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Humean Skepticism and Logic

Humean Skepticism and Logic

despinozist
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Posted 04/07/08 - 07:05 PM: Subject: Humean Skepticism and Logic	#1
So Hume says that "matters of fact" are not rationally or logically solid. The sun may not rise tomorrow because its rising tomorrow is a contingent truth. We base our argument for its rising on "sound" probability or something else equally meaningless and unphilosophical. The interesting point is this, and I ask for anyone to give me their views on the possible implication of such a note, if any. So Hume says all matters of fact formulate in our minds due to "customary conjunction." New day, Sun's back. Nothing logical about that. You cannot infer from "New day" that "Sun's back" follows necessarily or logically. In short, the sun, as said, may not rise tomorrow, for any number of reasons the Universe might throw at us. However, look at the logical form of the infamously charged "bad reasoning": If D, then S. But Hume says it's more like: D & S (over a long period of D and S hanging out side by side, or by "contiguity," as Hume puts it). At first, I was thinking Hume meant something like Not-[D & Not-S]. This would appeal more to the probabilistic or scientific framework. It's the negative approach scientists take when "weeding out" hypotheses. D & S would lead scientists, I suppose, into chasing ghosts for a bit longer. The interesting part is this: D & S entails D > S; and Not-[D & Not-S] entails D > S -(D&-S) Assum. D Prov. -S Prov. D&-S Conj. -(D&-S) Reit S Reductio D>S Cond. The other is simple enough. But I find it curious that we pick out inferences based on "customary conjunction" and establish them as "logical." Well, maybe that's not so interesting. Hume already said it's ill-founded when we do this. If we can show that "custom" precedes "inference," wouldn't that mean our basis for adopting Modus Ponens as a basic rule of logic is also ill-founded?
_____________________ Understanding is the first and only basis of virtue.

Brian Bosse
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Posted 04/09/08 - 02:13 PM:	#2
Hello Despinozist, But I find it curious that we pick out inferences based on "customary conjunction" and establish them as "logical." Well, maybe that's not so interesting. Hume already said it's ill-founded when we do this. If we can show that "custom" precedes "inference," wouldn't that mean our basis for adopting Modus Ponens as a basic rule of logic is also ill-founded? Hume is not speaking of sentential logic when he says that customary conjunction is ill-founded. Rather, he is saying that our observation of A followed by an observation of B does not establish a causal connection between A and B. In other words, we do not see causation. He uses his famous billiard example to illustrate this. The difference between this and the sentential logic is that implication in sentential logic is not to be understood as causal. "If A, then B" is not meant to convey that A causes B. If you are thinking in this manner, then you are importing more into the sentential logic than what is there. Now, this is not entirely uncontroversial. There are logicians that deny truth-functional implication precisely because in our ordinary understanding and use of language we normally understand implication to convey a causal connection. They will appeal to the non-intuitive consequences of truth-functional implication. However, none of this speaks against Modus Ponens as being a fundamental law of reasoning. Brian

Dschema
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Posted 04/21/08 - 03:46 AM: Subject: Hume's irrationality	#3
Dear Brian, when you wrote: >Hume is not speaking of sentential logic when he says >that customary conjunction is ill-founded. Rather, >he is saying that our observation of A followed by an >observation of B does not establish a causal connection >between A and B. If Hume is not speaking of the sentential logic behind Modus Ponens, what you say about the causal connection doesn't seem to make sense. Nevetheless Hume is very eloquent and can argue very well for what he thinks is true. Even though I agree with the later point, he does not provide evidence that it is impossible to demonstrate there is a causal connection. What he does do, which I think is far worse, is to claim without any proof: "... we have no reason to draw any inference concerning any object beyond those which we have had experience.". With this, the reason for doing anything seems pointless, but this seems to be what our scientific conventions about the causes, effects of chances are based on, as if the wrecking of our planet is something beyond our control! Clearly this is absurd. Paul

