 2006 (UTC)

Look at the Stanford Encyclopedia of Philosophy article (top external link). It shows in gory detail how you get all the traditional inferences if you put EI on AI but not EO. Namely, if the subject term is empty, then I is false, E is true, A is false, O is true. This satisfies subcontriety and the "negative half" of subalternation

Well, crap, I hate feeling stupid. You are right, these would save the square doctrines. It would force some revision on how obversion and contraposition work, but it would save the square. Bmorton3 16:35, 6 September 2006 (UTC)

[edit] Some extra information to think about

Hi Brian,

I'm researching an article on the Square at the moment – looking at what the 'traditional logicians' actually wrote, in Latin, as opposed to what some modern logicians, writing with hindsight and with the benefit of the assumptions behind modern predicate calculus, say that the traditional logicians said, in English.

E.g. Parsons writes "For most of this history, logicians assumed that negative particular propositions ("Some S is not P") are vacuously true if their subjects are empty." First of all, a huge sweeping assertion, apparently covering logicians as diverse as Aristotle, Apuleius, Boethius, Abelard, Ockham, Buridan, Zabarella, Sanderson, Hamilton, Mill, Brentano, and many in between. When you come to what such logicians actually wrote, of course you find that they are arguing and quarreling among themselves, proposing new theories, disputing old ones – pretty much the same as today. It's like characterising all logic between 1880 and 2006 as involving the same assumptions, which of course it doesn't.

In any case, most of the logicians Parsons is thinking about are the medieval ones, who wrote in Latin. Did they say anything that suggests they assumed what Parsons characterises iin English as 'assumed that … their subjects are empty'? It turns out that logicians before the 13C couldn't really express this assumption at all, since Parsons is talking about terms that stand for or denote nothing, and they had no word for that. The idea of 'standing for something' (supponens pro aliquo) was an innovation of the late 12C whose origins are mysterious. William of Sherwood mentions it, Ockham and Buridan write a great deal about it.

Before the 13c logicians talked about subjects 'not existing' (non existens). Thus the term 'chimera' does stand for something, as it were, namely a chimera, a thing that does not exist in reality (in rerum natura, in rebus, in rebus materialibus &c). Thus they are commited to the truth of "some things do not exist in reality". But the sentence "some things do not exist in reality" is of course an O proposition, and it is clear that if the A proposition 'all things exist in reality" is false, "some things do not exist in reality" is true, and the traditional relationships hold, but for very different reasons than Parsons claims.

Now there is a nominalistic tradition, of whom Ockham and Buridan are notable exponents, according to which there isn't a world of impossibilia and imaginary things. But this is a separate tradition, and it died out after the 14C. The tradition that survived is the Thomistic one which continues the pre-13C tradition of non-existent things. This survives until the nineteenth century and beyond (in the hands of the neo-thomistic logicians such as Joyce and Wade).

However, this probably counts as OR –just letting you know that the position is a little more complex than anything in this articles makes out. I'm still working on the paper. If I finish it and it is published, perhaps you can refer to it! Best. Dbuckner 10:40, 29 September 2006 (UTC)

Yeah, I have lots of worries here, but it is largely on the edges of my competence. First, when we think of an empty subject do we mean one that lacks 'standing for something' (supponens pro aliquo) or 'refering to something' (significans pro aliquo). Peter of Spain already wants to talk about the difference between signification and supposition. The doctrine of the difference between supposition proper and improper is all about this difference. In improper supposition a term might supposit, even though the term cannot significate. Consider the term "the cup I drank yesterday" in the claim "the cup I drank yesterday was poisoned." I didn't drink ANY cup yesterday, I drank the wine in it. So the term "the cup I drank yesterday" can't refer to anything, but it does nonetheless supposit for the liquid in the cup which I drank yesterday. Here is another wrinkle from Buridan's Sophismata Chap 2. For a affirmative statement to be true, it requires something of which the subject term can be truly affirmed. But in a claim like "Hominem esse animal est verum", ther is nothing for the subject term to be about because of the infinitive. In Paul Spade's word's there is nothing you can point to and say "this is for a man to be an animal" So the term can't be "taken significatively." There's lots of other problems but at minimum you have to figure out how the signification and supposition talk is supposed to map onto modern sensibilities, what was it for, what was it doing? Terms can be empty in lots of ways. A term can fail to mean anything. It can fail to refer to anything. I can fail to be used to mean anything. It can mean something other than what it is used to mean. It can be used to mean something other than what it refers to. It can even (one of my old papers) be used to mean something while failing to mean anything! Moderns step blithely between issues, medievals made fine distinctions on, like the difference between different kinds of ways that a term can be empty. Bmorton3 15:14, 29 September 2006 (UTC)

[edit] In contemporary terms...

Is it possible to make the following pairings:

contradictory: XOR

contrary: NAND

subcontrary: OR

subalternate: → (IMPLIES/IF)

--spAs 14:21, 15 March 2007 (UTC)