Working Paper Group: "Irreflexivity and Aristotle’s syllogismos"

I'm pleased to announce that Matt Duncombe has posted his paper, "Irreflexivity and Aristotle’s syllogismos", over at dropbox.com for our Working Paper Group. Here is a quick blurb about the paper:

Aristotle's definition of 'deduction' specifies that the conclusion cannot be identical to any premise. This would make entailment an irreflexive relation. This seems wrong: 'p, therefore p' seems as good an inference as it is possible to make. In this paper I explain Aristotle's insistence on irreflexivity by showing that, in any pragmatic context in which Aristotle envisions 'deductions' being used, irreflexivity is a necessary condition on a good deduction.  

Here, again, are the Working Paper Group groundrules:

• The paper is posted over at Dropbox.com. 
• In order to access it, you must email me at marvan@ut.edu for the login and password.  Once you have these, just login into dropbox and download the paper.
• Barring unforseen and unfortunate circumstances, our dropbox login and password will be the same for all future working papers.
• The login, password, and working papers themselves are in no circumstance to be distributed to anyone. In order to maintain the integrity of our forum, I alone am authorized to distribute them.
• In order to maintain the safe and supportive integrity of the paper discussion, I will only distribute the login and password to registered members of The Philosophers' Cocoon. 
• As always, any professional philosopher who wants to become a member of the Cocoon is welcome to email me to join. However, you must become a member to participate in the working paper group.
• Finally, here are some ground-rules for the paper discussion (which should simply proceed in the comments section below): 

1. You must have access to -- and presumably have read! -- the paper in order to comment.
2. Comments should aim to be helpful in nature. If you raise an objection, try to suggest potential way(s) of resolving it.  The purpose of this group is to help our friends here at the Cocoon improve their papers, not to show off one's awesome refutation skills.
3. Be a good dude/dude-ette.  Do everything you can to make this a positive experience for the paper presenters.

Let the discussion begin!

Comments

[Marcus Arvan]

Hi Luca,

Thanks for presenting your paper! I have to admit that I'm pretty out of my element here (I'm not a historian of philosophy by any stretch of the imagination, let alone an Aristotle scholar). Still, I'll do my best to present a few questions that I had while reading your paper. Maybe they're dumb questions. I don't know. But I hope you find them helpful. ;)

You say in your introduction (p. 1) that Aristotle scholars have generally taken irreflexivity to be:

(A) a logical condition
(B) introduced by Aristotle because of the pragmatic contexts in which syllogismoi were used,
(C) Specifically, to rule out the argumentative faux pas of begging the question.

You then argue that:

(D) Aristotle never formally distinguishes logical and pragmatic conditions, but Aristotle holds irreflexivity because,
(E) "reflexivity holds in no pragmatic context", and so
(F) "irreflexivity will be a logical property in all pragmatic contexts." (p. 16)
(G) Specifically, because there are *different* (pragmatic?) reasons to deny reflexivity in the four different types of syllogismoi (dialectical, eristic, etc.)

Here's my first set of questions: aren't claims (D)-(F) an inconsistent triad? If Aristotle held that reflexivity holds in no *pragmatic* contexts and so irreflexivity is a *logical* property, isn't this just to say that (D) is false (that he did distinguish logical from pragmatic conditions)?

Here's my second set of questions: aren't claims (E) and (F) precisely what the traditional interpretation asserts in (A) and (B)? As you note in your introduction (see A and B above), Aristotle introduced irreflexivity as a logical condition on pragmatic grounds. But this seems to be no different than what you assert in (E) and (F).

This brings me, finally, to what I think might be a more helpful comment, which is that it really seems to me that claim *(G)* is what distinguishes your interpretation from the traditional one. Your claim -- your really novel contribution to the debate here (as far as I can tell) -- has to do with denying (C) in favor of (G). On the traditional interpretation (claim (C)), Aristotle imposes irreflexivity to rule out *question-begging* arguments. This is the big claim you mean to deny, right? You mean to claim (and this is your claim G) that there are *four* different pragmatic reasons that he imposes irreflexivity.

Isn't that what you're up to? If so, then I think you might want to reframe the paper a bit. Since claims (A) and (B) of the traditional interpretation don't seem different from claims (E) and (F) of your interpretation -- and claim (D) of your interpretation seems (to me, at any rate) inconsistent with your claim (D) -- perhaps the paper would be better served by doing away with those purported contrasts in favor of the one *big* contrast you mean to make: (G) over (C) (i.e. "Aristotle's not on about question-begging -- he's on about *four* pragmatic elements!")

Of course, perhaps I'm just totally confused. I don't know...and goodness, I'm sorry for the convoluted comment. I'm a mess when it comes to writing today. Finals week...grading has fried my brain. ;)

[Matthew Duncombe]

Dear Marcus,

Thanks very much for your comments on the paper, especially at a busy time for you. I think you have seen the nail clearly and struck it squarely on the head. I'll definitely re-frame the paper in something like the way you suggest.

It now occurs to me that I may have thought to give (D) as a reason to reject (C), because, as what you say implies, (D) is inconsistent with (A) and (B) which are usually taken to support (C).

Also, in general, I think I want to deny that irreflexivity is a logical condition (i.e. deny (A)), if that means there are conditions on being an argument that are independent of pragmatic considerations. There are only pragmatic considerations. Now, if some condition holds in all pragamtic contexts then, ok, give it as a condition in your all purpose definition. But that does not mean that it is a context-independent condition. In short, I hope that writing (F) on p.16 was a slip! But I'll go back over it again.

But I think your point to re-frame the paper to emphasise that my contribution is to replace (C) with (G) is an excellent one; the other issue, about whether Aristotle distinguishes logical and pragmatic conditions isn't the core of the paper (and I think its only in there for biographical reasons, i.e. that is why I started working on this topic).

Again, thanks so much for your comments!

Best wishes,

Matt

[Marcus Arvan]

Glad to hear you found the comments helpful. I'm sorry more people haven't posted comments yet. I suspect it's because we don't have any other historians of philosophy as members. Hopefully that'll change in time!

[Moti Mizrahi]

Hi Matt,

Like Marcus, I am not an Aristotle scholar. As I was reading your paper, however, one point picked my interest and I thought I'd raise this question in the hopes that it might be useful as far as motivating your project is concerned.

You write: "From the point of view of modern logic, irreflexivity looks like a mistake. An inference like ‘p; therefore, p’ seems as good as can be. Modern logicians, of course, have no problems with reflexive inferences. Indeed, modern logic takes it that NTP is necessary and sufficient for the entailment relation. An entailment relation that denies irreflexivity (or indeed monotonicity or transitivity) will looks strange."

Couldn't one say (as some of the Aristotle scholars you cite seem to have said, given that they appeal to pragmatic considerations) that Aristotle was not interested in syllogistic entailment as a purely formal relation but also as an argumentative device. To put it in more contemporary terms, one could say that Aristotle was interested in informal logic (or critical thinking) as much as he was interested in formal logic. In that case, his syllogistic entailment could be construed as an attempt to avoid vicious circularity in arguments (i.e., arguments of the form 'p; therefore, p'). Does that make sense?

I hope this is helpful.