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proposition
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{{Short description|Bearer of truth or falsity}}
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Historical usage
By Aristotle
Aristotelian logic identifies a categorical proposition as a sentence which affirms or denies a predicate of a subject, optionally with the help of a copula. An Aristotelian proposition may take the form of "All men are mortal" or "Socrates is a man." In the first example, the subject is "men", predicate is "mortal" and copula is "are", while in the second example, the subject is "Socrates", the predicate is "a man" and copula is "is".WEB,weblink Aristotle: Logic â From Words into Propositions, Groarke, Louis, Internet Encyclopedia of Philosophy, 2019-12-10,By the logical positivists
Often, propositions are related to closed formulae (or logical sentence) to distinguish them from what is expressed by an open formula. In this sense, propositions are "statements" that are truth-bearers. This conception of a proposition was supported by the philosophical school of logical positivism.Some philosophers argue that some (or all) kinds of speech or actions besides the declarative ones also have propositional content. For example, yesâno questions present propositions, being inquiries into the truth value of them. On the other hand, some signs can be declarative assertions of propositions, without forming a sentence nor even being linguistic (e.g. traffic signs convey definite meaning which is either true or false).Propositions are also spoken of as the content of beliefs and similar intentional attitudes, such as desires, preferences, and hopes. For example, "I desire that I have a new car", or "I wonder whether it will snow" (or, whether it is the case that "it will snow"). Desire, belief, doubt, and so on, are thus called propositional attitudes when they take this sort of content.WEB,weblink Propositions (Stanford Encyclopedia of Philosophy), McGrath, Matthew, Frank, Devin, Plato.stanford.edu, 2014-06-23,By Russell
Bertrand Russell held that propositions were structured entities with objects and properties as constituents. One important difference between Ludwig Wittgenstein's view (according to which a proposition is the set of possible worlds/states of affairs in which it is true) is that on the Russellian account, two propositions that are true in all the same states of affairs can still be differentiated. For instance, the proposition "two plus two equals four" is distinct on a Russellian account from the proposition "three plus three equals six". If propositions are sets of possible worlds, however, then all mathematical truths (and all other necessary truths) are the same set (the set of all possible worlds).{{citation needed|date=November 2014}}Relation to the mind
In relation to the mind, propositions are discussed primarily as they fit into propositional attitudes. Propositional attitudes are simply attitudes characteristic of folk psychology (belief, desire, etc.) that one can take toward a proposition (e.g. 'it is raining,' 'snow is white,' etc.). In English, propositions usually follow folk psychological attitudes by a "that clause" (e.g. "Jane believes that it is raining"). In philosophy of mind and psychology, mental states are often taken to primarily consist in propositional attitudes. The propositions are usually said to be the "mental content" of the attitude. For example, if Jane has a mental state of believing that it is raining, her mental content is the proposition 'it is raining.' Furthermore, since such mental states are about something (namely, propositions), they are said to be intentional mental states.Explaining the relation of propositions to the mind is especially difficult for non-mentalist views of propositions, such as those of the logical positivists and Russell described above, and Gottlob Frege's view that propositions are Platonist entities, that is, existing in an abstract, non-physical realm.WEB,weblink Platonism in metaphysics: Propositions, Balaguer, Mark, 2016, Stanford Encyclopedia of Philosophy, 30 June 2021, So some recent views of propositions have taken them to be mental. Although propositions cannot be particular thoughts since those are not shareable, they could be types of cognitive eventsBOOK, Soames, Scott, 2014, New Thinking about Propositions,weblink New York, Oxford University Press, King, Jeffrey C., Soames, Scott, Speaks, Jeff, Propositions as cognitive event types,weblink 9780199693764, or properties of thoughts (which could be the same across different thinkers).JOURNAL, Joaquin, Jeremiah Joven B., Franklin, James, 2021, A causal-mentalist view of propositions,weblink Organon F, 28, 30 June 2021, Philosophical debates surrounding propositions as they relate to propositional attitudes have also recently centered on whether they are internal or external to the agent, or whether they are mind-dependent or mind-independent entities. For more, see the entry on internalism and externalism in philosophy of mind.Treatment in logic
Aristotelian logic
As noted above, in Aristotelian logic a proposition is a particular kind of sentence (a declarative sentence) that affirms or denies a predicate of a subject, optionally with the help of a copula. Aristotelian propositions take forms like "All men are mortal" and "Socrates is a man."Syntactic characterization
In modern logic, the term "proposition" is often used for sentences of a formal language. In this usage, propositions are formal syntactic objects which can be studied independently of the meaning they would receive from a semantics. Propositions are also called sentences, statements, statement forms, formulas, and well-formed formulas, though these terms are usually not synonymous within a single text. A formal language begins with different types of symbols. These types can include variables, operators, function symbols, predicate (or relation) symbols, quantifiers, and propositional constants.(Grouping symbols such as delimiters are often added for convenience in using the language, but do not play a logical role.) Symbols are concatenated together according to recursive rules, in order to construct strings to which truth-values will be assigned. The rules specify how the operators, function and predicate symbols, and quantifiers are to be concatenated with other strings. A proposition is then a string with a specific form. The form that a proposition takes depends on the type of logic.The type of logic called propositional, sentential, or statement logic includes only operators and propositional constants as symbols in its language. The propositions in this language are propositional constants, which are considered atomic propositions, and composite (or compound) propositions,WEB,weblink Mathematics {{!, Introduction to Propositional Logic {{!}} Set 1|date=2015-06-19|website=GeeksforGeeks|language=en-US|access-date=2019-12-11}} which are composed by recursively applying operators to propositions. Application here is simply a short way of saying that the corresponding concatenation rule has been applied.The types of logics called predicate, quantificational, or n-order logic include variables, operators, predicate and function symbols, and quantifiers as symbols in their languages. The propositions in these logics are more complex. First, one typically starts by defining a term as follows:- A variable, or
- A function symbol applied to the number of terms required by the function symbol's arity.