despinozist
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Posted 04/21/08 - 09:51 AM:	#4
Brian Bosse wrote: Hello Despinozist, But I find it curious that we pick out inferences based on "customary conjunction" and establish them as "logical." Well, maybe that's not so interesting. Hume already said it's ill-founded when we do this. If we can show that "custom" precedes "inference," wouldn't that mean our basis for adopting Modus Ponens as a basic rule of logic is also ill-founded? Hume is not speaking of sentential logic when he says that customary conjunction is ill-founded. Rather, he is saying that our observation of A followed by an observation of B does not establish a causal connection between A and B. In other words, we do not see causation. He uses his famous billiard example to illustrate this. The difference between this and the sentential logic is that implication in sentential logic is not to be understood as causal. "If A, then B" is not meant to convey that A causes B. If you are thinking in this manner, then you are importing more into the sentential logic than what is there. Now, this is not entirely uncontroversial. There are logicians that deny truth-functional implication precisely because in our ordinary understanding and use of language we normally understand implication to convey a causal connection. They will appeal to the non-intuitive consequences of truth-functional implication. However, none of this speaks against Modus Ponens as being a fundamental law of reasoning. Brian Thanks for this response. However, I think a part of my argument was missed; it may be because I did not clarify or emphasize well enough. I am thinking this: My argument is that not only do we not see causality in action, our basis for implication is itself originated from our tendency to incorrectly assert that we've witnessed causality. This is why I went though the A&B and Not-[A&-B] proofs. Hume says that we only see conjunction, and we assert causality. I am saying this: if there were no A&B to begin with, there would be no A->B. If there were no custom to begin with, we'd never formulate analytic truths which are the basis of logic. I'm not saying that If A then B is meant to convey A causes B. That would implicate logic as a necessarily probabilistic discourse; logic is analytic; this is sufficiently clear. What I am saying is that truth-functional implication depends on causality by our standards. We'd never conceive as analytic and logically inferred that there are no married bachelors unless we first "see" a particular bachelor and (customarily) conjoin that bachelor and many other bachelors with the words "bachelor" and the activities which go along with being a promiscuous male. Analytic truths presuppose content to derive meaning; therefore, I argue that when Hume attacks our supposition that we perceive causality, he also, but separately (and possibly unknowingly), attacks the foundations of our logical discourse. That logical and analytic truths are about meaning and implication of terms does not mean that terms are themselves logical and analytic. Logic talks about terms and manipulates them; a "wallet" is not analytic unless you accept that everything that exists now is not contingent and everything is necessitated. Edited by despinozist on 04/21/08 - 09:55 AM
_____________________ Understanding is the first and only basis of virtue.

Brian Bosse
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Posted 04/21/08 - 10:30 AM:	#5
Hello Paul, If Hume is not speaking of the sentential logic behind Modus Ponens, what you say about the causal connection doesn't seem to make sense. Hume's point about causation is simply that when you observe two events - one following the other - this is not an adequate basis to establish causality. The conjunction of... P(1) - Billard ball 'A' strikes a still standing billiard ball 'B'. P(2) - Billard ball 'B' begins to move after being struck by billard ball 'A'. ...does not entail the conclusion... P(3) - Billard ball 'A' was the cause of billiard ball 'B's movement. In other words, it is ill-founded to conclude P(3) from the conjunction of P(1) and P(2). Notice, the conclusion of P(3) from P(1) and P(2) is not an instance of Modus Ponens. As such, Hume's objection has nothing to do with Modus Ponens. What he does do, which I think is far worse, is to claim without any proof: "... we have no reason to draw any inference concerning any object beyond those which we have had experience." Hume provided a very strong argument for his conclusion. He wrote extensively on the issue. In fact, it remains one of the major problems in philosophy. On a side note, it was Hume's skepticism that supposedly awoke Kant from his slumber. With this, the reason for doing anything seems pointless, but this seems to be what our scientific conventions about the causes, effects of chances are based on, as if the wrecking of our planet is something beyond our control! I do not understand what you are saying here. I will note that Hume's conclusions have a direct application to science in that scientific conclusions are based on the principle of induction. The problem of induction is related to Hume's observations regarding causation. Hume argues concerning induction that there is no justification apart from a vicious begging of the question to assume the future is like the past. Here is a link that explains these issues: The Problem of Induction. Sincerely, Brian

Brian Bosse
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Posted 04/21/08 - 10:36 AM:	#6
Hello despinozist, I enjoyed reading your latest post. This will be a fun discussion. I do not have time to repond right now. I will try and respond by the end of the day. Sincerely, Brian

