I think you are missing the point I was trying to make, as you were looking at the situation from the point of view of logic mapped onto language, and I was looking at it from the point of view of language mapped onto logic.

The meaning of the English sentence “You can not have ice cream” has two parts: one explicit and one implicit. The utterer of the sentence is informing you, explicitly, that you have the option of not eating ice cream. (Throughout this discussion, “have” means “eat”.) That is, no one is forcing you eat ice cream. This is ¬Q. The implicit part, therefore, is the fact that you are still allowed to eat ice cream, should you desire to. This is Q. Thus, Q∨¬Q (or ¬Q∨Q, if you prefer).

The fact that Q∨¬Q is a tautology is, I believe, entirely part of my point. (As I’m reading it now, I think that both “may” and “can”, in these contexts, have the same ambiguity of meaning: one that allows/forbids and one that merely states possibility.) We are translating from natural language into logic notation, so there is no reason that the tautology should get its own letter: Q = “You have ice cream for dessert”.

I suppose the problem here, now that I’m reading it again and thinking more about it, is the difference between actually having ice cream and whether you’re allowed (or able) to have ice cream. Which is why the introduction of modals (or, really, the introduction of permission/ability altogether) is problematic. If Q is the act of actually having ice cream, you cannot represent the permission/ability of having ice cream using Q.

This, of course, would mean that (2) would be represented as P→¬R (if R = “you have permission to eat ice cream”) and one would not be able to conclude (4) directly, as the motivation for (3) becomes ambiguous: did you not have ice cream because you were forbidden from it, or did you just not want to have ice cream?

So, thinking about it further, your first claim of mistranslation is not true because of the fact of it being a tautology. But it may be true because of the fact that it uses the same letter to represent both possibility/ability and the actual act of doing it. Thus, rather than Q∨¬Q, perhaps “You can not have ice cream” is indeed ¬R.

With regards to your next point, I think it involves a misunderstanding of my notation (which I admit I did not make clear): (4), which is in bold, is the conclusion drawn from (1), (2), and (3). So, yeah, such a redundancy was intended—though I think this discussion has brought that into question now.

And again, as I mentioned offhandedly in the original introduction: philosophy is not really my thing, so I’m not really familiar with the works of Quine or Kripke.

Secondly, we agree that the translation of “If you have cake for dessert, you cannot have ice cream.” is P→¬Q

However, you propose that the symbolic translation of “If you have cake for dessert, you may not have ice cream.” is P→(Q∨¬Q)

This is also false since this translation is equivalent to P→T ie T (another meaningless tautology)

In fact, much like with your mistranslation of “You can not have ice cream” as Q V ~Q, when it should have it’s own symbolic letter, the translation of “If you have cake for dessert, you may not have ice cream.” should actually be P→R (where R stands for “You man not have ice cream”)

I should also note that the original sentences (1)-(4), assuming we use ‘cannot’, contains a redundant sentence. That is, for any x, y, z, w in A={(1), (2), (3), (4) }, y&z&w → x where x != y != z != w.

I will agree with you however that such PHL10X type logic courses are terrible. I’ve had so called analytic philosophy experts not realize that translating P→Q as “P implies Q” confuses use and mention!!!1 (long live WVO Quine)

Also, If you did want to examine sentences with ‘may’ or ‘must’ from a finer grained perspective, Kripke style modal logic is probably your best bet.

As-is, the sentence is a fragment. Either it is missing a subject or an auxiliary verb.

“This is a picture of Patton and me having a last minute brawl before the show.” – What you assumed the caption’s sentence is.

OR

“Patton and I are having a last minute brawl before the show.” – What Jacinta seems to have assumed it is.

Either way, this is Schrödinger’s Cat. Both of you are right and wrong until someone confirms with Al what it is he originally meant to say. You could argue that, as a caption, your version /should/ be what he meant, but that doesn’t change the reality of what he actually meant to say. The question is the mechanics of the sentence as Al meant it, not which sentence Al should have used to fit the classical style of proper photo-captioning.

Although, I do have it in mind to eventually support PostgreSQL in addition to MySQL. I would imagine that would make using CAST() slightly more difficult.

But still, thanks for the tip!

I had a similar problem. A solution I found was to CAST the binary data inside your mysql query to an integer. MySQL then returns it as a string (bizarrely) which can itself then be cast as an int in PHP. Example:

<?php

$query = "SELECT CAST(`days` AS unsigned integer) AS `days` FROM `table`";
$result = query($query);
$row = $result->fetch_assoc();

$days = (int) $row['days'];

// $days is now an int, upon which you can perform various bitwise checks

// TA-DA!

?>

This works perfectly on both my machines, one running MySQL 5.0.51 (with PHP 5.2.6) and the other running 5.1.37 (with PHP 5.2.10).

Now I’m not certain of the entire scope of the backwards/forwards compatability of this as I’ve only tested it on the versions mentioned above, so if anyone else can test on other versions and post their results, I’d be grateful!

Cheers,

Dai

[GPH Editor's Note: I've combined the two comments that were posted in succession to (hopefully) express the original intent of the first comment.]

But, apparently, the sense I was getting was actually objective case, rather than an actual object. (I was unaware of the concept itself.)

This just goes back to grammatical intuition, I suppose: I knew what was right; I just didn’t know why.

As is normal, the subject of a non-finite verb is in the objective case. e.g. in “Me finding the way was a miracle.”, ‘Me’ is the subject of ‘finding’ but it has objective case.

So it is correct that it should be ‘me’ not ‘I’; but your explanation is flawed.