A sign relation is the basic construct in the theory of signs, or semiotic theory, as developed by Charles Sanders Peirce (1839-1914). Sign can denote any of the following: Look up sign on Wiktionary, the free dictionary. ... In mathematics, a relation is a generalization of arithmetic relations, such as = and <, which occur in statements, such as 5 < 6 or 2 + 2 = 4. See relation (mathematics), binary relation and relational algebra. ... Semiotics (also spelled Semeiotics) is the study of signs and sign systems. ... Charles Sanders Peirce Charles Sanders Peirce (September 10, 1839 – April 19, 1914) was an American logician, philosopher, scientist, and mathematician. ...

Six ways of looking at a sign relation

So in a triadic fact, say, the example

we make no distinction in the ordinary logic of relations between the subject nominative, the direct object, and the indirect object. We say that the proposition has three logical subjects. We regard it as a mere affair of English grammar that there are six ways of expressing this:

These six sentences express one and the same indivisible phenomenon. (C.S. Peirce, "The Categories Defended", MS 308 (1903), EP 2, 170-171).

The subject of a sentence is one of the two main parts of a sentence, the other being the predicate. ... The nominative case is a grammatical case for a noun. ... The accusative case of a noun is, generally, the case used to mark the direct object of a verb. ... The dative case is a grammatical case for nouns and/or pronouns. ...

IOS

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ISO

(Text in preparation, 20 January 2006)

OIS

Words spoken are symbols or signs (συμβολα) of affections or impressions (παθηματων) of the soul (ψυχη); written words are the signs of words spoken. As writing, so also is speech not the same for all races of men. But the mental affections themselves, of which these words are primarily signs (σημεια), are the same for the whole of mankind, as are also the objects (πραγματα) of which those affections are representations or likenesses, images, copies (ομοιωματα). (Aristotle, "On Interpretation", 1.16^a4).

OSI

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SIO

Logic will here be defined as formal semiotic. A definition of a sign will be given which no more refers to human thought than does the definition of a line as the place which a particle occupies, part by part, during a lapse of time. Namely, a sign is something, A, which brings something, B, its interpretant sign determined or created by it, into the same sort of correspondence with something, C, its object, as that in which itself stands to C. It is from this definition, together with a definition of "formal", that I deduce mathematically the principles of logic. I also make a historical review of all the definitions and conceptions of logic, and show, not merely that my definition is no novelty, but that my non-psychological conception of logic has virtually been quite generally held, though not generally recognized. (C.S. Peirce, "Application to the Carnegie Institution", L75 (1902), NEM 4, 20-21). The Carnegie Institution of Washington (CIW) is a foundation established by Andrew Carnegie in 1902 to support scientific research. ...

SOI

A Sign is anything which is related to a Second thing, its Object, in respect to a Quality, in such a way as to bring a Third thing, its Interpretant, into relation to the same Object, and that in such a way as to bring a Fourth into relation to that Object in the same form, ad infinitum. (CP 2.92; quoted in Fisch 1986: 274) Sign can denote any of the following: Look up sign on Wiktionary, the free dictionary. ... WordNet gives four main senses for the English noun object: a physical entity; something that is within the grasp of the senses; an aim, target or objective — see Object (task); a grammatical Object — either a direct object or an indirect object the focus of cognitions or feelings. ... Quality refers to the inherent or distinctive characteristics or properties of a person, object, process or other thing. ... An interpretant, in Semiotics, is the effect of a sign on someone who reads or comprehends it. ... WordNet gives four main senses for the English noun object: a physical entity; something that is within the grasp of the senses; an aim, target or objective — see Object (task); a grammatical Object — either a direct object or an indirect object the focus of cognitions or feelings. ... WordNet gives four main senses for the English noun object: a physical entity; something that is within the grasp of the senses; an aim, target or objective — see Object (task); a grammatical Object — either a direct object or an indirect object the focus of cognitions or feelings. ...

Peirce (CP 2.228-230) stipulated that signhood requires that four conditions be met (Liszka 1996: 18-19). A sign must:

• Representative: Represent, or correlate with, an Object.
• Presentative: Satisfy the Representative condition with respect to some capacity, i.e., the Ground of the sign.
• Interpretive: Determine, potentially if not actually, an Interpretant, i.e., a sign that translates and extends the original sign in the mind of some interpreter.
• Triadic relation: Give rise to an irreducibly triadic relation among Sign, Object, and Interpretant. "Triadic relation" is here employed in the sense of mathematical logic.

The following table (Deledalle 2000: 19) captures the essence of the semeiotic:

Moreover, there are three types of argument: deduction, induction, and abduction; see section 3.2 above. The type-token distinction later proved crucial to the thinking of Frank P. Ramsey. Frank Plumpton Ramsey (February 22, 1903 – January 19, 1930) was a British mathematician, philosopher and economist. ...

Peirce never wrote a definitive treatment of his semeiotic, instead revisiting it intermittently, renaming certain concepts several times and altering the definitions of key terms. His correspondence over 1903-1911 with Victoria, Lady Welby, published in Hardwick (2001), contains much bearing on his mature views. Also see his unpublished 1894 essay "What Is a Sign?". Liszka (1996) and Deledalle (2000) are earnest attempts at a coherent exposition of the semeiotic. Victoria, Lady Welby (1837–1912), also styled the Hon. ...

Examples of sign relations

(Text in preparation, 20 January 2006)

References

See also

• Finitary or polyadic relation

In mathematics, an n-ary relation (or n-place relation or often simply relation) is a generalization of binary relations such as = and < which occur in statements such as 5 < 6 or 2 + 2 = 4. It is the fundamental notion in the relational model for databases. ...

External links

• The Commens Dictionary of Peirce's Terms
  • Entry for Semeiotic