Talk:Truth table
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The comments about "finite mathematics" are silly. "Finite mathematics" is not a field within mathematics, but rather a collection of diverse topics in elementary mathematics that the curriculum brings togetther in a single undergraduate course for business students. Truth tables are not different in "finite mathematics" than in other disciplines. -- Mike Hardy
The "arrow" connective, it is to be understood as a truth-functional operator, should not be described as "implication." Call it "conditional" or "if-then." Doing otherwise involves confusing the use-mention distinction that Quine first noticed and spent his whole career trying to enforce (Perhaps hopelessly: quantified modal logic is deeply infected with use-mention confusions.) See his Mathematical Logic, Section 5.
In any case, "if...then" is not the same as "implies." "Implies" is a relation between sentences: a two-place predicate that takes sentences as the values of its variables and produces a sentence from them: it is a function from names of sentences--terms--to a sentence.
By constrast "if then" is a not a predicate but a connective; it is a funtion from sentences to a sentence. It does not take anything as values because it does not contain variables.
"Implies" talks about--mentions--two sentences, and can only be used in a meta-language. "If...then" uses two sentences; it mentions whatever the sentences mention, and is itself a term within the object language. Shortly:
If A then B. If the light goes out then the monsters will come.
but
"A" implies "B". "The light goes out" implies "The monsters will come".
Sorry for the rant. If anyone sees this mistake elsewhere, please correct it.
(Added) Same goes for equivalence. Sentences are equivalent to one another; but the things they say are related as "...if and only if ..."
Also, variables don't generally have truth-values. That's too confused to explain at all. P, Q, and R here aren't being used as variables, (though if they were, they'd have sentences, not truth-values, as their values). They're schemata; their standing in for sentences, but there's no assumption that you can quantify over them. The best way to explain this stuff is using Quine-corners and his Greek-letter metavariables. But, alas, no one cares about being rigorous anymore. Sigh.
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[edit] Peirce
Can anyone provide a reference for Charles Peirce’s development of truth tables? I would like to check the form that they took. It appears from a quick bit of research that the tables he developed were substantially different in form to those presented here (see http://plato.stanford.edu/entries/peirce-logic/ ) Those sources that support the claim appear to derive from the Wikipedia. Was it Wittgenstein who developed the form that is now used? Banno 22:59, May 15, 2004 (UTC)
- Discussed in depth in this thread: http://sunsite.utk.edu/math_archives/.http/hypermail/historia/apr00/0117.html
An excellent summary of the issue. Thanks for pointing it out to me. The conclusion appears to be that Frege, Peirce, and Schröder all played a part in the development of the truth table, and so the attribution of them to Peirce alone should be altered. Wittgenstein perhaps had the role of popularising their use. Banno 00:04, May 16, 2004 (UTC)
[edit] Truth table for most commonly used logical operators
The given truth table gives definitions of the 6 (NOT 7) of the 16 possible truth functions of 2 binary variables.
- ∨ (XNOR or exclusive nor) and ↔ (biconditional or "if-and-only-if") have identical values 202.173.204.250 08:36, 7 November 2005 (UTC)
[edit] AND / OR symbols
The symbols arent working for the most part they show up as squares in my browser.
JA: The formats used are fairly standard for WP. I tried substituting TeX formats. Let me know if it's any better. Jon Awbrey 14:46, 25 April 2006 (UTC)
[edit] Use TeX! And a small concern
Firstly, keep consistent with usage the <math> tags; if it's simple enough (like in most examples on this page), WP will render it as plain text if the user so wishes; otherwise, it is renderred into a PNG via TeX. The symbols for boolean algebra typically are \or (
), \and (
), and \neg (
). You can use the \underline{} and \overline{} functions as you wish.
Secondly, I'm concerned that there doesn't appear to be a uniform method of notating XOR, XNOR, and NAND. Some use overline, some use underline, and other articles use a plus sign. I'm no boolean algebra expert, so I don't know the common notation used, nor can I find a predefined symbol for such in any TeX packages I can find. -Matt 06:43, 20 May 2006 (UTC)
JA: JVz, all of the pages on boolean logic, propositional logic, and so on are in the process of being cleaned up and formatted in a more or less standard way, but nobody got around to this one yet until now. Thanks for the improvements. As a rule though, local practice tries to avoid in-line use of TeX eXcepT when it can't be helped. Thanks again, Jon Awbrey 16:24, 20 May 2006 (UTC)
[edit] Consistency
There needs to be consistency with the use of the operators on this page. Each one should have it's own section and used the same as they are represented in their own section. Right now it is very confusing, because some things are mentioned, others are not, and some are introduced into the article at the end with different symbolic representations. 70.111.238.17 14:52, 1 October 2006 (UTC)
