Proposition

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In philosophy, a proposition is a tentative and conjectural relationship between constructs that is stated in a declarative form. An example of a proposition is: “An increase in student intelligence causes an increase in their academic achievement.” This declarative statement does not have to be true, but must be empirically testable using data, so that we can judge whether it is true or false. Propositions are generally derived based on deductive logic or empirical observation (induction). Because propositions are associations between abstract constructs, they cannot be tested directly. Instead, they are tested indirectly by examining the relationship between corresponding measures (variables) of those constructs. The empirical formulation of propositions, stated as relationships between variables, is called hypotheses [1] . The term proposition has a broad use in contemporary analytic philosophy. It is used to refer to some or all of the following: the primary bearers of truth-value, the objects of belief and other "propositional attitudes" (i.e., what is believed, doubted, etc.), the referents of that-clauses, and the meanings of declarative sentences. Propositions are the sharable objects of attitudes and the primary bearers of truth and falsity. This stipulation rules out certain candidates for propositions, including thought- and utterance-tokens which are not sharable, and concrete events or facts, which cannot be false. [2]

Conjecture proposition in mathematics that is unproven

In mathematics, a conjecture is a conclusion or proposition based on incomplete information, for which no proof or disproof has yet been found. Conjectures such as the Riemann hypothesis or Fermat's Last Theorem have shaped much of mathematical history as new areas of mathematics are developed in order to prove them.

Construct (philosophy) ideal object, whose existence depends upon a subjects mind

A construct in the philosophy of science is an ideal object, where the existence of the thing may be said to depend upon a subject's mind. This contrasts with a real object, where existence does not seem to depend on the existence of a mind.

Truth philosophical concept

Truth is most often used to mean being in accord with fact or reality, or fidelity to an original or standard. Truth is also sometimes defined in modern contexts as an idea of "truth to self", or authenticity.

Contents

Historical usage

By Aristotle

Aristotelian logic identifies a proposition as a sentence which affirms or denies a predicate of a subject with the help of a 'Copula'. An Aristotelian proposition may take the form "All men are mortal" or "Socrates is a man." In the first example the subject is "men", predicate is "mortal" and copula is "are". In the second example the subject is "Socrates", the predicate is "a man" and copula is "is".[ citation needed ]

The subject in a simple English sentence such as John runs, John is a teacher, or John was run over by a car is the person or thing about whom the statement is made, in this case 'John'. Traditionally the subject is the word or phrase which controls the verb in the clause, that is to say with which the verb agrees. If there is no verb, as in John - what an idiot!, or if the verb has a different subject, as in John - I can't stand him!, then 'John' is not considered to be the grammatical subject, but can be described as the 'topic' of the sentence.

By the logical positivists

Often propositions are related to closed sentences to distinguish them from what is expressed by an open sentence. In this sense, propositions are "statements" that are truth-bearers. This conception of a proposition was supported by the philosophical school of logical positivism.

In mathematical logic, a sentence of a predicate logic is a boolean-valued well-formed formula with no free variables. A sentence can be viewed as expressing a proposition, something that must be true or false. The restriction of having no free variables is needed to make sure that sentences can have concrete, fixed truth values: As the free variables of a (general) formula can range over several values, the truth value of such a formula may vary.

A truth-bearer is an entity that is said to be either true or false and nothing else. The thesis that some things are true while others are false has led to different theories about the nature of these entities. Since there is divergence of opinion on the matter, the term truth-bearer is used to be neutral among the various theories. Truth-bearer candidates include propositions, sentences, sentence-tokens, statements, concepts, beliefs, thoughts, intuitions, utterances, and judgements but different authors exclude one or more of these, deny their existence, argue that they are true only in a derivative sense, assert or assume that the terms are synonymous, or seek to avoid addressing their distinction or do not clarify it.

Logical positivism and logical empiricism, which together formed neopositivism, was a movement in Western philosophy whose central thesis was verificationism, a theory of knowledge which asserted that only statements verifiable through empirical observation are meaningful. The movement flourished in the 1920s and 1930s in several European centers.

Some philosophers argue that some (or all) kinds of speech or actions besides the declarative ones also have propositional content. For example, yes–no 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.

In linguistics, a yes–no question, formally known as a polar question or a general question is a question whose expected answer is either "yes" or "no". Also known as an “open ended question” Formally, they present an exclusive disjunction, a pair of alternatives of which only one is acceptable. In English, such questions can be formed in both positive and negative forms.

In logic and mathematics, a truth value, sometimes called a logical value, is a value indicating the relation of a proposition to truth.

Semiotics is the study of sign process (semiosis). It includes the study of signs and sign processes, indication, designation, likeness, analogy, allegory, metonymy, metaphor, symbolism, signification, and communication. It is not to be confused with the Saussurean tradition called semiology, which is a subset of semiotics.

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, and so on, are thus called propositional attitudes when they take this sort of content.[ citation needed ]

Belief is the attitude we have whenever we take something to be the case or regard it as the truth.

