Talk:Truth value

message: Is "truth-value" a British spelling or something?
In American English, it seems inappropriate unless used as an attributive.
("In topos theory, the truth-value object takes the place of the set of truth values.")
-- Toby 04:22 Mar 3, 2003 (UTC)
Changed accordingly.
-- Toby 05:26 Apr 15, 2003 (UTC)
Truth-value occurs in US and UK English & is I believe the more common usage.  See e.g. http://www.m-w.com/dictionary/truth-value :-
Main Entry: truth–value 
Function: noun 
Date: 1903 
the truth or falsity of a proposition or statement
and Truth-value semantics
--Philogo 14:18, 8 November 2007 (UTC)
thread_title:  untitled 

message: I ran into this in Paul C. Rosenbloom, The Elements of Mathematical Logic, Dover Publications, Inc. Mineola, NY, first published 1950, Dover edition 2005. Unfortunately my edition is flawed and contains no bibliography (!), hence the empty references [ ]:
:"The notion of truth value may be regarded as a special case of that of probability, which is, in turn, essentially equivalent to that of measure. (See Kolmogoroff, Grundbegriffe der Wahrscheinlichketsrechnung, Berlin 1933; Cramer, Methods of Mthematical Statistics, Princeton, 1946, Reichenbach [ ], Koopman [ ], Kleene and Evans [ ]). In most of the precise treatments of probability the concept is defined on an algebra of classes. Since propostions also form a Boolean algebra, it should be easy and desirable to treat directly the notion of the probability of a propostion." (p. 198)
I believe that this has progressed through the years into "machine learning"... but am otherwise unfamiliar with the concepts, except this: they seem to echo the philosophy of Bertrand Russell. Does anyone have any comments? Thanks, wvbaileyWvbailey 21:08, 27 June 2006 (UTC)
thread_title:  "Truth value" as a special case of probability? 

message: It was a mistake to move the article from Truth value to Logical value. The phrase truth value is the established terminology in the logic community. Frege 21:36, 21 November 2006 (UTC)
thread_title:  "Truth value" is better than "Logical value" 

message: This is just to hold the references:
: From Principia Mathematica 2nd Edition page 7 and repeated on page 72:
::"Truth-values. The "truth-value" of a proposition is truth if it is true, and falsehood if it is false*.
:::[In footnote:] "*This phrase is due to Frege" [PM 2nd edition p. 7]
I have not located this in Frege so far [Begriffsschrift, van Heijenoort 1967:1ff]. Frege uses the notions 'affirmation' and 'denial' in his definition of "conditionality":
:"§5. If A and B  stand for contents that can become judgements (§2), there are the following four possibilities:
::(1) A is affirmed and B is affirmed;
::(2) A is affirmed and B is denied;
::(3) A is denied and B is affirmed;
::(4) A is denied and B is denied.
:"Now [drawing here symbolizing (~B V A)] stands for the judgment that the third of these possibilites does not take place, but one of the three others does. Accordingly, if [the sign (~B V A)] is denied, this means that the third possibility takes place, hence that A is denied and B affirmed." (van Heijenoort 1967:13-14) [see Begriffsschrift ]
Peano 1889 defines two signs ∧ to represent "the false" and ∨ to represent the true:
: "[The sign ∨ means the true, or identity; but we never use this sign.]
: "The sign ∧ means the false, or the absurd." (brackets in original, Peano 1889 in van Heijenoort 1967:86-87
These sign ∧ also "denotes the class that contains no individuals". Again in brackets, Peano states that the sign ∨ "denotes the class composed of all individuals under consideration" and that this sign will not be used. (page 88).
Other places to search: Russell 1903 (Principles of Mathematics), Hilbert in van Heijenoort, Dedekind. Back further to Boole.
Wittgenstein in Tractatus (in particular 4.2ff:
: "4.3 The truth-possibilities of the elementary propositions mean the possibiliites of the existence and nonexistence of the atomic facts. 
: "4.31 The truth-possibiliites can be presented by schemata [truth tables] of the following kind ("T" means "true", "F" "false" . . .."  BillWvbailey (talk) 17:18, 13 November 2012 (UTC)
thread_title:  Definition of "truth value", PM, Frege, Peano, Wittgenstein, etc 

message: In this revision, the intro was moved into the body - but the sentence on intuitionistic logic was removed altogether. As there is no mention of this in the edit summary, I'm assuming that this was accidental. Because logical statements in intuitionistic logic are of course assigned truth values. I'll add something back in there.
http://en.wikipedia.org/w/index.php?title=Truth_value&diff=479091554&oldid=477141741
Have added it back and expanded it, as Truth_value#Intuitionistic_and_constructive_Logic
Robert Walker (talk) 07:13, 15 June 2014 (UTC)
thread_title: Intuitionistic logic