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Ideas for 'Thinking About Mathematics', 'Summa quaestionum super Sententias' and 'Physics'

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4 ideas

8. Modes of Existence / A. Relations / 1. Nature of Relations
The separation from here to there is not the same as the separation from there to here [Aristotle]
     Full Idea: Even though two separated things have a single interval between them, still the separation from here to there is not one and the same as the separation from there to here.
     From: Aristotle (Physics [c.337 BCE], 202b19)
     A reaction: His example is the road from Athens to Thebes. Since we tend to quantify distances between places more than Aristotle did, we are less impressed by this distinction, which seems a bit subjective. Aristotle seems to be thinking of vectors.
Relations do not add anything to reality, though they are real aspects of the world [Olivi]
     Full Idea: It does not seem that a relation adds anything real to that on which it is founded, but only makes for another real aspect belonging to the same thing. It is real since an aspect exists in re, not solely in the intellect, but it is not another thing.
     From: Peter John Olivi (Summa quaestionum super Sententias [1290], II.54), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 12.4
8. Modes of Existence / B. Properties / 8. Properties as Modes
The features of a thing (whether quality or quantity) are inseparable from their subjects [Aristotle]
     Full Idea: It is impossible to separate [affections/accidents], both in respect of quantity and of quality - of quantity, because there is no minimum magnitude, and of quality, because affections are inseparable.
     From: Aristotle (Physics [c.337 BCE], 188a11)
     A reaction: This is an aspect of his famous view that universals, if there are such, are inherent in objects, and can't float free. It was important for scholastic philosophers, who need accidents to float free for the doctrine of Transubstantiation.
8. Modes of Existence / C. Powers and Dispositions / 1. Powers
Heavy and light are defined by their tendency to move down or up [Aristotle]
     Full Idea: It is the nature of light and heavy things to tend in certain directions, and this is what it is to be light or heavy; to be light is defined by an upwards tendency, and to be heavy is defined by a downwards tendency.
     From: Aristotle (Physics [c.337 BCE], 255b14)
     A reaction: The discredited 'teleological' view of gravity, and yet if we define 'heavy' in Newtonian terms we are in danger of circularity, and of proposing laws which are bafflingly imposed from outside. Hence the 'New Essentialists' prefer Aristotle's view.