E.G.

This post will just be a reiteration of my previous argument in what I hope will be a clearer and more correct form.

Here is how I now want to put the thing I am calling "entitlement closure": "For any propositions p and q, if I know p, and I know p=>q, then I am in a position to be weak epistemically entitled to write ‘q.’"  And here is how I now want to put the thing I am calling "knowledge closure": "For any propositions p and q, if I know p, and I know p=>q, then I am in a position to know q."

The proposition "(p, and p=>q) => q" is always and necessarily true.  Let us call this the "underlying fact" of modus ponens.  As argued previously, this underlying fact of modus ponens is not modus ponens itself, because modus ponens is not a fact at all; it is a rule.  I want to understand modus ponens as a rule which entitles one to write some proposition q under certain circumstances.  In the previous post, I suggested three ways to understand how this rule is supposed to work:

(i) Logical MP: For any p and q, whenever I have already written "p," and already written "p=>q," then logical MP entitles me to write "q."
(ii) Weak Epistemic MP ("WEMP" for short): For any p and q, whenever I believe p, and believe p=>q, then weak epistemic MP entitles me to write "q."
(iii) Strong Epistemic MP ("SEMP" for short): For any p and q, whenever I know p, and know p=>q, then strong epistemic MP entitles me to write "q."

I think there are more than three senses in which a person can be "entitled to write q."  But I think the three rules above highlight three of the most important of these senses.  I will say a person is "logically entitled" to write q whenever it is Logical MP which entitles her to write q; a person is "weak epistemically entitled" to write q whenever it is WEMP which entitles her to write q; and a person is "strong epistemically entitled" to write q whenever it is SEMP which entitles her to write q.  I will say a rule "works" when the rule really does provide the sort of entitlement it is supposed to provide, and that a rule "always works" when the rule always provides such entitlement.

Here’s my argument for the view that "entitlement to write" is closed (i.e., for the view that "entitlement closure" is true):

1. If WEMP does not "always work," then Logical MP is an arbitrary rule; it cannot be given a plausible rationale. (Assumption)
2. If "entitlement to write" is not closed, then WEMP does not "always work." (Assumption)
3. Logical MP is not an arbitrary rule. (Assumption)
4. So, WEMP does "always work." (1,3)
5. Thus, entitlement is closed.  (2,4)

I take it that premise 3 is obviously true.  Given the way I’ve defined terms above, I think premise 2 has to be true.  So premise 1 is hopefully the only premise which might be controversial.  That is the premise I will try to defend here.  Premise 1 would be true if (a) the claim that WEMP always works provides a plausible rationale for adopting Logical MP as a rule, and (b) no other rationale for adopting Logical MP as a rule would be plausible. 

We can see that (a) is true simply by considering an example.  Suppose that Pete is trying to explain basic logic to John.  Pete has written the following things on the blackboard:

(1) George Bush is made of iron;
(2) If George Bush is made of iron, then ketchup glows.

Pete claims that he is now entitled to write "(3) Ketchup glows."  John objects: "Why should you be allowed to write such an absurd thing?  It’s obviously false."  Pete replies: "Yes, (3) is obviously false, but it follows from (1) and (2)."  John: "But (1) and (2) are obviously false also."  John: "Well, in logic, we are acting as though we believe the assumed premises of any argument under consideration.  And surely you see that, if I did believe (1) and (2), then I would be entitled, in some sense or other, to write (3).  In other words: I am logically entitled to write (3) because, if I did believe (1) and (2), then I would be entitled to write (3)."

In this example, I think Pete hopes that John will intuitively "see" that, given belief in some "p" and some "p=>q," no matter how absurd "p" and "p=>q" happen to be, one would be entitled in some sense to write "q."  That is, Pete hopes that John will have an intuition that WEMP "works."  And this hoped-for intuition plays a central role in Pete’s attempt to motivate logical entitlement to write (3).  At any rate, this line of support would probably not succeed if John thought there were exceptions to WEMP.  For instance, if John were to say: "I can imagine cases in which I believe (1) and believe (2), but am still not entitled in any sense to write (3)," then Pete would not be able to appeal to WEMP to get John to see that Pete is logically entitled to write (3); Pete would need to appeal to something else.

This example makes it reasonable to think that it is at least possible to use WEMP to support Logical MP.  Is there any other way to support Logical MP?  Of course, I cannot show that there is not any other way; at best, I can only show that a few of the main other ways which have been proposed cannot succeed.

Sometimes people try to support Logical MP by appeal to what I have called the "underlying fact" of modus ponens — the fact that "(p, and p=>q) => q" is true.  But this clearly cannot provide full support for Logical MP, because "(p, and p=>q) => q" is always true, but Logical MP does not always entitle me to write any q.  However, one might be able to use the underlying fact of modus ponens in conjunction with something else to motivate acceptance of Logical MP.  We can get an example of that kind of strategy by returning to Pete and John.  Suppose John is still not convinced that Pete is entitled to write "(3)," so Pete tries another line:

Pete: "If (1) is true, and (2) is true, then (3) must be true.  You see that, don’t you, John?"
John: "Yes, I see it; but I see no reason to think that (1) or (2) might be true."
Pete: "Well, suppose (1) and (2) were true.  Then (3) would have to be true."
John: "I agree.  But how does that entitle you to write (3)?  You have not shown that (1) and (2) are true; you’ve only written (1) and (2)."
Pete: "When I write (1) and (2), I’m asking you to suppose they are true.  If you make that supposition, you’re committed to say that (3) has got to be true.  I’m entitled to write anything which has got to be true, so, given the supposition that (1) and (2) are true, which I have asked you to make by writing (1) and (2), you have to admit that I am entitled to write (3)."

In the first line, Pete tries to support his employment of Logical MP by direct appeal to the underlying fact of modus ponens.  John is not satisfied by this, so Pete brings in the supposition that (1) and (2) are true.  This supposition, in conjunction with the underlying fact of modus ponens, should get John to admit that Pete is entitled, in some sense at least, to write (3).  But of course to "suppose" (1) and (2) is merely to assume (1) and (2) are true.  And to "assume (1) and (2) are true" is nothing more than to proceed as though one believes (1) and (2).  But now we are back to an appeal to WEMP; for it is WEMP which entitles one to write (3) whenever one believes (1) and (2).

In this case, then, it seems to me that some sort of implicit use of WEMP is necessary in order to bridge the gap between the underlying fact of modus ponens, and the claim that Logical MP "works."  I do not see any way to motivate acceptance of Logical MP without appealing to WEMP.  My failure to see such a way does not, of course, show that no such way exists, but perhaps it gives us reason to think no such way exists.  If no such way exists, then we have good reason to accept premise 1 in the argument above.  So, if I am right that premises 2 and 3 are clearly true, then it should follow that we have good reason to accept the conclusion of the argument: "Entitlement to write" is closed.