In philosophy and logic, proposition refers to both the content or meaning of a declarative sentence and the string of symbols, marks, or sounds that make up a written or spoken declarative sentence. Philosophy is the study of general problems concerning matters such as existence knowledge truth beauty justice validity mind and language Logic is the study of the principles of valid demonstration and Inference. In Linguistics, a sentence is a grammatical unit of one or more words bearing minimal syntactic relation to the words that precede or follow it often preceded and followed Propositions are intended to be the truth-bearers, that is, they are either true or false. Truthbearer is a term used by philosophers and linguists to designate entities that are either True or False and nothing else The meaning of the word truth extends from Honesty, Good faith, and Sincerity in general to agreement with Fact or Reality A Falsity is a perversion of truth originating in the deceitfulness of one party and culminating in the damage of another party

The existence of propositions (in both senses described above), and the existence of meanings is disputed, and where admitted their nature is controversial. In earlier texts writers have not always made it sufficiently clear whether they are using the term proposition in sense of the words or the ideas behind the words. To avoid the controversies and ontological implications, the term sentence is often now used instead of proposition or statement to refer to just those strings of symbols that are truth-bearers, being either true or false under an interpretation.

Common usage contrasted with philosophical usage

In common usage, different sentences express the same proposition when they have the same meaning. 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. Another way to express this proposition is , "Tiny crystals of frozen water are white. " In common usage, this proposition is true.

Philosophical usage often makes more subtle judgments. A philosopher might observe that "snow" is a softer word than the German "schnee", and therefore produces a different reaction in the person who hears the word, while "tiny crystals of frosen water" suggests an entirely different context, and therefore a subtly different meaning. In fact, some philosophers have observed that meaning occurs in the mind of the person hearing or reading the statement, and therefore changes from person to person, and in the same person from time to time.

Further, a philosopher might observe that snow reflecting the setting sun appears red, that snow at night may appear blue, and remind the reader of the common advice, "Never eat yellow snow. " This philosopher might conclude that the proposition "Snow is white," has no universally agreed upon truth value, and some would go so far as to say that no proposition has a universally agreed upon truth value.

Historical usage

Usage in Aristotle

Aristotelian logic identifies a proposition as a sentence which affirms or denies the predicate of a subject. The Organon is the name given by Aristotle 's followers the Peripatetics to the standard collection of his six works on Logic. Sometimes it is inconvenient or impossible to describe a set by listing all of its elements Not to be confused with the subiectum or Hypokeimenon in Aristotelianism An Aristotelian proposition may take the form "All men are mortal" or "Socrates is a man. " In the first example, which a mathematicial logician would call a quantified predicate (note the difference in usage), the subject is "men" and the predicate "all are mortal". Quantification has two distinct meanings In Mathematics and Empirical science, it refers to human acts known as Counting and Measuring In the second example, which a mathematicial logician would call a statement, the subject is "Socrates" and the predicate is "is a man". In the area of Mathematics called Symbolic logic a statement is a Declarative sentence that is either True or False. The second example is an atomic element in Propositional logic, the first example is a statement in predicate logic. This is a technical mathematical article about the area of mathematical logic variously known as "propositional calculus" or "propositional logic" In Mathematical logic, predicate logic is the generic term for symbolic Formal systems like First-order logic, Second-order logic, Many-sorted The compound proposition, "All men are mortal and Socrates is a man," combines two atomic propositions, and is considered true if and only if both parts are true.

Usage by the Logical Positivists

Often propositions are related to closed sentences, to distinguish them from what is expressed by an open sentence, or predicate. In Linguistics, a sentence is a grammatical unit of one or more words bearing minimal syntactic relation to the words that precede or follow it often preceded and followed Sometimes it is inconvenient or impossible to describe a set by listing all of its elements In this sense, propositions are statements that are either true or false. The meaning of the word truth extends from Honesty, Good faith, and Sincerity in general to agreement with Fact or Reality This conception of a proposition was supported by the philosophical school of logical positivism. Logical positivism (later and more accurately called logical empiricism) is a school of philosophy that combines Empiricism, the idea that observational evidence is

Some philosophers, such as John Searle, hold that other kinds of speech or actions also assert propositions. John Rogers Searle (born July 31 1932 in Denver Colorado) is an American Philosopher and the Slusser Professor of Philosophy at the University Yes-no questions are an inquiry into a proposition's truth value. A question may be either a linguistic expression used to make a request for Information, or else the request itself made by such an expression Traffic signs express propositions without using speech or written language. Most countries post signage known as traffic signs or road signs, at the side of Roads to It is also possible to use a declarative sentence to express a proposition without asserting it, as when a teacher asks a student to comment on a quote; the quote is a proposition (that is, it has a meaning) but the teacher is not asserting it. "Snow is white" expresses the proposition that snow is white without asserting it (i. e. claiming snow is white).

