# Talk:Logical conjunction

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Field: Foundations, logic, and set theory

## electronics circuits

I removed this:

In electronic circuits, TRUE is often represented by a higher voltage level - positive logic, and is denoted by the symbol 1. Its complement, FALSE is then denoted by 0.

since it's really about electronic circuits. — Toby 19:47 Aug 22, 2002 (PDT)

And I removed the 0's and 1's from the truth table and substituted the actual truth values "T" and "F"; this also makes this article consistent with the Wiki article on truth tables.Warren Platts (talk) 15:53, 17 June 2012 (UTC)

## and/or

I'd like an article about the use of "and/or". -- Davidme

Logical disjunction - Patrick 02:55 Feb 23, 2003 (UTC)

Proposition should be removed or at least a note given since they are controversial for several reasons, first they don't exist, second whenever a conjunction is used, it is expressions or statements of a language that are conjoined, not propositions.

## Disjunctive

Yes I agree this should be merged with Logical disjunction.

Also on the electrical circuits, often logic uses a 0v level to assert something. Chip select is typically active low. So I agree with the removal of the higher voltage level thing too.

Robin48gx Sun Aug 14 20:11:46 BST 2005

## Rhetorical considerations

I'm not sure about this as a section heading. "English connectives and logical conjunction" seems a lot clearer and less medieval. The section is, after all, about the relationship of English connectives to logical conjunction. Furthermore, the sentence 'Natural languages are evolved for many purposes beyond their use in logical argumentation, and so any study of logic in a natural language context must sort out those aspects of natural language that are pertinent to its use in logic and those that are not." seems to imply that all distinctions between NL connectives and 1-0-0-0 logical conjunction are irrelevant to logic. Not every logician would agree. Jon Awbrey, your thoughts? Adrian Mander

Edit: just got a proper account. adrianmander Double edit: sorry for meefy formatting.

JA: Strictly speaking, English connective, more generally, grammatical connective, refers to a linguistic form that connects words or word groups, with no reference to a potential logical meaning, if any. One cannot speak of its intended interpretation without passing to logical considerations, and one cannot speak of the different ways of making that passage without engaging in what is properly still called either pragmatics or rhetoric. Jon Awbrey 23:38, 4 June 2006 (UTC)

AM: I'm not sure what you mean. Linguists doing semantics often assume that the "core meaning" of connectives like and, but, unless, &c is some kind of truth-function, and that you get from there to their behaviour in actual coversation via pragmatic phenomena like implicature. This seems irrelevant, however. Again, the point of the section is to compare the way seemingly conjunctive English connectives behave in actual conversation with the way a 1-0-0-0 conjunction would behave without extra technology added (pragmatic or otherwise). For this reason, your section heading seems unnecessarily confusing. Why not use a heading that requires no explanation?

JA: Again, "English connective" is a much broader term than "logical connective", as not all syncategorematic forms for connecting syntactic elements necessarily have much to do with logical forms. But if you are going to talk about "logical connectives in English", then you are going to have to say what you mean. The definition of that term will have to be something like "syntactic element that has one of a well-defined set of logical interpretations". So far so good, but then there is the problem of individuation, and whether to treat the syntactic level or the semantic level as the primary one in taxonomy. For example, is the string "or" that gets interpreted as the truth-functional or the same lexical element as the string "or" that gets interpreted as the truth-functional and, or should it be counted as a distinct lexical element? Historically speaking, both strategies have been explored. Jon Awbrey 11:44, 5 June 2006 (UTC)

AM: OK, but how does this necessarily involve rhetoric, or even pragmatics, rather than semantics? Furthermore, are you suggesting that merely mentioning English connectives necessarily brings in all these complex issues? I had intended it to be just a label for the words discussed in the section (since all are English connectives), such that the section is a discussion of those words, and not of the entire category they belong to. What if we just called the section "The relationship of *some* English connectives to logical conjunction"?

