Colin and I have been having an argument about the principle of sufficient reason. I now think he is substantially right on several things. I wrote a long comment at his but screwed up somehow and lost it.
In brief, I think Colin’s view is that the principle of sufficient reason holds, along the lines of an affirmation of the proposition (a), “For any Y there is an X which is the reason or a reason for Y.” Colin holds, I think, that we can not reject proposition (a) without contradiction, and that this is not a matter of how we must think but a fact about the world independent of us.
I’m convinced of the first, I’m willing to go along with the latter but feel less strongly about it. Where Colin and I disagree, I think, is on two things. First, I want to maintain a difference between the phrase “we can not conclude other than” and “we can not other than conclude”, in relation to (a). This is in large part due to my having read a dialog by Lewis Carroll wherein Carroll implies that the act of drawing a conclusion is not guaranteed by the premises of a syllogism.
I’m convinced with regard regard to (a) we can not conclude other than (a) in any case. That is we can not conclude (~a). But I’m not convinced that this means one must conclude (a). “We can not conclude other than” means other conclusions are barred. “We can not other than conclude” means non-conclusion is barred. If “we can not other than conclude (a)” then (a) is guaranteed. If “we can not conclude other than (a)” we have eliminated the possibility of any other conclusions but concluding is not necessarily guaranteed, in the sense that we can still introduce intermediary premises before conclusion, as in the Carroll. I may be simply enganging in wordplay sophistry here, I’m not sure, but I think part of what’s involved here is a question as to whether (a) = (~(~a)), that is, if the negation of the negation of a term is equal to the term.
Second, Colin and my discussion has been vexed by a confusion on my part about what precisely is being claimed in (a). Recall that (a) is the proposition “For any Y there is an X which is the reason or a reason for Y.” (Part of what affirmation of this proposition aims to do is rule out any assertion like “For some Y there is no X which is the reason or a reason for Y.” Colin rightly argues that this is impossible.) It’s not clear, though, what “is a reason for” means. I’ll call this phrase “(r)”. On the one hand, (r) could refer to justification, the line of reasoning which makes something reasonable. In that case, (r) is related to the practice of reason giving and is something like an acceptable claim according to the standards of reason (the definition of which I’ll bracket). In that case, (r) is part of an answer to a question like “why do you hold Y?”
On the other hand, (r) could refer to causality, that which brings about a state of affairs. In that case, (r) is part of an answer to a question “why is Y the case?”
Colin holds that the reason for (a) is that contradiction results if we reject (a), that (~a) is out of bounds. This is unproblematic with regard to reason giving. In this case, (a) satisfies itself, it meets the criteria it insists upon. That is, if we take (a) as a value for Y, we can say “For (a) there is some X which is reason for (a).” That reason is that we can not reject (a) without contradiction. On the other hand, things seem murkier if we take this as a matter of causality. In terms of causality, taking (a) as a value for Y, we get “for (a) there is some X which is the reason for (a)” such that X causes (a) to be the case, X made (a) come about. Now, I may have a poor notion of causality here, but it seem to me that this version is more problematic. If we take some object, like a chair, we can find a temporally prior condition and some actor(s) in that condition which caused the chair. We can do the same with a proposition like “nuclear war will result in widespread loss of life” - we can find various causes for this proposition without too much trouble, including explanations as to why the proposition is true. I’m not clear what the cause could be for (a), though. Prior to doing so and proving it so, it seems to me that this should render (a) uncertain. Given that we don’t want (a) to be uncertain, then it seems to me that we should bracket (a) in terms of cause, which means instead we should limit ourselves to (a) in terms of reason-giving for now.
I think this is a really interesting exploration of the problem, Nate.
First, I’d like to say that I regard the principle of sufficent reason as a logical principle. I’m not particularly concerned with physics or metaphysics (movement or existence) when I make that claim. Basically, I think the principle extends from logic to physics and metaphysics, because logic is soemthing like the “form” through which things become thinkable. What we’re doing in physics and metaphysics is thinking about certain things in a certain way, so, in those cases, logical principles must hold for those sciences.
Because I regard the principle of sufficient as a logical principle, I regard it as something like a “law of thought.” It’s not just useful or normal, but necessary. Thinking anything at all means thinking there’s a “reason” involved in thinking it, that we can’t think it without a reason. The reason may be implicit, but it can always be made explicit, at least in principle.
