Abstract
Aristotle’s core conception of abstraction (
) is: selective attention
. Although he at times uses ‘abstraction’ in the sense of ‘subtraction
’ of the Greek mathematicians, Aristotle extends the use to other cases where certain aspects of an object are focused upon and selected out. Aristotle then allows for these aspects to be treated in the sciences as if they were subjects in their own right, in a way to which Frege
would object. Unlike the later British empiricists, Aristotle takes abstraction to isolate real aspects of objects and not to construct concepts pertaining only to how we think of the world.
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Notes
- 1.
LSJ s. v.
and 
. - 2.
Although some have argued that Aristotle or some Aristotelian commentators took geometry to be about the particular figures and diagrams perceived by the senses. See Mueller 1979 for a general discussion.
- 3.
Reeve (2000) also recognizes both universal and particular intelligible matter , as I shall discuss more below.
- 4.
Unless Aristotle holds that these individuals are abstracted directly from perceptions of individual substances . On this account, e.g., when I see a particular bronze sphere, upon abstraction I have also an individual sphere, the mathematical object . So too when I see the iron sphere I see another individual sphere. Also, looking at the spheres, I have upon abstraction an individual 2, an individual mathematical object . Cf. Simplicius , in Cat. 124, 28–125, 2. Yet, even so, if we are to have items in mathematics for which we have no exemplars in re, such as very large numbers or very complex geometrical figures, we still cannot reduce mathematical individuals directly to perceptible individuals.
- 5.
Moreover, as the equation itself can be stated or written in many particular speech acts or writing acts, the numeral itself will need to have some way to have many instances, just as we can have many repetitions of the same statement (
), as when we all utter the same true sentence in a chorus. Yet Aristotle does not seem to pursue this issue much, although some medieval Aristotelians did, in subdivisions of material supposition. - 6.
“…objects in the world…present themselves as concrete individuals and simultaneously as exemplifications of universals” (Modrak 2001: 96).
- 7.
- 8.
I agree with Cleary (1985: 15) that either translation is possible.
- 9.
Barnes (1975: 161) notes that Aristotle claims here only that induction can make abstractions familiar to us, not that it alone can do so. He claims that Aristotle argues for that stronger claim at An. 432a3–6 [discussed below].
- 10.
Cleary (1995: 488) agrees that abstraction/subtraction is not a third way of learning, in addition to demonstration and induction .
- 11.
Scaltsas (1994: 11–2, 34, 116) suggests that abstraction generates two objects. However he focuses on the abstraction of matter and form from a substance, and there we have a form, capable of definition, and, with the ultimate if not the proximate matter, an indefinite stuff. So unlike subtraction abstraction does not yield two equally definite things.
- 12.
Lewis (1991: 286–7, 307) takes ‘
’ as ‘stripping off’ as Descartes
speaks of stripping off the attributes of the piece of wax in Meditation 2. He ends up calling this “selective inattention”. - 13.
On the status of differentiae and propria , see Bäck (2000: 151–8).
- 14.
Reeve (2000: 40) translates ‘
’ as “positing”, with “abstraction” for ‘
’. But this seems too far removed from the mathematical background of the two terms. - 15.
Rollinger (1993: 13, n. 21) has likewise used ‘selective attention ’ to characterize Meinong’s view, although not in the same sense. Studtmann (2002: 219) has noted that some scholars have taken Aristotle’s abstraction as selective attention . Annas (1976: 29–30) finds this vague, as Aristotle has no formal theory of abstraction. We shall see.
Bodéüs (2001: 124) defines periaireo as ‘to find a remainder while suppressing all the rest’; cf. Metaphysics 1029a11–2. This interpretation of Aristotle would make him fit in not too badly with work on perception and cognition in modern psychology. See, e.g., Ballard 1996: 116–9.
- 16.
Bechler (1995: 171) goes on to say that “…by qua as an abstraction operator Aristotle means an infinite, or absolute potentiality , construction.” (He gets this from the mathematical texts, where the items abstracted, like line and point, do not seem to exist in perceptible substances.)
- 17.
Likewise Detel (1993: 211–4) takes intelligible matter to be the spatial continuum.
- 18.
As discussed above re types and tokens.
- 19.
Of course, in the case of animals, certain types of selective attention may require consciousness. My conception of selective attention agrees with Caston 2002: 759: “…Aristotle cannot plausibly mean that animals are continually aware of such changes as a result of deliberately observing them and directing their intention towards them.” I.e., not introspection; rather: “not unaware” [Phys. 244b12–245a2; cf. 437a26–9; 447a15–7] in “an unobtrusive way”. Also Wedin 1993: 153: “…an object is suitable for consideration in abstraction only if there is no such object, but we nevertheless have some idea of what such an object would be like.” Cf. Wedin 1989.
- 20.
So too Spruyt 2004: 126–7.
- 21.
- 22.
- 23.
Trans. Findlay 1970 II.
- 24.
- 25.
Thus, for instance according to Priest (2006: 73) abstraction occurs when “the factors which are deemed to be of central importance are selected out …other factors which are of no or of only secondary importance are ignored.”
- 26.
Mackie (1976: 107–12) and Taylor (1978) argue that Locke takes abstraction to be selective attention . Cf. Essays II.13.13. Winkler (1989: 40–1) claims that Locke does not connect up selective attention with abstraction. Donald Baxter (1997: 314–5) takes Locke, Berkeley and Hume to remove properties to get an idea in abstraction. But see his n. 59 & 328–9 where Baxter cites many who take Locke to have a view of selective attention . Baxter attributes that to Berkeley but not to Locke.
- 27.
Cf. Skirry 2004; Flage 1987: 21; Winkler 1989: 37.
On the empiricist side: John Norris (1701–1704) says that when things are really distinct considering them separately is not abstraction. Abstraction is “the drawing away of a thing from its self.” Isaac Watts (1725: 200) says that negative abstraction: consider things apart which can exist separately; precisive abstraction: consider things apart which cannot exist separately. Thomas Reid (Essays on the Intellectual Powers V.vi) calls the separation of two singular qualities that appear together “abstraction strictly so called”; the latter “generalizing”. Cf. Winkler 1989: 26–8.
- 28.
Cf. van der Schaar 2004: 208.
- 29.
Quoted in Angelelli 1984: 458.
- 30.
Cf. Dummett 1981: 402: “Frege has laid down that the value-range of a function f is the same as that of a function g…just in case f and g have the same value for every argument.” Frege then says that this does not suffice “to determine uniquely the reference of every value-range term.” “…for an object not given as a value-range, we have no means of deciding whether it is a value-range …”
Frege ’s method of definition by abstraction is having a current renaissance though. Cf. K. Fine 2002; the articles by Fine and Wright in Schirn 1998; Wright 1983, 1997, 1999; Schirn 1996.
- 31.
and 
.
), as when we all utter the same true sentence in a chorus. Yet Aristotle does not seem to pursue this issue much, although some medieval Aristotelians did, in subdivisions of material supposition.
’ as ‘stripping off’ as Descartes
speaks of stripping off the attributes of the piece of wax in Meditation 2. He ends up calling this “selective inattention”.
’ as “positing”, with “abstraction” for ‘
’. But this seems too far removed from the mathematical background of the two terms.References
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Bäck, A. (2014). The Conception of Abstraction. In: Aristotle's Theory of Abstraction. The New Synthese Historical Library, vol 73. Springer, Cham. https://doi.org/10.1007/978-3-319-04759-1_2
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