Combining Texts

All the ideas for 'fragments/reports', 'Explanation in Mathematics' and 'Metaphysics: a very short introduction'

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6 ideas

1. Philosophy / D. Nature of Philosophy / 3. Philosophy Defined
Even pointing a finger should only be done for a reason [Epictetus]
     Full Idea: Philosophy says it is not right even to stretch out a finger without some reason.
     From: Epictetus (fragments/reports [c.57], 15)
     A reaction: The key point here is that philosophy concerns action, an idea on which Epictetus is very keen. He rather despise theory. This idea perfectly sums up the concept of the wholly rational life (which no rational person would actually want to live!).
9. Objects / B. Unity of Objects / 2. Substance / a. Substance
Substances, unlike aggregates, can survive a change of parts [Mumford]
     Full Idea: Substances can survive a change in their parts in a way that a mere aggregate of parts.
     From: Stephen Mumford (Metaphysics: a very short introduction [2012], 3)
     A reaction: A simple but very important idea. If we then distinguish between 'substances' and 'aggregates' we get a much clearer grip on things. Is the Ship of Theseus a substance or an aggregate? There is no factual answer to that. What do you want to explain?
9. Objects / D. Essence of Objects / 7. Essence and Necessity / b. Essence not necessities
Essences are no use in mathematics, if all mathematical truths are necessary [Mancosu]
     Full Idea: Essences and essential properties do not seem to be useful in mathematical contexts, since all mathematical truths are regarded as necessary (though Kit Fine distinguishes between essential and necessary properties).
     From: Paolo Mancosu (Explanation in Mathematics [2008], §6.1)
     A reaction: I take the proviso in brackets to be crucial. This represents a distortion of notion of an essence. There is a world of difference between the central facts about the nature of a square and the peripheral inferences derivable from it.
10. Modality / B. Possibility / 3. Combinatorial possibility
Maybe possibilities are recombinations of the existing elements of reality [Mumford]
     Full Idea: It has been suggested that we could think of possibilities as recombinations of all the existing elements of reality.
     From: Stephen Mumford (Metaphysics: a very short introduction [2012], 8)
     A reaction: [Armstrong 1989 is the source] The obvious problem would be that the existence of an entirely different reality would be impossible, if this was all possibility could be. It seems to cramp the style of the possible too much. Are properties elements?
Combinatorial possibility has to allow all elements to be combinable, which seems unlikely [Mumford]
     Full Idea: The combinatorial account only works if you allow that the elements are recombinable. ...But could Lincoln really have been green? It seems possible that you could jump to the moon, unless we impose some restrictions.
     From: Stephen Mumford (Metaphysics: a very short introduction [2012], 8)
     A reaction: Mumford suggests different combination rules for logical and natural possibility. The general objection is that combinatorial possibility is too permissive - which it clearly is.
Combinatorial possibility relies on what actually exists (even over time), but there could be more [Mumford]
     Full Idea: Can combinatorial possibility deliver enough possibilities? It uses the existing elements, but there might have been one more particular or one more property. Even extended over time, the elements seem finite, yet there could have been more.
     From: Stephen Mumford (Metaphysics: a very short introduction [2012], 8)
     A reaction: [compressed] One objection is that the theory allows too much, and now the objection is that it allows too little. Both objections are correct, so that's the end of that. But I admire the attempt to base modality on actuality.