I just wanted to explain that, to clarify that I’m not concerned to make a claim about what is objectively the case in the world. I’m only concerned with what’s necessarily implied by thinking of the world, or ourselves, or anything else.
I also think we read the Carroll dialogue a little bit differently. I read it as a question about the possibility of deductive inference, rather than the possibility of adding new premises and delaying conclusion. If we question the validity of the hypothetical syllogism, for instance, then we call into question our ability to pass from the major premise, to the minor premise, to the conclusion of any and all syllogisms. In that case, deductive reasoning is no more legitimate than inductive reasoning. What’s really interesting is that I can’t think of a reason why the hypothetical syllogism is valid.
“(r) is part of an answer to a question like “why do you hold Y?” I think this is precisely what I want to argue, and what you’ve presented it very clearly. I want to use the principle to make claims about 1) it is necessary to justify the affirmation or negation of certain propositions with reasons, and 2) to eliminate the possibility that there could be a set of propositions which must be or should be affirmed, though no reason can or should be given. I’m not particularly concerned with physical, causal determinism.
The problem with the principle of sufficient reason, in my view, is more a problem of application than of the principle in itself. Say that the cat is on the mat. Giving a reason why the cat is on the mat could amount to saying that the cat walked over and sat down there, on the mat. But it could also be satisfied by saying something like “the cat was conjured by a sorcerer, who put it on the mat to deceive you.” Divination and sorcery count as reasons, according to the principle of sufficient reason.
Does the principle of sufficient reason give us a reason to accept relatively simple and natural claims like “the cat is on the mat because it walked over there and sat down” and absurd and impossible claims like “the sorcerer conjured the cat, and put it on the mat to deceive you?” I’m not sure. It seems to me that we cannot deduce particular reasons from the principle, even though the principle assures us of the existence of those reasons.
So, deduction from the principle of sufficient reason to particular reasons or causes has the same problems as the inductive examples you give in the last paragraph, of trying to go from a chair or a nuclear war to its causes. We may be able to prove that the chair didn’t fart into existence for no reason, or that nuclear war didn’t make the world fart out of existence for no reason, but the principle itself doesn’t tell us what the reasons are.
I hope that’s clear.
cm
Comment by colin — March 11, 2007 @ 8:10 am
hi Colin,
I’m in a bit of a rush so I need to try to be brief so I don’t miss my bus. I nearly bought a copy of a Quine book on the philosophy of logic at a used bookstore the other day, maybe I’ll go back and get it. At this point, I don’t think we have substantive disagreements on the above (in part because you’ve convinced me, in the discussion at your blog). Where I think we might disagree is here.
We agree on (a). If we plug (a) into (a) as a value for Y we get an argument for the necessity of (a), which I’ll call (n). If we plug (n) into (a) as a value for Y, we get the following, basically:
There must be some X which is a reason or the reason why (a) is necessary for thought. Let’s call that (o). In short, this proposition (o) and it’s status troubles me. This is in part because I’ve got - and I expect you do as well - an intuion a rational reconstruction of which is representable along the lines of “For any phenomenon Z, take Z as a value for Y and attempt to find X. Inability to do so should be troublesome, though it is likely an ineliminable condition given the quantity of phenomena one encounters.” I think we could introduce an implied principle of selection, to economize, something like “prioritize more important over less important phenomena.” “Important” is problematic and interpetible, but surely (a) should could as one important phenomenon. Hence, inability to find the X relative to (a), that is, the lack of answer to (a), is troublesome. I hope this makes sense. I gotta run.
big hug,
Nate
Comment by Nate — March 11, 2007 @ 5:46 pm
hi again Colin,
I’m home now, thought I’d talk about the Carroll piece a sec. I don’t think the piece has a retroactive critical force so much as a critical force in media res. That is, I don’t think the Carroll has any negative (in the sense of undoing or reversing) impact on already completed moves from premises to conclusions: the Tortoise threatens no already completed syllogisms. Rather, I think it has a sort of braking or delaying effect during the process of drawing an inference in the face of a demand (an Achilles command) “you must conclude” the conclusion from the premises, by introducing subsidiary premises prior to the conclusion.
take care,
Nate
Comment by Nate — March 12, 2007 @ 1:08 am
Let’s be clear what we’s be talking about is logical implication. Set the necessity of conclusion aside cause it muddles it. Carroll is talking about how we are justified in concluding a conclusion based on premises in deductive reasoning. He points out, in essence, that it itself is unjustified and assumed. It is a kind of argument against logic per say. Mathematicians and logicians deal with this by taking such a principle as an axiom. I personally think its awesome, but am not worried about it. I’m ok saying it’s part of the laws of human thought
Comment by todd — March 19, 2007 @ 8:51 pm
I keep forgetting to do this. Me and Todd had a gmailchat about this stuff, an edited version of which is pasted below.
