15 ideas
| 8755 | Maddy replaces pure sets with just objects and perceived sets of objects [Maddy, by Shapiro] |
| Full Idea: Maddy dispenses with pure sets, by sketching a strong set theory in which everything is either a physical object or a set of sets of ...physical objects. Eventually a physiological story of perception will extend to sets of physical objects. | |
| From: report of Penelope Maddy (Realism in Mathematics [1990]) by Stewart Shapiro - Thinking About Mathematics 8.3 | |
| A reaction: This doesn't seem to find many supporters, but if we accept the perception of resemblances as innate (as in Hume and Quine), it is isn't adding much to see that we intrinsically see things in groups. |
| 10718 | A natural number is a property of sets [Maddy, by Oliver] |
| Full Idea: Maddy takes a natural number to be a certain property of sui generis sets, the property of having a certain number of members. | |
| From: report of Penelope Maddy (Realism in Mathematics [1990], 3 §2) by Alex Oliver - The Metaphysics of Properties | |
| A reaction: [I believe Maddy has shifted since then] Presumably this will make room for zero and infinities as natural numbers. Personally I want my natural numbers to count things. |
| 8756 | Intuition doesn't support much mathematics, and we should question its reliability [Maddy, by Shapiro] |
| Full Idea: Maddy says that intuition alone does not support very much mathematics; more importantly, a naturalist cannot accept intuition at face value, but must ask why we are justified in relying on intuition. | |
| From: report of Penelope Maddy (Realism in Mathematics [1990]) by Stewart Shapiro - Thinking About Mathematics 8.3 | |
| A reaction: It depends what you mean by 'intuition', but I identify with her second objection, that every faculty must ultimately be subject to criticism, which seems to point to a fairly rationalist view of things. |
| 17733 | We know mind-independent mathematical truths through sets, which rest on experience [Maddy, by Jenkins] |
| Full Idea: Maddy proposes that we can know (some) mind-independent mathematical truths through knowing about sets, and that we can obtain knowledge of sets through experience. | |
| From: report of Penelope Maddy (Realism in Mathematics [1990]) by Carrie Jenkins - Grounding Concepts 6.5 | |
| A reaction: Maddy has since backed off from this, and now tries to merely defend 'objectivity' about sets (2011:114). My amateurish view is that she is overrating the importance of sets, which merely model mathematics. Look at category theory. |
| 12312 | The real essence of a thing is its powers, or 'dispositional properties' [Copi] |
| Full Idea: With respect to scientific usage, we can say that the real essence of a thing will consist very largely of powers or, in modern terms, dispositional properties. | |
| From: Irving M. Copi (Essence and Accident [1954], p.718) | |
| A reaction: Once again, Copi is a hero. I personally love the word 'powers' in metaphysics (and dislike the word 'properties', which is lost in a fog of confusion). See Molnar on 'powers' and Mumford on 'dispositions'. |
| 10937 | Essential properties are the 'deepest' ones which explain the others [Copi, by Rami] |
| Full Idea: The 'explanatory characterization' says that the essential properties of an object are the object's deepest explanatory properties, which explain the other properties of the object - and which Copi claims is mind-independent. | |
| From: report of Irving M. Copi (Essence and Accident [1954]) by Adolph Rami - Essential vs Accidental Properties §2 | |
| A reaction: It is, of course, normal to see a good explanation as being dependent on the interests of the audience. Perhaps this account should be in terms of causal powers. See Shoemaker on properties. |
| 12308 | In modern science, nominal essence is intended to be real essence [Copi] |
| Full Idea: In the sphere of scientific enquiry the distinction between real and nominal essence tends to disappear; the scientist's classification of things is intended to be in terms of their real essences. | |
| From: Irving M. Copi (Essence and Accident [1954], p.716) | |
| A reaction: Thus we have disputes over what is the 'real' classification of natural kinds such as animals. There is not much point in a classification system that does not at least reflect some aspects of reality. |
| 12303 | Within the four types of change, essential attributes are those whose loss means destruction [Copi] |
