## Abstract

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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## Notes

- 1.
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.* - 2.
Before we explicate the notion of concept, we will use capitals to indicate that we mean the respective concept.

- 3.
See Carnap (1950), §2-3

- 4.
- 5.
Cf. Materna, Petrželka (2008).

- 6.
- 7.
More generally: see Ad ii).

- 8.
“Of the sense we say that it

*determines*the denotation, or*is a concept*of the denotation.” - 9.
“…anything which is capable of being the sense of some name in some language, actual or possible, is a concept” (Church 1985, p. 41).

- 10.
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. - 11.
Carnap himself did not accept Quine´s critique.

- 12.
The detailed story of Church´s creating his alternatives and his final choice can be found in Anderson (1998).

- 13.
See also Jespersen (2010)

- 14.
“Intensions” here are not the standard intensions, i.e. functions from possible worlds.

- 15.
Cresswell recognized the role of functions as “a universal medium of explication, not just in mathematics but in general” (Tichý, see above).

- 16.
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).

- 17.
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. - 18.
Otherwise, we would have to define such a language, which would lead to an infinite regress.

- 19.
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. - 20.
By ‘planet’ we mean here ‘planet of our Solar system’.

- 21.
Not taking into account the mentalist, cognitivist theories.

- 22.
Of course, these proponents of concept complexity would appreciate Bolzano as well.

- 23.
*the*is a function that is defined only on Singletons K and constructs that unique member of K. - 24.
When not specified, we mean real numbers.

- 25.
α- and η-equivalence: terminology of λ-calculi.

- 26.
See Ken Daley (2009), where the notion of

*simplification*is defined. - 27.
See Materna (2004, p.2.2).

- 28.
It is unnecessary (and often impossible) to present some fictive conceptual systems in a way other than as fragments relevant for some purpose.

- 29.
See Duží (2010), where refinement was first defined. Our Definition 12 is the Definition 5.5 from DJM, p. 524.

- 30.
Types of expressions are derivatively the same as the types of respective denotations.

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## Acknowledgements

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

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### Keywords

- Concept
- Conceptual system
- Constructions
- Set-theoretical paradigm
- Transparent intensional logic