Editing Charles Sanders Peirce (section)

==== Logic as formal semiotic ====
Peirce sought, through his wide-ranging studies through the decades, formal philosophical ways to articulate thought's processes, and also to explain the workings of science. These inextricably entangled questions of a dynamics of inquiry rooted in nature and nurture led him to develop his semiotic with very broadened conceptions of signs and inference, and, as its culmination, a theory of inquiry for the task of saying 'how science works' and devising research methods. This would be logic by the medieval definition taught for centuries: art of arts, science of sciences, having the way to the principles of all methods.<ref name="ars"/> Influences radiate from points on parallel lines of inquiry in [[Aristotle]]'s work, in such ''loci'' as: the basic terminology of [[psychology]] in ''[[On the Soul]]''; the founding description of [[sign relation]]s in ''[[On Interpretation]]''; and the differentiation of [[inference]] into three modes that are commonly translated into English as ''[[Abductive reasoning|abduction]]'', ''[[Deductive reasoning|deduction]]'', and ''[[Inductive reasoning|induction]]'', in the ''[[Prior Analytics]]'', as well as inference by [[analogy]] (called ''paradeigma'' by Aristotle), which Peirce regarded as involving the other three modes.

Peirce began writing on semiotic in the 1860s, around the time when he devised his system of three categories. He called it both ''[[semiotic]]'' and ''semeiotic''. Both are current in singular and plural. He based it on the conception of a triadic [[sign relation]], and defined ''[[semiosis]]'' as "action, or influence, which is, or involves, a cooperation of ''three'' subjects, such as a sign, its object, and its interpretant, this tri-relative influence not being in any way resolvable into actions between pairs".<ref>Peirce 1907, ''Collected Papers of Charles Sanders Peirce'', 5.484. Reprinted, ''The Essential Peirce'', 2:411 in "Pragmatism" (398–433).</ref> As to signs in thought, Peirce emphasized the reverse: "To say, therefore, that thought cannot happen in an instant, but requires a time, is but another way of saying that every thought must be interpreted in another, or that all thought is in signs."<ref name="QFM"/>

Peirce held that all thought is in signs, issuing in and from interpretation, where ''sign'' is the word for the broadest variety of conceivable semblances, diagrams, metaphors, symptoms, signals, designations, symbols, texts, even mental concepts and ideas, all as determinations of a mind or ''quasi-mind'', that which at least functions like a mind, as in the work of crystals or bees<ref>See "[http://www.helsinki.fi/science/commens/terms/quasimind.html Quasi-mind]" in ''Commens Digital Companion to C.S. Peirce''.</ref>—the focus is on sign action in general rather than on psychology, linguistics, or social studies (fields which he also pursued).

Inquiry is a kind of inference process, a manner of thinking and semiosis. Global divisions of ways for phenomena to stand as signs, and the subsumption of inquiry and thinking within inference as a sign process, enable the study of inquiry on semiotics' three levels:

# Conditions for meaningfulness. Study of significatory elements and combinations, their grammar.
# Validity, conditions for true representation. Critique of arguments in their various separate modes.
# Conditions for determining interpretations. Methodology of inquiry in its mutually interacting modes.

Peirce uses examples often from common experience, but defines and discusses such things as assertion and interpretation in terms of philosophical logic. In a formal vein, Peirce said:

{{quote|''On the Definition of Logic''. Logic is ''formal semiotic''. A sign is something, ''A'', which brings something, ''B'', its ''interpretant'' sign, determined or created by it, into the same sort of correspondence (or a lower implied sort) with something, ''C'', its ''object'', as that in which itself stands to ''C''. This definition no more involves any reference to human thought than does the definition of a line as the place within which a particle lies during a lapse of time. It is from this definition that I deduce the principles of logic by mathematical reasoning, and by mathematical reasoning that, I aver, will support criticism of [[Weierstrass]]ian severity, and that is perfectly evident. The word "formal" in the definition is also defined.<ref>Peirce, "Carnegie Application", ''[[#NEM|The New Elements of Mathematics]]'' v. 4, p. 54.</ref>}}