To talk about simple concepts presupposes that the notion of concept has been aptly explicated. I argue that a most adequate explication should abandon the set-theoretical paradigm and use a procedural approach. Such a procedural approach is offered by Tichý´s Transparent Intensional Logic (TIL). Some main notions and principles of TIL are briefly presented, and as a result, concepts are explicated as a kind of abstract procedure. Then it can be shown that simplicity, as applied to concepts, is well definable as a property relative to conceptual systems, each of which is determined by a finite set of simple (‘primitive’) concepts. Refinement as a method of replacing simple concepts by compound concepts is defined.
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Not taking into account idioms, of course, and not trying to get a most precise definition. As for idioms, it is clear that, e.g., an old maid need not be old or a maid and that old maid means the same property as spinster.
Before we explicate the notion of concept, we will use capitals to indicate that we mean the respective concept.
See Carnap (1950), §2-3
Cf. Materna, Petrželka (2008).
More generally: see Ad ii).
“Of the sense we say that it determines the denotation, or is a concept of the denotation.”
“…anything which is capable of being the sense of some name in some language, actual or possible, is a concept” (Church 1985, p. 41).
Why “constructing”? This will be clear later, below. Why not simply “a function”? Consider the principle Fu: I´ and II´ are one and the same function. Both expressions I and II would have one and the same sense.
Carnap himself did not accept Quine´s critique.
The detailed story of Church´s creating his alternatives and his final choice can be found in Anderson (1998).
See also Jespersen (2010)
“Intensions” here are not the standard intensions, i.e. functions from possible worlds.
Cresswell recognized the role of functions as “a universal medium of explication, not just in mathematics but in general” (Tichý, see above).
See Montague (1974). Montague´s system shares some features with TIL, but differs in some important points. First of all, it has not reached the higher levels of types and essentially remained on the set-theoretical 1st order λ-calculus. As for a critical comparison with TIL, see Tichý (1994) or DJM (2010).
The result of constructing often depends on valuation of variables (see later). Then construct means v-construct, where v is a parameter of valuation. We omit this v here.
Otherwise, we would have to define such a language, which would lead to an infinite regress.
This function associates every variable with an object. (Tarski´s definition!) A detailed explication can be found in Tichý (1988, p. 56–61). Remember also that the letters we usually declare to be variables (like x, y, z, …,f, g,…, m, n, …) are names of variables: the latter are special constructions and, therefore, extra-linguistic procedures.
By ‘planet’ we mean here ‘planet of our Solar system’.
Not taking into account the mentalist, cognitivist theories.
Of course, these proponents of concept complexity would appreciate Bolzano as well.
the is a function that is defined only on Singletons K and constructs that unique member of K.
When not specified, we mean real numbers.
α- and η-equivalence: terminology of λ-calculi.
See Ken Daley (2009), where the notion of simplification is defined.
See Materna (2004, p.2.2).
It is unnecessary (and often impossible) to present some fictive conceptual systems in a way other than as fragments relevant for some purpose.
See Duží (2010), where refinement was first defined. Our Definition 12 is the Definition 5.5 from DJM, p. 524.
Types of expressions are derivatively the same as the types of respective denotations.
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I am grateful to the anonymous reviewer for his/her valuable improvements of the text.
This paper has been supported by the Grant Agency of Czech Republic Project No. P401/10/0792.
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Materna, P. Simple Concepts. Acta Anal 28, 295–319 (2013). https://doi.org/10.1007/s12136-012-0176-y
- Conceptual system
- Set-theoretical paradigm
- Transparent intensional logic