*
me: I don’t think the Carroll piece justifies an attack on a case of someone having drawn an inference, in that sense it’s not critical. I think it serves for specific instances - during the drawing of an inference, so to speak - to arrest the proceedings.
todd: my impression was that it applied to all logic, and so was challening the notion of implication
me: I think it does in one sense but not in another. I don’t think it serves as an attack on past instances. I do think it serves to undermine the necessity of reaching conclusions in the instance, though. This is flakey but … say inference drawing is a performance on a stage. Carroll doesn’t provide any grounds for critically evaluating past performances or criticizing their contents. Rather, he provides resources for audience members who want to climb on stage (or actors who want to step off stage) in order to interrupt the proceedings.
todd: take the argument:
if p–> q
p
therefore q
my impression of carroll was that he was saying that if you have those two premises which you know, you have to justify the conclusion you do so by the law of logic but then he says, how do you justify that? and the idea being that there is no end to the justification and thus implication is thrown into question hence the tortoise and hare bit
todd: is that a different argument from the one you were looking at?
me: No, that’s similar, but smarter put. I think that I think the scope is more limited here than you do. We have: ” there is no end to the justification and thus implication is thrown into question.” Let’s make this two premises:
n = there is no end to the justification
i = implication is thrown into question
todd: ah i see. yeah i am missing some assumptions i made
me: if there’s a principle in Carroll’s piece then it applies to itself, such that the bridge between n and i — the implication — is shortcircuited.
I hadn’t actually thought of this before now, this is really interesting. The argument I was making was different. I agree with both n and i, but I don’t think the “thrown into question” part means that already-made implications are now rendered suspect. One can still move from n to i, implication can still happen without being a problem. I think it means, though, that one doesn’t HAVE to move so, one can arrest implication without contradiction because the process of drawing an inference isn’t representable in logical rules.
todd: its really close to hume’s argument about the justification of inductive logic actually (except that one is more sophisticated)
me: huh. what’s that in?
todd: i think the one on human understanding. i’d have to dig it up. i think its actually an argument outside of time since all arguments use implication. hume’s argument to give an analogy is that how do we justify induction? either we justify it inductively or deductively deduction can’t work since everything is contained in the premises, but induction goes beyond the premises. it can’t be by induction, or its circular therefore induction isn’t justified (until we find some 3rd possibility)
me: hence the turn to making it axiomatic, right? (making it a law or requirement of human thought is another way of saying “axiomatic”, right?)
todd: yeah with deduction it’s more sensible, with induction people get angry or deny it partly because it would invalidate all science i mean it’s really just saying you can’t know the sun will rise tomorrow in a sense
me: “we presume a world because that works pretty well.” That’s how I want to read the Carroll - there’s no (philosophically) strong justifications for implication, but that doesn’t mean we can’t use it because it’s wicked useful to do so.
todd: i like thinking of logic as the laws of thought (kant get out of my brain), so its one of those i chaulk up to that’s just how deduction works. f* justification
me: I’m okay with that. It amounts to basically “oh yea? well try to think without doing this!”
todd: exactly! fucking skeptics
me: Technically though, I think, if someone says “I already do! I just can’t present it to you without using a format which uses deduction” I don’t think we can actually prove them wrong. We can just say, “well, I only care about what you can present to me.” Which kind of amounts to “I’m not gonna talk to you if you insist on talking in a way I can’t understand.” = a kind of force or power relation, minimally that of withdrawing from conversation.
todd: did you ever hear GE Moore’s disproof of skepticism about knowledge of the external world?
me: no, how’s it go?
todd: to prove he has hands he goes: here’s a hand, and here’s another one. it’s actually published too. i call it proof by belligerence.
me: that’s not really a disPROOF, it’s a DISproof.
todd: i call it proof by belligerence.
Comment by Nate — April 3, 2007 @ 5:50 am