This article is within the scope of WikiProject Philosophy, a collaborative effort to improve the coverage of content related to
philosophy on Wikipedia. If you would like to support the project, please visit the project page, where you can get more details on how you can help, and where you can join the general discussion about philosophy content on Wikipedia.PhilosophyWikipedia:WikiProject PhilosophyTemplate:WikiProject PhilosophyPhilosophy articles
This article is within the scope of WikiProject Mathematics, a collaborative effort to improve the coverage of
mathematics on Wikipedia. If you would like to participate, please visit the project page, where you can join
the discussion and see a list of open tasks.MathematicsWikipedia:WikiProject MathematicsTemplate:WikiProject Mathematicsmathematics articles
An
equation doesn't say that two open sentences are equal.
Rather, the open sentence is itself (in some cases) an equation.
--
Toby 11:54 19 May 2003 (UTC)
I doubt you can find me a mathematician who uses the term "open sentence". I think it's part of the "new math" of the '60s. Good riddance.
Michael Hardy 19:38 23 May 2003 (UTC)
Somewhere on my plans for the future is to write
Predicate; I'll work these together somehow then.
--
Toby Bartels 06:05 12 Jun 2003 (UTC)
the explanation ought not to limit itself to polynomial equations; the classical examples from logic aren't numerical in nature, and i think today databases are a more obvious application of predicates that deserves to be mentioned as well
Gack. The definition here conflicts strongly with (what I see as) common math usage. It sure would be nice to have some explanation of who uses this mangled terminology, and why.
linas (
talk)
17:23, 14 June 2011 (UTC)reply
Order of quantifiers in the given example(s) of closed formula
I see that an example of closed formula has been given. Other examples derived from it can generated by changing order of quantifiers or of x and y.--
109.166.130.48 (
talk)
17:36, 15 August 2019 (UTC)reply
I'd say that more examples are needed to illustrate by contrast both true and false truth values of closed formulae, as a small error in the order of quantifiers or of variables has an immediate consequence on the truth value of the proposition thus formed.--
109.166.132.132 (
talk)
21:51, 26 August 2019 (UTC)reply
Sentence with (at least) a variable and open sentence
In mathematical logic, sentence is a formula that contains no free variables. "sentence with a variable x which is free" is contradicting itself. --
emk (
talk)
08:41, 13 December 2022 (UTC)reply
Examples of open or closed formulas can be given when the variables x or y from the formulae Px, Rxy are in fact sequence variables xn, yn like in the case of numerical sequences (
Cullen number,
Sierpinski number,
Riesel number, etc) where each individual number term of the sequence has a property like being composite or prime for all natural values of the index number n which is present in the generating formula of the sequence. In these cases an infinite sequence of propositions with singular terms are generated and domain of discourse for the sequences variables is also infinite, in connection to an aspect discussed at
talk:quantifier (logic)--
109.166.129.57 (
talk)
02:52, 10 September 2019 (UTC)reply
Examples from Wikipedia in German version of this article
In der (geschlossenen) Formel ist die Variable gebunden und nicht frei.
In der (offenen) Formel kommt die Variable sowohl gebunden als auch frei vor: Gebunden ist ihr Vorkommen in der Teilformel , frei ist ihr Vorkommen in der Teilformel , auf die sich der Allquantor nicht mehr erstreckt.
In der (offenen) Formel ist gebunden und ist frei.
In der Formel für die
Klasse ist die Variable gebunden und nicht frei.
In der Formel für die
Potenzmenge ist die Variable gebunden und frei.
Bei der Kennzeichnung , zu lesen als: „dasjenige x, für das F(x) gilt“ (Eindeutigkeit vorausgesetzt).
The first set of examples may nicely fit in
free and bound variables, but they don't fit here, as they concern
terms (
expressions), not formulas. The same applies to the seconde set of examples, except where "∀" is involved. BTW: the second set confuses "free/bound occurrence" (2nd example, , "kommt frei vor") and "free/bound variable" (3rd example: "ist frei"); the latter doesn't make sense at all when - as usual - the same variable may occur inside and outside the range of a quantifier. -
Jochen Burghardt (
talk)
19:19, 10 September 2019 (UTC)reply
Bibliographic references from German article
I think that the two books from the section "Literatur" of the German article can be inserted here. One of the German mathematician authors has article here.--
109.166.129.57 (
talk)
12:26, 10 September 2019 (UTC)reply
I think that fact of you being a native German speaker has little relevance here because it is not as if you were the author of one the books and try to promote your work for self-citation. Also presumably there is no indication that these books be of a low quality. Also is not mandatory that only English language sources should be allowed for citation.--
109.166.129.57 (
talk)
19:37, 10 September 2019 (UTC)reply
Link to predicate symbol (predicate variable or predicate constant)
I see that a link to
predicate variable has been removed by saying that it is not about a variable, but a constant. The reason of removal is weak, the (free or bound) individual variables or the individual constants attached to a
predicate letter have the same status due to the equivalence of logical quantifiers to substitution with individual constants (from a domain) in specifying closed formulae (having truth values). The lack of a link to predicate letter does not justify the removal of the link to the existing name predicate variable.--
178.138.195.100 (
talk)
21:54, 13 June 2021 (UTC)reply