13 ideas
| 12302 | Definitions formed an abstract hierarchy for Aristotle, as sets do for us [Fine,K] |
| Full Idea: For us it is sets which constitute the most natural example of a hierarchical structure within the abstract realm; but for Aristotle it would have been definitions, via their natural division into genus and differentia. | |
| From: Kit Fine (Aristotle on Matter [1992], §1 n4) | |
| A reaction: I suppose everyone who thinks about reality in abstraction ends up with a hierarchy. Compare the hierarchy of angelic hosts, or Greek gods. Could we get back to the Aristotelian view, instead of sets, which are out of control at the top end? |
| 14266 | Aristotle sees hierarchies in definitions using genus and differentia (as we see them in sets) [Fine,K] |
| Full Idea: For us, sets constitute the most natural example of a hierarchical structure within the abstract realm. But for Aristotle it would have been definitions, via their natural division into genus and differentia. | |
| From: Kit Fine (Aristotle on Matter [1992], 1 n4) | |
| A reaction: Genus and differentia are only part of the story in Aristotle, and this remarks strikes me as perceptive. It is precisely the mapping of the explanatory hierarchy which Aristotle seeks in a good definition. |
| 18170 | The Axiom of Reducibility is self-effacing: if true, it isn't needed [Quine] |
| Full Idea: The Axiom of Reducibility is self-effacing: if it is true, the ramification it is meant to cope with was pointless to begin with. | |
| From: Willard Quine (Introduction to Russell's Theory of Types [1967], p.152), quoted by Penelope Maddy - Naturalism in Mathematics I.1 | |
| A reaction: Maddy says the rejection of Reducibility collapsed the ramified theory of types into the simple theory. |
| 14268 | Maybe bottom-up grounding shows constitution, and top-down grounding shows essence [Fine,K] |
| Full Idea: It may be that the two forms of grounding have a different source; the one from the bottom up is required for the constitution of the thing to be intelligible; the one from the top down is required for the essence of the thing to be intelligible. | |
| From: Kit Fine (Aristotle on Matter [1992], 2) | |
| A reaction: [He cites Aristotle Met. 1019a8-10 in support] Close reading of Fine would be needed to elucidate this properly, but it is a suggestive line of thought about how we should approach grounding. |
| 10502 | We can rise by degrees through abstraction, with higher levels representing more things [Arnauld,A/Nicole,P] |
| Full Idea: I can start with a triangle, and rise by degrees to all straight-lined figures and to extension itself. The lower degree will include the higher degree. Since the higher degree is less determinate, it can represent more things. | |
| From: Arnauld / Nicole (Logic (Port-Royal Art of Thinking) [1662], I.5) | |
| A reaction: [compressed] This attempts to explain the generalising ability of abstraction cited in Idea 10501. If you take a complex object and eliminate features one by one, it can only 'represent' more particulars; it could hardly represent fewer. |
| 14267 | There is no distinctive idea of constitution, because you can't say constitution begins and ends [Fine,K] |
| Full Idea: If the parts of a body can constitute a man, then why should men not constitute a family? Why draw the line at the level of the man? ...Thus the idea of a distinctive notion of constitution, terminating in concrete substances, should be given up. | |
| From: Kit Fine (Aristotle on Matter [1992], 1) | |
| A reaction: This is in the context of Aristotle, but Fine's view seems to apply to Rudder Baker's distinctive approach. |
| 14264 | Is there a plausible Aristotelian notion of constitution, applicable to both physical and non-physical? [Fine,K] |
| Full Idea: There is a question of whether there is a viable conception of constitution of the sort Aristotle supposes, one which is uniformly applicable to physical and non-physical objects alike, and which is capable of hierarchical application. | |
| From: Kit Fine (Aristotle on Matter [1992], 1) | |
| A reaction: This is part of an explication of Aristotle's 'matter' [hule], which might be better translated as 'ingredients', which would fit non-physical things quite well. |
| 18258 | We can only know the exterior world via our ideas [Arnauld,A/Nicole,P] |
| Full Idea: We can have knowledge of what is outside us only through the mediation of ideas in us. | |
| From: Arnauld / Nicole (Logic (Port-Royal Art of Thinking) [1662], p.63), quoted by J. Alberto Coffa - The Semantic Tradition from Kant to Carnap 1 'Conc' |
| 16784 | Forms make things distinct and explain the properties, by pure form, or arrangement of parts [Arnauld,A/Nicole,P] |
| Full Idea: The form is what renders a thing such and distinguishes it from others, whether it is a being really distinct from the matter, according to the Schools, or whether it is only the arrangement of the parts. By this form one must explain its properties. | |
| From: Arnauld / Nicole (Logic (Port-Royal Art of Thinking) [1662], III.18 p240), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 27.6 | |
| A reaction: If we ask 'what explains the properties of this thing' it is hard to avoid coming up with something that might be called the 'form'. Note that they allow either substantial or corpuscularian forms. It is hard to disagree with the idea. |
| 10499 | We know by abstraction because we only understand composite things a part at a time [Arnauld,A/Nicole,P] |
| Full Idea: The mind cannot perfectly understand things that are even slightly composite unless it considers them a part at a time. ...This is generally called knowing by abstraction. (..the human body, for example). | |
| From: Arnauld / Nicole (Logic (Port-Royal Art of Thinking) [1662], I.5) | |
| A reaction: This adds the interesting thought that the mind is forced to abstract, rather than abstraction being a luxury extra feature. Knowledge through analysis is knowledge by abstraction. Also a nice linking of abstraction to epistemology. |
| 10501 | A triangle diagram is about all triangles, if some features are ignored [Arnauld,A/Nicole,P] |
| Full Idea: If I draw an equilateral triangle on a piece of paper, ..I shall have an idea of only a single triangle. But if I ignore all the particular circumstances and focus on the three equal lines, I will be able to represent all equilateral triangles. | |
| From: Arnauld / Nicole (Logic (Port-Royal Art of Thinking) [1662], I.5) | |
| A reaction: [compressed] They observed that we grasp composites through their parts, and now that we can grasp generalisations through particulars, both achieved by the psychological act of abstraction, thus showing its epistemological power. |
| 10500 | No one denies that a line has width, but we can just attend to its length [Arnauld,A/Nicole,P] |
| Full Idea: Geometers by no means assume that there are lines without width or surfaces without depth. They only think it is possible to consider the length without paying attention to the width. We can measure the length of a path without its width. | |
| From: Arnauld / Nicole (Logic (Port-Royal Art of Thinking) [1662], I.5) | |
| A reaction: A nice example which makes the point indubitable. The modern 'rigorous' account of abstraction that starts with Frege seems to require more than one object, in order to derive abstractions like direction or number. Path widths are not comparatives. |
| 14265 | The components of abstract definitions could play the same role as matter for physical objects [Fine,K] |
| Full Idea: If one considers Aristotle's standard example of a definition, then it is plausible that its defining terms ('plane figure' in the case of a circle) should be constitutive of it in the same general way as physical matter constitutes something physical. | |
| From: Kit Fine (Aristotle on Matter [1992], 1) | |
| A reaction: It strikes me that an appropriate translation for the Greek 'hule' might be the English 'ingredients', since Fine seems to be right about the broad application of hule in Aristotle. |