- A predicate symbol applied to the number of terms required by its arity, or
- An operator applied to the number of propositions required by its arity, or
- A quantifier applied to a proposition.
Semantic characterization
Propositions are standardly understood semantically as indicator functions that take a possible world and return a truth value. For example, the proposition that the sky is blue could be represented as a function f such that f(w)=T for every world w , if any, where the sky is blue, and f(v)=F for every world v , if any, where it is not. A proposition can be modeled equivalently with the inverse image of T under the indicator function, which is sometimes called the characteristic set of the proposition. For instance, if w and w' are the only worlds in which the sky is blue, the proposition that the sky is blue could be modeled as the set {w, w'} .BOOK, Gamut, L.T.F., L.T.F. Gamut, 1991, Logic, Language and Meaning: Intensional Logic and Logical Grammar, University of Chicago Press, 122, 0-226-28088-8, {{Citation|last=King|first=Jeffrey|title=Structured Propositions|date=2019|url=http://plato.stanford.edu/entries/propositions-structured/|encyclopedia=The Stanford Encyclopedia of Philosophy|editor-last=Zalta|editor-first=Edward N.|edition=Winter 2016|publisher=Metaphysics Research Lab, Stanford University|access-date=2022-12-30|at=Section 2}}BOOK, Irene Heim, Angelika Kratzer, Semantics in generative grammar, 1998, Wiley-Blackwell, 978-0-631-19713-3, 304, ENCYCLOPEDIA, Pragmatics, Semantics, 1972, Stalnaker, Robert, Davidson, Donald, Harman, Gilbert, 381, Numerous refinements and alternative notions of proposition-hood have been proposed including inquisitive propositions and structured propositions.BOOK, Ciardelli, Ivano, Groenendijk, Jeroen, Roelofsen, Floris, 2019, Inquisitive Semantics, Oxford University Press, 13,20â22, 9780198814795, Propositions are called structured propositions if they have constituents, in some broad sense.{{Citation|last1=Fitch|first1=Greg|title=Singular Propositions|date=2018|url=https://plato.stanford.edu/archives/spr2018/entries/propositions-singular/|encyclopedia=The Stanford Encyclopedia of Philosophy|editor-last=Zalta|editor-first=Edward N.|edition=Spring 2018|publisher=Metaphysics Research Lab, Stanford University|access-date=2019-12-11|last2=Nelson|first2=Michael}} Assuming a structured view of propositions, one can distinguish between singular propositions (also Russellian propositions, named after Bertrand Russell) which are about a particular individual, general propositions, which are not about any particular individual, and particularized propositions, which are about a particular individual but do not contain that individual as a constituent.Structured Propositions by Jeffrey C. KingObjections to propositions
Attempts to provide a workable definition of proposition include the following:Two meaningful declarative sentences express the same proposition, if and only if they mean the same thing.{{citation needed|date=June 2016}}which defines proposition in terms of synonymity. For example, "Snow is white" (in English) and "Schnee ist weiÃ" (in German) are different sentences, but they say the same thing, so they express the same proposition. Another definition of proposition is:Two meaningful declarative sentence-tokens express the same proposition, if and only if they mean the same thing.{{citation needed|date=June 2016}}The above definitions can result in two identical sentences/sentence-tokens appearing to have the same meaning, and thus expressing the same proposition and yet having different truth-values, as in "I am Spartacus" said by Spartacus and said by John Smith, and "It is Wednesday" said on a Wednesday and on a Thursday. These examples reflect the problem of ambiguity in common language, resulting in a mistaken equivalence of the statements. âI am Spartacusâ spoken by Spartacus is the declaration that the individual speaking is called Spartacus and it is true. When spoken by John Smith, it is a declaration about a different speaker and it is false. The term âIâ means different things, so âI am Spartacusâ means different things.A related problem is when identical sentences have the same truth-value, yet express different propositions. The sentence âI am a philosopherâ could have been spoken by both Socrates and Plato. In both instances, the statement is true, but means something different.These problems are addressed in predicate logic by using a variable for the problematic term, so that âX is a philosopherâ can have Socrates or Plato substituted for X, illustrating that âSocrates is a philosopherâ and âPlato is a philosopherâ are different propositions. Similarly, âI am Spartacusâ becomes âX is Spartacusâ, where X is replaced with terms representing the individuals Spartacus and John Smith.In other words, the example problems can be averted if sentences are formulated with precision such that their terms have unambiguous meanings.A number of philosophers and linguists claim that all definitions of a proposition are too vague to be useful. For them, it is just a misleading concept that should be removed from philosophy and semantics. W. V. Quine, who granted the existence of sets in mathematics,{{Citation|last1=McGrath|first1=Matthew|title=Propositions|date=2018|url=https://plato.stanford.edu/archives/spr2018/entries/propositions/|encyclopedia=The Stanford Encyclopedia of Philosophy|editor-last=Zalta|editor-first=Edward N.|edition=Spring 2018|publisher=Metaphysics Research Lab, Stanford University|access-date=2020-08-20|last2=Frank|first2=Devin}} maintained that the indeterminacy of translation prevented any meaningful discussion of propositions, and that they should be discarded in favor of sentences.BOOK, Quine, W. V., Philosophy of Logic, Prentice-Hall, NJ USA, 1970, 1â14, 0-13-663625-X,weblink P. F. Strawson, on the other hand, advocated for the use of the term "statement".See also
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