Brian Bosse
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Posted 04/21/08 - 03:44 PM:	#7
Hello Despinozist, My argument is that not only do we not see causality in action, our basis for implication is itself originated from our tendency to incorrectly assert that we've witnessed causality. In modern logic, implication is defined in terms of truth-value and does not make assumptions about causality. That is to say, the only concern between the antecedent and the consequent are their truth-values. No other issues (like causality) matter. Now, when you and I informally think about "if...then..." statements, we may attach a certain causality between the antecedent and the consequent. This is why traditional logicians do not accept truth-functional implication. They would argue that certain implications like "If OJ is innocent, then my uncle is King Kong" are more about rheorical affect than being an actual proposition with a truth-value. The basis for this conclusion is that they cannot see any causal connection between OJ's innocence and my uncle being King King. They argue that truth-functional implication is not an accurate reflection of how we use language. I am saying this: if there were no A&B to begin with, there would be no A->B. I might state the following, "If one can square a circle, then all politicians are honest." The antecedent and the consequent are both false; yet, the implication is true. So, in this sense there is no A and B (both are false), and there is an A-->B (this is true). What I am saying is that truth-functional implication depends on causality by our standards. I am arguing precisely the opposite, namely, implication within the sentential and predicate calculus is truth-value dependent, and not causality dependent. I argue that when Hume attacks our supposition that we perceive causality, he also, but separately (and possibly unknowingly), attacks the foundations of our logical discourse. I explained why this is not the case in more detail in my post to Paul. From that post, the "logic" that allows one to go from P(1) and P(2) to the conclusion of P(3) is not formal logic. As such, his critique of this thinking does not undermine the sentential and predicate calculus. Am I still missing the point of your argument? Brian

Dschema
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Posted 04/21/08 - 04:46 PM: Subject: Hume's irrationality	#8
Hello Brian, thank you for your reply; it is a long time since I've had a discussion with someone who knows there philosphy as well as you and is willing to be challenged and engage in a serious inquiry/critique. Back to your point about observing two events, as not being an adequate basis to establish causality. I agree with this, if they can be taken independently from having states of affairs; when I was making a reference to Modus Ponens, I was thinking of it as a general linguitic structure. Rather like Quine, in the way he uses contradiction; in his 'Philosophy of Logic'. So consider: If A is a set of conditions that can be satisfied, B is the consequence of those conditions. A therefore B This can then be developed further: if p and q are states of affairs for some event, you have the one-way principle for chance: if (i) P obtained, (ii) Q obtained, and (iii) P raised the chance of Q, P and Q belong to a single causal network. (from Carroll, John, W. 1994. Laws of Nature. Cambridge. Page 124) This I think can be developed into a functional analysis quite different from the conventional ones found on the Stanford site you made a reference to; that perhaps can even avoid the ambiguity of natural language by focusing on the value of the categories for the cognition of an agent. That is, I wouldn't say this if I didn't think I found a reason to show that it is possible to draw an inference beyond those which we have experienced; if I have understood Hume properly, this just entails finding a way of calulating probabilities that is more effective then the combinatorial or the frequency approach, So I think you can demonstrate whether certain acts are the most likely causes of some effect e.g. the use of GM crops resulting in a crash of locale bio-diversity. My last point to which you refer, is just that if our intuition cannot tell us anything about where our human nature is taking this planet, it appears there can be no basis for morality or ethics; we can wash our hands like Pontius Pilate. Paul

the.yangist
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Posted 04/22/08 - 02:25 AM:	#9
despinozist wrote: Hume says that we only see conjunction, and we assert causality. I am saying this: if there were no A&B to begin with, there would be no A->B. That's hard to swallow for two reasons: First, 'A & B' and 'A ⊃ B' can both be expressed in terms of NOR or NAND operations. For NOR, (A & B) ≡ ~(~(A v B) v ~(A v B)) (A ⊃ B) ≡ ~(~(~(A v B) v B) v ~(~(A v B) v B)) Thus, it seems perfectly reasonable to imply that we can afford the convenience of both conjunction and implication if we wish to employ them. Second, there is a truth-function assignment wherein the implication '~(A & B) ⊃ ~(A ⊃ B)' is false -- TFFTFFFTT. Edited by the.yangist on 04/22/08 - 02:38 AM
_____________________ "If it were not for the laughter, the Way would not be what it is." -- Laozi

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