11 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. |
| 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). |
| 1748 | Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius] |
| Full Idea: Archelaus was the first person to say that the universe is boundless. | |
| From: report of Archelaus (fragments/reports [c.450 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 02.Ar.3 |
| 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. |
| 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. |
| 5989 | Archelaus said life began in a primeval slime [Archelaus, by Schofield] |
| Full Idea: Archelaus wrote that life on Earth began in a primeval slime. | |
| From: report of Archelaus (fragments/reports [c.450 BCE]) by Malcolm Schofield - Archelaus | |
| A reaction: This sounds like a fairly clearcut assertion of the production of life by evolution. Darwin's contribution was to propose the mechanism for achieving it. We should honour the name of Archelaus for this idea. |