A propositional attitude is a mental state held by an agent toward a proposition.

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 that two plus two equals four is distinct on a Russellian account from 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 ]

Bertrand Russell British philosopher, mathematician, historian, writer, and activist

Bertrand Arthur William Russell, 3rd Earl Russell, was a British philosopher, logician, mathematician, historian, writer, essayist, social critic, political activist, and Nobel laureate. At various points in his life, Russell considered himself a liberal, a socialist and a pacifist, although he also confessed that his sceptical nature had led him to feel that he had "never been any of these things, in any profound sense." Russell was born in Monmouthshire into one of the most prominent aristocratic families in the United Kingdom.

Ludwig Wittgenstein Austrian-British philosopher

Ludwig Josef Johann Wittgenstein was an Austrian philosopher who worked primarily in logic, the philosophy of mathematics, the philosophy of mind, and the philosophy of language.

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. 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 (see the entry on internalism and externalism in philosophy of mind).

Treatment in logic

As noted above, in Aristotelian logic a proposition is a particular kind of sentence, one which affirms or denies a predicate of a subject with the help of a copula. Aristotelian propositions take forms like "All men are mortal" and "Socrates is a man."

Propositions show up in modern formal logic as objects of a formal language. 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 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 propositions, 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, terms must be defined. A term is (i) a variable or (ii) a function symbol applied to the number of terms required by the function symbol's arity. For example, if + is a binary function symbol and x, y, and z are variables, then x+(y+z) is a term, which might be written with the symbols in various orders. A proposition is (i) a predicate symbol applied to the number of terms required by its arity, (ii) an operator applied to the number of propositions required by its arity, or (iii) a quantifier applied to a proposition. For example, if = is a binary predicate symbol and is a quantifier, then ∀x,y,z [(x = y) → (x+z = y+z)] is a proposition. This more complex structure of propositions allows these logics to make finer distinctions between inferences, i.e., to have greater expressive power.

In this context, propositions are also called sentences, statements, statement forms, formulas, and well-formed formulas, though these terms are usually not synonymous within a single text. This definition treats propositions as syntactic objects, as opposed to semantic or mental objects. That is, propositions in this sense are meaningless, formal, abstract objects. They are assigned meaning and truth-values by mappings called interpretations and valuations, respectively.

Propositions are called structured propositions if they have constituents, in some broad sense. [3] [4]

Assuming a structured view of propositions, we 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. [5]

Objections to propositions

Attempts to provide a workable definition of proposition include

Two meaningful declarative sentences express the same proposition if and only if they mean the same thing.[ citation needed ]

thus defining proposition in terms of synonymity. For example, "Snow is white" (in English) and "Schnee ist weiß" (in German) are different sentences, but they say the same thing, so they express the same proposition.

Two meaningful declarative sentence-tokens express the same proposition if and only if they mean the same thing.[ citation needed ]

Unfortunately, the above definitions have the result that two sentences/sentence-tokens which have the same meaning and thus express the same proposition could have different truth-values, e.g. "I am Spartacus" said by Spartacus and said by John Smith; and e.g. "It is Wednesday" said on a Wednesday and on a Thursday.

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 maintained that the indeterminacy of translation prevented any meaningful discussion of propositions, and that they should be discarded in favor of sentences. [6] Strawson advocated the use of the term "statement".

See also

Related Research Articles

Existence objective persistence independent of ones presence; state of being, existing, or occurring; beinghood

Existence is the ability of an entity to interact with physical or mental reality.

First-order logic—also known as predicate logic and first-order predicate calculus—is a collection of formal systems used in mathematics, philosophy, linguistics, and computer science. First-order logic uses quantified variables over non-logical objects and allows the use of sentences that contain variables, so that rather than propositions such as Socrates is a man one can have expressions in the form "there exists x such that x is Socrates and x is a man" and there exists is a quantifier while x is a variable. This distinguishes it from propositional logic, which does not use quantifiers or relations; in this sense, propositional logic is the foundation of first-order logic.

A syllogism is a kind of logical argument that applies deductive reasoning to arrive at a conclusion based on two or more propositions that are asserted or assumed to be true.

In predicate logic, an existential quantification is a type of quantifier, a logical constant which is interpreted as "there exists", "there is at least one", or "for some". Some sources use the term existentialization to refer to existential quantification. It is usually denoted by the logical operator symbol ∃, which, when used together with a predicate variable, is called an existential quantifier. Existential quantification is distinct from universal quantification, which asserts that the property or relation holds for all members of the domain.

In mathematical logic, a predicate is commonly understood to be a Boolean-valued function P: X→ {true, false}, called the predicate on X. However, predicates have many different uses and interpretations in mathematics and logic, and their precise definition, meaning and use will vary from theory to theory. So, for example, when a theory defines the concept of a relation, then a predicate is simply the characteristic function of a relation. However, not all theories have relations, or are founded on set theory, and so one must be careful with the proper definition and semantic interpretation of a predicate.