JA: The classical scope of "rhetoric" was "forms of argument that consider the character of the intended interpreter". This got warped in popular usage to mean "the art of persuasion", very often with insidious connotations, but the classical sense is still preserved in many academic contexts. The scope of rhetoric is somewhat wider than mere semantics, where the symbols for logical connectives usually have a very small number of intended interpretations, with none of the context-dependent flexibility of the examples that were being discussed in the section in question. So the wider term seemed more apt for those kinds of examples. It has been necessary in several other cases to split the articles into a logical moiety and a rhetorical moiety, for instance, with negation and tautology. Jon Awbrey 02:38, 7 June 2006 (UTC)

## Example

Everyone should vote.
Democracy is the best system of government.
Therefore, everyone should vote and democracy is the best system of government.

This is not a good example because the two propositions are open to debate. In fact they both reflect a particularly American POV.

A less contentious example should be substituted, e.g.:

The sky is overcast.
Rain is falling.
Therefore the sky is overcast and rain is falling.

--84.9.78.198 12:56, 27 November 2006 (UTC)

## Proposed project

I have been working on all of the logical operators recently. I would like to see a consistent format for them. There is a wikiproject proposal for this at: Wikipedia:WikiProject_Council/Proposals#Logical_Operators. Also see Talk:Logical connective.

I would like to see the logical, grammatical, mathematical, and computer science applications of all of the operators on the single page for each of those concepts.

Gregbard 08:52, 28 June 2007 (UTC)

## Merger?

Why would and/or merge here? And/or is a logical disjunction, not a conjunction anyway. Unless there's strong opposition, I'm removing the tags. Oren0 16:32, 16 October 2007 (UTC)

## And meaning or?

Consider this paragraph: The word "and" can also serve as a logical disjunction (called OR in logic), e.g. "Damage caused by scratches and dents is not reimbursable," when what is meant is that damage cause by one or the other isn't reimbursable. This overload of meaning on "and" happens when the word is used to amplify "or"; the second sentence, on an insurance contract, looks and reads weak. In the same way "or" can be used to mean AND: the sentence "It might work, or it might not" is equivalent to "It might work, and it might not".

I think it should go. The first sentence IS a conjunction. To me, it reads "damage caused by scratches is not reimbursable AND damage caused by dents is not reimbursable." Interpreting it as the article does is just an application of DeMorgan's Law. Additionally, the sentence "it might work, or it might not" is a logical disjunction plain and simple. Logically, the sentence "it might work, and it might not" is false. Oren0 16:50, 16 October 2007 (UTC)

## My textbook uses a different symbol

I'm reading Susanna S. Epp Discrete Mathematics with Applications (Third Edition) and they use an upside down logical disjunction symbol for logical conjunction. What's up with that? --ScWizard (talk) 02:41, 6 February 2009 (UTC)

You mean ${\displaystyle \land }$? — Carl (CBM · talk) 04:07, 6 February 2009 (UTC)

## Properties

Can we put only the necessary ones first then state the rest as corollaries? Right distributivity, "falsehood preserving" are derivable from the others. 118.90.6.70 (talk) 10:16, 3 August 2009 (UTC)

## Natural Language

The Natural Language is completely messed up. I am going to completely rewrite it unless someone objects soon. For example, it may be the case that there is an implied order to "They got married and they had children", but it's not at all clear that the "and" is what is carrying the weight of the implied order, as evidenced by the reverse "They had children and they got married". The latter is an awkward phrasing because it's not clear that the children did in fact precede the marriage; one would rather say "They had children and then they got married" in order to convey the surprising order. In "They got married and they had children", the order is not conveyed by the "and" but is instead conveyed by the fact that children after marriage is the "natural" temporal order.

What would be more useful would be discussion about how several English conjunctions, e.g., 'p and q', 'p in addition to q', 'p but q', 'p however q', 'p although q', 'p nevertheless q', 'p including q' may all have differing connotations, they all function similarly in terms of the propositional logic truth function "p ∧ q".

Warren Platts (talk) 16:15, 17 June 2012 (UTC)