Combining Philosophers

All the ideas for H.Putnam/P.Oppenheim, Nicholas P. White and Daniel Garber

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5 ideas

5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems
17813 Löwenheim-Skolem says any theory with a true interpretation has a model in the natural numbers [White,NP]
     Full Idea: The Löwenheim-Skolem theorem tells us that any theory with a true interpretation has a model in the natural numbers.
     From: Nicholas P. White (What Numbers Are [1974], V)
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
17812 Finite cardinalities don't need numbers as objects; numerical quantifiers will do [White,NP]
     Full Idea: Statements involving finite cardinalities can be made without treating numbers as objects at all, simply by using quantification and identity to define numerically definite quantifiers in the manner of Frege.
     From: Nicholas P. White (What Numbers Are [1974], IV)
     A reaction: [He adds Quine 1960:268 as a reference]
7. Existence / C. Structure of Existence / 6. Fundamentals / c. Monads
12695 Epicurean atomists say body is sensible, to distinguish it from space. [Garber]
     Full Idea: The Epicurean atomists also defined body in terms of the property of being sensible, in order to distinguish it from empty space, which is not sensible.
     From: Daniel Garber (Leibniz:Body,Substance,Monad [2009], 1)
     A reaction: This is a very illuminating bit of background, for those of us who have the knee-jerk reaction that monadology is barking mad.
14. Science / D. Explanation / 2. Types of Explanation / j. Explanations by reduction
20653 Six reduction levels: groups, lives, cells, molecules, atoms, particles [Putnam/Oppenheim, by Watson]
     Full Idea: There are six 'reductive levels' in science: social groups, (multicellular) living things, cells, molecules, atoms, and elementary particles.
     From: report of H.Putnam/P.Oppenheim (Unity of Science as a Working Hypothesis [1958]) by Peter Watson - Convergence 10 'Intro'
     A reaction: I have the impression that fields are seen as more fundamental that elementary particles. What is the status of the 'laws' that are supposed to govern these things? What is the status of space and time within this picture?
26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / g. Atomism
12705 Epicurean atoms are distinguished by their extreme hardness [Garber]
     Full Idea: In Epicurean atomism (of Cordemoy, for example) there is a world of basic things distinguished by virtue of their extreme hardness.
     From: Daniel Garber (Leibniz:Body,Substance,Monad [2009], 2)
     A reaction: Garber says that Leibniz espouses 'substantial atomism', which is different from this. Leibniz's atoms have active power, where these atoms just embody total resistance.