In philosophy, term logic, also known as traditional logic, syllogistic logic or Aristotelian logic, is a loose name for an approach to logic that began with Aristotle and that was dominant until the advent of modern predicate logic in the late nineteenth century. This entry is an introduction to the term logic needed to understand philosophy texts written before it was replaced as a formal logic system by predicate logic. Readers lacking a grasp of the basic terminology and ideas of term logic can have difficulty understanding such texts, because their authors typically assumed an acquaintance with term logic.

In mathematical logic, propositional logic and predicate logic, a well-formed formula, abbreviated WFF or wff, often simply formula, is a finite sequence of symbols from a given alphabet that is part of a formal language. A formal language can be identified with the set of formulas in the language.

A definite description is a denoting phrase in the form of "the X" where X is a noun-phrase or a singular common noun. The definite description is proper if X applies to a unique individual or object. For example: "the first person in space" and "the 42nd President of the United States of America", are proper. The definite descriptions "the person in space" and "the Senator from Ohio" are improper because the noun phrase X applies to more than one thing, and the definite descriptions "the first man on Mars" and "the Senator from some Country" are improper because X applies to nothing. Improper descriptions raise some difficult questions about the law of excluded middle, denotation, modality, and mental content.

In philosophy and logic, a deflationary theory of truth is one of a family of theories that all have in common the claim that assertions of predicate truth of a statement do not attribute a property called "truth" to such a statement.

In logic, an atomic sentence is a type of declarative sentence which is either true or false and which cannot be broken down into other simpler sentences. For example, "The dog ran" is an atomic sentence in natural language, whereas "The dog ran and the cat hid." is a molecular sentence in natural language.

David Benjamin Kaplan is the Hans Reichenbach Professor of Scientific Philosophy at the University of California, Los Angeles Department of Philosophy. His philosophical work focuses on the philosophy of language, logic, metaphysics, epistemology and the philosophy of Frege and Russell. He is best known for his work on demonstratives, propositions, and reference in intensional contexts. He was elected a Fellow of the American Academy of Arts & Sciences in 1983 and a Corresponding Fellow of the British Academy in 2007.

Logical form form for logical arguments, obtained by abstracting from the subject matter of its content terms

In philosophy and mathematics, a logical form of a syntactic expression is a precisely-specified semantic version of that expression in a formal system. Informally, the logical form attempts to formalize a possibly ambiguous statement into a statement with a precise, unambiguous logical interpretation with respect to a formal system. In an ideal formal language, the meaning of a logical form can be determined unambiguously from syntax alone. Logical forms are semantic, not syntactic constructs; therefore, there may be more than one string that represents the same logical form in a given language.

In mathematical logic, an atomic formula is a formula with no deeper propositional structure, that is, a formula that contains no logical connectives or equivalently a formula that has no strict subformulas. Atoms are thus the simplest well-formed formulas of the logic. Compound formulas are formed by combining the atomic formulas using the logical connectives.

Logic is the formal science of using reason and is considered a branch of both philosophy and mathematics. Logic investigates and classifies the structure of statements and arguments, both through the study of formal systems of inference and the study of arguments in natural language. The scope of logic can therefore be very large, ranging from core topics such as the study of fallacies and paradoxes, to specialized analyses of reasoning such as probability, correct reasoning, and arguments involving causality. One of the aims of logic is to identify the correct and incorrect inferences. Logicians study the criteria for the evaluation of arguments.

In logic, the formal languages used to create expressions consist of symbols, which can be broadly divided into constants and variables. The constants of a language can further be divided into logical symbols and non-logical symbols.

In logic, the monadic predicate calculus is the fragment of first-order logic in which all relation symbols in the signature are monadic, and there are no function symbols. All atomic formulas are thus of the form , where is a relation symbol and is a variable.

An interpretation is an assignment of meaning to the symbols of a formal language. Many formal languages used in mathematics, logic, and theoretical computer science are defined in solely syntactic terms, and as such do not have any meaning until they are given some interpretation. The general study of interpretations of formal languages is called formal semantics.

In logic, quantification specifies the quantity of specimens in the domain of discourse that satisfy an open formula. The two most common quantifiers mean "for all" and "there exists". For example, in arithmetic, quantifiers allow one to say that the natural numbers go on forever, by writing that for all n, there is another number which is one bigger than n.

References

  1. Bhattacherjee, Anol (2012-04-05). Social Science Research: Principles, Methods, and Practices. CreateSpace Independent Publishing Platform. ISBN   9781475146127.
  2. "Propositions (Stanford Encyclopedia of Philosophy)". Plato.stanford.edu. Retrieved 2014-06-23.
  3. Propositions by Matthew McGrath
  4. Singular Propositions by Greg Fitch
  5. Structured Propositions by Jeffrey C. King
  6. Quine, W. V. (1970). Philosophy of Logic. NJ USA: Prentice-Hall. pp. 1–14. ISBN   0-13-663625-X.