| Full Idea: If we can distinguish the different kinds of change (alteration, locomotion, growth, diminution), then we can say that a given attribute is essential to an object if its loss would result in the destruction of that object. | |
| From: Irving M. Copi (Essence and Accident [1954], p.707-8) | |
| A reaction: As Copi is aware, this is a necessary condition for a property for essence, but not sufficient. If an attribute were necessary but non-essential, its loss would also be destruction. We say the essential attributes must also have some explanatory role. |
| 13195 | To explain a house we must describe its use, as well as its parts [Leibniz] |
| Full Idea: A house would be badly explained if we were to describe only the arrangement of its parts, but not its use. | |
| From: Gottfried Leibniz (On Body and Force, Against the Cartesians [1702], p.255) | |
| A reaction: This must partly fall under pragmatics (i.e. what the enquirer is interested in). But function plays a genuine role in artefacts, and also in evolved biological organs. |
| 13193 | Active force is not just potential for action, since it involves a real effort or striving [Leibniz] |
| Full Idea: Active force should not be thought of as the simple and common potential [potentia] or receptivity to action of the schools. Rather, active force involves an effort [conatus] or striving [tendentia] toward action. | |
| From: Gottfried Leibniz (On Body and Force, Against the Cartesians [1702], p.252) | |
| A reaction: This is why Leibniz is lured into making his active forces more and more animistic, till they end up like proto-minds (though never, remember, conscious and willing minds). |
| 13194 | God's laws would be meaningless without internal powers for following them [Leibniz] |
| Full Idea: To say that, in creation, God gave bodies a law for acting means nothing, unless, at the same time, he gave them something by means of which it could happen that the law is followed. | |
| From: Gottfried Leibniz (On Body and Force, Against the Cartesians [1702], p.253) | |
| A reaction: This is the beginning of the modern rebellion against the medieval view of laws as imposed from outside on passive matter. Unfortunately for Leibniz, once you have postulated active internal powers, the external laws become redundant. |
| 12307 | Modern science seeks essences, and is getting closer to them [Copi] |
| Full Idea: Modern science seeks to know the real essences of things, and its increasing successes seem to be bringing it progressively nearer to that goal. | |
| From: Irving M. Copi (Essence and Accident [1954], p.715) | |
| A reaction: This is from a notable pioneering paper, which outlined scientific essentialism even before Marcus and Kripke began to offer a modern account of essence to give it backing. Compare Popper, who thinks essences are will-o-the-wisps. |
| 12310 | Real essences are scientifically knowable, but so are non-essential properties [Copi] |
| Full Idea: Contrary to Locke, I should hold that real essences are in principle knowable, and contrary to Aristotle, I should hold that non-essential or accidental properties can also be objects of scientific knowledge. | |
| From: Irving M. Copi (Essence and Accident [1954], p.717) | |
| A reaction: Copi has just become my hero. Aristotle's account of definition is on the brink of allowing fine-tuned essences, but he thinks universal understanding blocks knowledge of individuals. But cross-referencing of universals pinpoints individuals. |
| 13196 | All qualities of bodies reduce to forces [Leibniz] |
| Full Idea: All qualities of bodies .....are in the end reduced [revoco] to forces. | |
| From: Gottfried Leibniz (On Body and Force, Against the Cartesians [1702], p.256) | |
| A reaction: The dots conceal a long qualification, but he is essentially standing by this simple remark. If you substitute the word 'powers' for 'forces', I think that is just about right. |
| 13192 | Power is passive force, which is mass, and active force, which is entelechy or form [Leibniz] |
| Full Idea: The dynamicon or power [potentia] in bodies is twofold, passive and active. Passive force [vis] constitutes matter or mass [massa], and active force constitutes entelechy or form. | |
| From: Gottfried Leibniz (On Body and Force, Against the Cartesians [1702], p.252) | |
| A reaction: This is explicitly equating the innate force understood in physics with Aristotelian form. The passive force is to explain the resistance of bodies. I like the equation of force with power. He says the entelechy is 'analogous' to a soul. |