I second Manfred’s suggestion about the use of beliefs expressed as probabilities.
In puzzle (1) you essentially have a proof for T and a proof for ~T. We don’t wish the order in which we’re exposed to the evidence to influence us, so the correct conclusion is that you should simply be confused*. Thinking in terms of “Belief A defeats belief B” is a bit silly, because you then get situations where you’re certain T is true, and the next day you’re certain ~T is true, and the day after that you’re certain again that T is true after all. So should beliefs defeat each other in this manner? No. Is it rational? No. Does the order in which you’re exposed to evidence matter? No.
In puzzle (2) the subject is certain a proposition is true (even though he’s still free to change his mind!). However, accepting contradicting evidence leads to confusion (as in puzzle 1), and to mitigate this the construct of “Misleading Evidence” is introduced that defines everything that contradicts the currently held belief as Misleading. This obviously leads to Status Quo Bias of the worst form. The “proof” that comes first automatically defeats all evidence from the future, therefore making sure that no confusion can occur. It even serves as a Universal Counterargument (“If that were true I’d believe it and I don’t believe it therefore it can’t be true”). This is a pure act of rationalization, not of rationality.
*) meaning that you’re not completely confident of T and ~T.
Thank you, Zed.
You are right: I didn’t specified the meaning of ‘misleading evidence’. It means evidence to believe something that is false (whether or not the cognitive agent receiving such evidence knows it is misleading).
Now, maybe it I’m missing something, but I don’t see any silliness in thinking of terms of “belief A defeats belief B”. On the basis of having an experiential evidence, I believe there is a tree in front of me. But then, I discover I’m drugged with LCD (a friend of mine put it in my coffee previously, unknown to me). This new piece of information defeats the justification I had for believing there is a tree in front of me—my evidence does not support this belief anymore. There is a good material on defeasible reasoning and justification in John Pollock’s website: http://oscarhome.soc-sci.arizona.edu/ftp/publications.html#reasoning
If you’re certain that belief A holds you cannot change your mind about that in the future. The belief cannot be “defeated”, in your parlance. So given that you can be exposed to information that will lead you to change your mind we conclude that you weren’t absolutely certain about belief A in the first place. So how certain were you? Well, this is something we can express as a probability. You’re not 100% certain a tree in front of you is, in fact, really there exactly because you realize there is a small chance you’re drugged or otherwise cognitively incapacitated.
So as you come into contact with evidence that contradicts what you believe you become less certain your belief is correct, and as you come into contact with evidence that confirms what you believe you become more confident your belief is correct. Apply Bayes’ rules for this (for links to Bayes and Bayesian reasoning see other comments in this thread).
I’ve just read a couple of pages of Defeasible Reasoning by Pollock and it’s a pretty interesting formal model of reasoning. Pollock argues, essentially, that Bayesian epistemology is incompatible with deductive reasoning (pg 15). I semi-quote: “[...] if Bayesian epistemology were correct, we could not acquire new justified beliefs by reasoning from previously justified beliefs” (pg 17). I’ll read the paper, but this all sounds pretty ludicrous to me.
I second Manfred’s suggestion about the use of beliefs expressed as probabilities.
In puzzle (1) you essentially have a proof for T and a proof for ~T. We don’t wish the order in which we’re exposed to the evidence to influence us, so the correct conclusion is that you should simply be confused*. Thinking in terms of “Belief A defeats belief B” is a bit silly, because you then get situations where you’re certain T is true, and the next day you’re certain ~T is true, and the day after that you’re certain again that T is true after all. So should beliefs defeat each other in this manner? No. Is it rational? No. Does the order in which you’re exposed to evidence matter? No.
In puzzle (2) the subject is certain a proposition is true (even though he’s still free to change his mind!). However, accepting contradicting evidence leads to confusion (as in puzzle 1), and to mitigate this the construct of “Misleading Evidence” is introduced that defines everything that contradicts the currently held belief as Misleading. This obviously leads to Status Quo Bias of the worst form. The “proof” that comes first automatically defeats all evidence from the future, therefore making sure that no confusion can occur. It even serves as a Universal Counterargument (“If that were true I’d believe it and I don’t believe it therefore it can’t be true”). This is a pure act of rationalization, not of rationality.
*) meaning that you’re not completely confident of T and ~T.
Thank you, Zed. You are right: I didn’t specified the meaning of ‘misleading evidence’. It means evidence to believe something that is false (whether or not the cognitive agent receiving such evidence knows it is misleading). Now, maybe it I’m missing something, but I don’t see any silliness in thinking of terms of “belief A defeats belief B”. On the basis of having an experiential evidence, I believe there is a tree in front of me. But then, I discover I’m drugged with LCD (a friend of mine put it in my coffee previously, unknown to me). This new piece of information defeats the justification I had for believing there is a tree in front of me—my evidence does not support this belief anymore. There is a good material on defeasible reasoning and justification in John Pollock’s website: http://oscarhome.soc-sci.arizona.edu/ftp/publications.html#reasoning
If you’re certain that belief A holds you cannot change your mind about that in the future. The belief cannot be “defeated”, in your parlance. So given that you can be exposed to information that will lead you to change your mind we conclude that you weren’t absolutely certain about belief A in the first place. So how certain were you? Well, this is something we can express as a probability. You’re not 100% certain a tree in front of you is, in fact, really there exactly because you realize there is a small chance you’re drugged or otherwise cognitively incapacitated.
So as you come into contact with evidence that contradicts what you believe you become less certain your belief is correct, and as you come into contact with evidence that confirms what you believe you become more confident your belief is correct. Apply Bayes’ rules for this (for links to Bayes and Bayesian reasoning see other comments in this thread).
I’ve just read a couple of pages of Defeasible Reasoning by Pollock and it’s a pretty interesting formal model of reasoning. Pollock argues, essentially, that Bayesian epistemology is incompatible with deductive reasoning (pg 15). I semi-quote: “[...] if Bayesian epistemology were correct, we could not acquire new justified beliefs by reasoning from previously justified beliefs” (pg 17). I’ll read the paper, but this all sounds pretty ludicrous to me.