7 ideas
18189 | ZFC could contain a contradiction, and it can never prove its own consistency [MacLane] |
Full Idea: We have at hand no proof that the axioms of ZFC for set theory will never yield a contradiction, while Gödel's second theorem tells us that such a consistency proof cannot be conducted within ZFC. | |
From: Saunders MacLane (Mathematics: Form and Function [1986], p.406), quoted by Penelope Maddy - Naturalism in Mathematics | |
A reaction: Maddy quotes this, while defending set theory as the foundation of mathematics, but it clearly isn't the most secure foundation that could be devised. She says the benefits of set theory do not need guaranteed consistency (p.30). |
17368 | Essentialism concerns the nature of a group, not its category [Devitt] |
Full Idea: Essentialism is concerned with the nature of a group, whatever the category it falls under. | |
From: Michael Devitt (Resurrecting Biological Essentialism [2008], 6) | |
A reaction: This seems to me such a simple and obvious point that I am amazed that anyone rejects it, yet lots of people seem to think that an essence is just some sort of category. |
17370 | Things that gradually change, like species, can still have essences [Devitt] |
Full Idea: An intrinsic essence does not have to be 'neat and tidy'. ...Essentialism can accept the gradual change of one thing into another. | |
From: Michael Devitt (Resurrecting Biological Essentialism [2008], 11) | |
A reaction: My thesis is that essentialism is a response to the needs of explanation, so as long as there is some core explanation to be found, even in something transitory, then the concept of an essence can apply to it. |
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 |
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. |
17369 | We name species as small to share properties, but large enough to yield generalisations [Devitt] |
Full Idea: Our explanatory purposes in introducing a name for a species demand that we draw the lines around a group that is small enough to share a whole lot of important properties and large enough to yield broad generalizations. | |
From: Michael Devitt (Resurrecting Biological Essentialism [2008], 10 'Arb') | |
A reaction: Grist to my mill. In this reaction slot (16th Oct 2013) I launch my new metaphysical school - welcome to EXPLANATIONISM! Folk metaphysics, and the best philosophical metaphysics, is entirely driven by the needs of explanation. |
17367 | Species are phenetic, biological, niche, or phylogenetic-cladistic [Devitt, by PG] |
Full Idea: The four main concepts of a species are 'phenetic' (similarity of traits), 'biological species' (interbreeding and isolated), 'ecological niche' (occupying an adaptive zone), or 'phylogenetic-cladistic' (start and finish at splits in lineage) | |
From: report of Michael Devitt (Resurrecting Biological Essentialism [2008], 4) by PG - Db (ideas) | |
A reaction: [my summary of Devitt's list] Devitt attacks the whole lot, in favour of essentialism - the species being fixed by its underlying explanatory mechanisms. |