Combining Texts

All the ideas for 'There Are No Abstract Objects', 'Statements about Universals' and 'Elements of Mathematical Logic'

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6 ideas

4. Formal Logic / E. Nonclassical Logics / 3. Many-Valued Logic
8942 Lukasiewicz's L3 logic has three truth-values, T, F and I (for 'indeterminate') [Lukasiewicz, by Fisher]
     Full Idea: In response to Aristotle's sea-battle problem, Lukasiewicz proposed a three-valued logic that has come to be known as L3. In addition to the values true and false (T and F), there is a third truth-value, I, meaning 'indeterminate' or 'possible'.
     From: report of Jan Lukasiewicz (Elements of Mathematical Logic [1928], 7.I) by Jennifer Fisher - On the Philosophy of Logic
     A reaction: [He originated the idea in 1917] In what sense is the third value a 'truth' value? Is 'I don't care' a truth-value? Or 'none of the above'? His idea means that formalization doesn't collapse when things get obscure. You park a few propositions under I.
8. Modes of Existence / D. Universals / 4. Uninstantiated Universals
8499 Nominalists cannot translate 'red resembles pink more than blue' into particulars [Jackson]
     Full Idea: It is not always possible for nominalists to translate all statements putatively about universals as statements about particulars. It is not possible for 'red is a colour' and 'red resembles pink more than blue'
     From: Frank Jackson (Statements about Universals [1977], p.89)
     A reaction: His second example strikes me as the biggest challenge facing nominalism. I wish they wouldn't use secondary qualities as examples. I am unconvinced that the existence of universals will improve the explanation. It's a mystery.
8. Modes of Existence / E. Nominalism / 1. Nominalism / c. Nominalism about abstracta
14596 Call 'nominalism' the denial of numbers, properties, relations and sets [Dorr]
     Full Idea: Just as there are no numbers or properties, there are no relations (like 'being heavier than' or 'betweenness'), or sets. I will provisionally use 'nominalism' for the conjunction of these four claims.
     From: Cian Dorr (There Are No Abstract Objects [2008], 1)
     A reaction: If you are going to be a nominalist, do it properly! My starting point in metaphysics is strong sympathy with this view. Right now [Tues 22nd Nov 2011, 10:57 am GMT] I think it is correct.
8. Modes of Existence / E. Nominalism / 2. Resemblance Nominalism
8500 Colour resemblance isn't just resemblance between things; 'colour' must be mentioned [Jackson]
     Full Idea: Some red things resemble some blue things more than some pink things because of factors other than colour. Nominalists must offer 'anything red colour-resembles anything pink', but that may contain a universal in disguise.
     From: Frank Jackson (Statements about Universals [1977], p.90)
     A reaction: Hume and Quine are probably right that we spot resemblances instantly, and only articulate the respect of the resemblance at a later stage.
8. Modes of Existence / E. Nominalism / 5. Class Nominalism
14597 Natural Class Nominalism says there are primitive classes of things resembling in one respect [Dorr]
     Full Idea: Natural Class Nominalists take as primitive the notion of a 'natural' class - a class of things that all resemble one another in some one respect and resemble nothing else in that respect.
     From: Cian Dorr (There Are No Abstract Objects [2008], 4)
     A reaction: Dorr rejects this view because he doesn't believe in 'classes'. How committed to classes do you have to be before you are permitted to talk about them? All vocabulary (such as 'resemble') seems metaphysically tainted in this area.
10. Modality / A. Necessity / 11. Denial of Necessity
14598 Abstracta imply non-logical brute necessities, so only nominalists can deny such things [Dorr]
     Full Idea: If there are abstract objects, there are necessary truths about these things that cannot be reduced to truths of logic. So only the nominalist, who denies that there are any such things, can adequately respect the idea that there are no brute necessities.
     From: Cian Dorr (There Are No Abstract Objects [2008], 4)
     A reaction: This is where two plates of my personal philosophy grind horribly against one another. I love nominalism, and I love natural necessities. They meet like a ring-species in evolution. I'll just call it a 'paradox', and move on (swiftly).