Talk:Predicate (mathematical logic)

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Any chance of anyone explaining this so the average reader could get an understanding of what it means? Tyrenius 18:46, 24 October 2006 (UTC)

Follow the new external link for an explanation.

S Sepp 14:04, 26 October 2006 (UTC)

Thanks for the reference, but that's hardly an acceptable solution to a poor article. Hoping someone actually has this on their watch list and notices that the problem still exists. MJKazin (talk) 18:34, 23 April 2008 (UTC)

Merge

See Talk:Predicate (mathematics). --Abdull 11:04, 3 December 2007 (UTC)

See Talk: Predicate variable. Sae1962 (talk) 07:27, 2 March 2011 (UTC)

• Don't merge. Cleanup instead. There's a lot of confusion between the articles on propositional logic, first-order logic, term algebra, model theory, type theory, philosophy, general mathematics, and semantics(?). All have similar-but-different notions of predicates, but differ sharply in the details. I tried to clean up this article to make this clear, but I believe it has a loooong way to go. linas (talk) 17:05, 9 June 2011 (UTC)

Atomic formula

The follwoing in the article does not accord with Atomic formula and is surely wrong

• In first-order logic, atomic formulae are called predicate variables. A predicate can take the role as either a property or a relation between entities. When P is a predicate on X, one sometimes says that P is a property of X.

— Philogos (talk) 22:07, 16 June 2011 (UTC)

There were a lot of problems with the text, but I think I have removed most of them. — Carl (CBM · talk) 02:03, 17 June 2011 (UTC)

Confusion

Thus seems confusing:

• Informally, a predicate is a statement that may be true or false depending on the values of its variables.[citation needed] It can be thought of as an operator or function that returns a value that is either true or false.

better sruely would be

• Informally, a predicate is an operator or function that returns a value that is either true or false. depending on the values of its variables.

I think it's better to say something like "a predicate can be represented by a function that ...". This avoids using the word "is" about the predicate. — Carl (CBM · talk) 02:40, 17 June 2011 (UTC)

Interesting. Then we have (a) predicate symbols(b) predicates (c) functions, and a predicate can be represented by a function. Eg

• 'F' is a predicate symbol [type (a)]
• under an intepretation it, 'F', can be associated with a predicate, egs. prime, even [type (b)]
• the prime, even and green can be represented by functions (from numbers to {t,f}

That gives us three ontological classes. On the princile of Ackhams razor, would it not be simpler to say

• under an intepretation 'F', can be associated with a predicate, egs. prime, even which are functions (from numbers to {t,f}

— Philogos (talk) 01:31, 18 June 2011 (UTC)

formal definition

The following in para formal definition do not provide formal definitions of the term predicate.

• In propositional logic, atomic formulae are called propositional variables.
• In first-order logic, an atomic formula consists of a predicate symbol applied to an appropriate number of terms.

The article is about predicates not predicate symbols— Philogos (talk) 02:29, 17 June 2011 (UTC)

Indeed. — Carl (CBM · talk) 02:39, 17 June 2011 (UTC)

So the items quoted do not provide a formal definition of the term predicate. (not to be conmsuded with the term predicate symbol or predicate letter

"atomic formula and an atomic sentence" ??? I was reading the article, and it was reasonable to follow, until I came across mention of "atomic formula and an atomic sentence". I've no idea what these are. No clue is given. What is this going on about? — Preceding unsigned comment added by 109.145.82.159 (talk) 10:46, 19 August 2011 (UTC)

Cleanup needed

In its current form, the article augments rather than reduces confusion. To begin with, proposition and predicate are mixed up. Simply put, using the notation of the article, P(x) is a proposition and P is a predicate. This is the most commonly (although not universally) used terminology. The article should be cleaned up to reflect this. Boute (talk) 07:06, 19 October 2015 (UTC)

Wrong assertion at "Simplified overview" section

• RIGHT.  If t is an element of the set {x | P(x)}, then the statement P(t) is true.

• WRONG.  Here, P(x) is referred to as the predicate, and x the subject of the proposition.

The x variable is not the subject (supposing a context of subject–predicate–object). See this example:

A = {x | the square is a subclass of x} and see the set of elements here. So, the set A was defined by the use of x as object not as subject of the phrase (the predicate of the set),

A = {rectangle, rhombus, hypercube, cross-polytope, ...}

P(x) is a template function, as in "Hello %!" where the symbol % is a placeholder to be replaced to anything. Correcting the WRONG to RIGHT:

• RIGHT.  Here, P(x) is referred to as the predicate, and x the placeholder of the proposition.
  Sometimes, P(x) is also called a (template in the role of) propositional function, as each choice of the placeholder x produces a proposition.

--Krauss (talk), 26 November 2017

non-first-order logic

The statement "While first-order logic only includes predicates that apply to individual objects, other logics may allow predicates that apply to collections of objects defined by other predicates" may mislead a reader because of the phrase "collections of objects". A set theory can be a first-order theory in which sets are both individual objects and sets of objects, with a predicate like "element of" being applied to sets construed as individual objects. The statement seems to imply however that set theories are never first-order. User693147 (talk) 09:00, 20 November 2024 (UTC)

As far as I know, there is no infinite set in a first-order set theory. In particular, the integers do not form a set in such a set theory. Also, the real numbers cannot be defined in a first-order theory. So, there are first-order set theories, but they are too poor for being useful. D.Lazard (talk) 10:10, 20 November 2024 (UTC)

I am not a mathematician, so I will quote from a mathematics researcher’s teaching materials. The first statement is “The language L of set theory is the first-order language with the binary relation-symbol ∈.” See https://www.math.uni-hamburg.de/home/geschke/teaching/ModelsSetTheory.pdf With this first-order language he introduces the axioms for standard Zermelo-Frankel-Choice set theory, and within this first-order framework is able to define such things as a set with the cardinality of the natural numbers, but also proceed with the usual more advanced matters.

But perhaps that is not essential for this wikipedia article and set theory need not be mentioned anyway. The phrase “collections of objects” suggests however that sets are meant.

Isn’t the essential point for predication in first-order logic that predicate symbols do not occur in those positions where symbols for objects occur to which predicates are applicable? This is sometimes paraphrased as predicates not being applied to predicates. User693147 (talk) 16:01, 20 November 2024 (UTC)