Propositions are also spoken of as the content of beliefs and similar intentional attitudes such as desires, preferences, and hopes. Belief is the psychological state in which an individual holds a Proposition or Premise to be true A propositional attitude is a relational mental state connecting a person to a Proposition. 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.

Usage by Russell

Bertrand Russell held that propositions were structured entities with objects and properties as constituents. Bertrand Arthur William Russell 3rd Earl Russell, OM, FRS (18 May 1872 – 2 February 1970 was a British Philosopher, Historian Others have held that a proposition is the set of possible worlds/states of affairs in which it is true. One important difference between these views 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 are the same set (the set of all possible worlds).

Relation to the mind

In relation to the mind, propositions are discussed primarily as they fit into propositional attitudes. A propositional attitude is a relational mental state connecting a person to a Proposition. Propositional attitudes are simply attitudes characteristic of folk psychology (belief, desire, etc. Folk psychology (also known as common sense psychology naϊve psychology or vernacular psychology is a set of assumptions constructs and convictions about everyday behaviors of ourselves and others ) 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. Philosophy of mind is the branch of Philosophy that studies the nature of the Mind, Mental events Mental functions mental properties Psychology (from Greek grc ψῡχή psȳkhē, "breath life soul" and grc -λογία -logia) is an Academic and 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. The term intentionality is often simplistically summarised as "aboutness" 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). Internalism and externalism are now part of the standard jargon of philosophical discourse and are central to important debates

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. The Organon is the name given by Aristotle 's followers the Peripatetics to the standard collection of his six works on Logic. Sometimes it is inconvenient or impossible to describe a set by listing all of its elements Not to be confused with the subiectum or Hypokeimenon in Aristotelianism Aristotelian propositions take forms like "All men are mortal" and "Socrates is a man. "

In mathematical logic, propositions, also called "propositional formulas" or "statement forms", are statements that do not contain quantifiers. Mathematical logic is a subfield of Logic and Mathematics with close connections to Computer science and Philosophical logic. In Propositional logic, a propositional formula is a type of syntactic formula which is well formed and has a Truth value. Quantification has two distinct meanings In Mathematics and Empirical science, it refers to human acts known as Counting and Measuring They are composed of well-formed formulas consisting entirely of atomic formulas, the five logical connective, and symbols of grouping. In Mathematical logic, a well-formed formula (often abbreviated WFF, pronounced "wiff" or "wuff" is a Symbol or string of symbols (a In Mathematical logic, an atomic formula (also known simply as an atom) is a formula with no deeper Propositional structure that is a formula Table of logic symbolsIn Logic, two sentences (either in a formal language or a natural language may be joined by means of a logical connective to form a compound sentence Grouping is form of hierarchical knowledge representation similar to mind mapping, concept mapping and argument mapping, all of which need to observe propositional logic is one of the few areas of mathematics that is totally solved, in the sense that it has been proven internally consistent, every theorem is true, and every true statement can be proved. This is a technical mathematical article about the area of mathematical logic variously known as "propositional calculus" or "propositional logic" Mathematics is the body of Knowledge and Academic discipline that studies such concepts as Quantity, Structure, Space and ^[1] (From this fact, and Gödel's Theorem, it is easy to see that propositional logic is not sufficient to construct the set of integers. In Mathematical logic, Gödel's incompleteness theorems, proved by Kurt Gödel in 1931 are two Theorems stating inherent limitations of all but the most ) The most common extension of predicate logic is called propositional logic, which adds variables and quantifiers. In Mathematical logic, predicate logic is the generic term for symbolic Formal systems like First-order logic, Second-order logic, Many-sorted This is a technical mathematical article about the area of mathematical logic variously known as "propositional calculus" or "propositional logic" A variable (ˈvɛərɪəbl is an Attribute of a physical or an abstract System which may change its Value while it is under Observation. Quantification has two distinct meanings In Mathematics and Empirical science, it refers to human acts known as Counting and Measuring

Objections to propositions

A number of philosophers and linguists claim that the philosophical definition of a proposition is too vague to be useful. For them, it is just a misleading concept that should be removed from philosophy and semantics. Semantics is the study of meaning in communication The word derives from Greek σημαντικός ( semantikos) "significant" from 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. Willard Van Orman Quine (June 25 1908 Akron, Ohio &ndash December 25 2000 (known to intimates as "Van" This article is a technical mathematical article in the area of predicate logic

See also

• Main contention
• Premise
• Statement (logic)
• Sentence (mathematical logic)

References

External links

• Stanford Encyclopedia of Philosophy articles on:
  • Propositions, by Matthew McGrath
  • Singular Propositions, by Greg Fitch
  • Structured Propositions, by Jeffrey C. The Stanford Encyclopedia of Philosophy (SEP is a freely-accessible Online encyclopedia of Philosophy maintained by Stanford University. King