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All the ideas for '', 'Freedom and Action' and 'Mathematics without Numbers'

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9 ideas

5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic

11211	If a sound conclusion comes from two errors that cancel out, the path of the argument must matter [Rumfitt]
	Full Idea: If a designated conclusion follows from the premisses, but the argument involves two howlers which cancel each other out, then the moral is that the path an argument takes from premisses to conclusion does matter to its logical evaluation.
	From: Ian Rumfitt ("Yes" and "No" [2000], II)
	A reaction: The drift of this is that our view of logic should be a little closer to the reasoning of ordinary language, and we should rely a little less on purely formal accounts.

5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives

11210	Standardly 'and' and 'but' are held to have the same sense by having the same truth table [Rumfitt]
	Full Idea: If 'and' and 'but' really are alike in sense, in what might that likeness consist? Some philosophers of classical logic will reply that they share a sense by virtue of sharing a truth table.
	From: Ian Rumfitt ("Yes" and "No" [2000])
	A reaction: This is the standard view which Rumfitt sets out to challenge.

11212	The sense of a connective comes from primitively obvious rules of inference [Rumfitt]
	Full Idea: A connective will possess the sense that it has by virtue of its competent users' finding certain rules of inference involving it to be primitively obvious.
	From: Ian Rumfitt ("Yes" and "No" [2000], III)
	A reaction: Rumfitt cites Peacocke as endorsing this view, which characterises the logical connectives by their rules of usage rather than by their pure semantic value.

6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / c. Nominalist structuralism

8698	Modal structuralism says mathematics studies possible structures, which may or may not be actualised [Hellman, by Friend]
	Full Idea: The modal structuralist thinks of mathematical structures as possibilities. The application of mathematics is just the realisation that a possible structure is actualised. As structures are possibilities, realist ontological problems are avoided.
	From: report of Geoffrey Hellman (Mathematics without Numbers [1989]) by Michèle Friend - Introducing the Philosophy of Mathematics 4.3
	A reaction: Friend criticises this and rejects it, but it is appealing. Mathematics should aim to be applicable to any possible world, and not just the actual one. However, does the actual world 'actualise a mathematical structure'?

9557	Statements of pure mathematics are elliptical for a sort of modal conditional [Hellman, by Chihara]
	Full Idea: Hellman represents statements of pure mathematics as elliptical for modal conditionals of a certain sort.
	From: report of Geoffrey Hellman (Mathematics without Numbers [1989]) by Charles Chihara - A Structural Account of Mathematics 5.3
	A reaction: It's a pity there is such difficulty in understanding conditionals (see Graham Priest on the subject). I intuit a grain of truth in this, though I take maths to reflect the structure of the actual world (with possibilities being part of that world).

10263	Modal structuralism can only judge possibility by 'possible' models [Shapiro on Hellman]
	Full Idea: The usual way to show that a sentence is possible is to show that it has a model, but for Hellman presumably a sentence is possible if it might have a model (or if, possibly, it has a model). It is not clear what this move brings us.
	From: comment on Geoffrey Hellman (Mathematics without Numbers [1989]) by Stewart Shapiro - Philosophy of Mathematics 7.3
	A reaction: I can't assess this, but presumably the possibility of the model must be demonstrated in some way. Aren't all models merely possible, because they are based on axioms, which seem to be no more than possibilities?

19. Language / F. Communication / 3. Denial

11214	We learn 'not' along with affirmation, by learning to either affirm or deny a sentence [Rumfitt]
	Full Idea: The standard view is that affirming not-A is more complex than affirming the atomic sentence A itself, with the latter determining its sense. But we could learn 'not' directly, by learning at once how to either affirm A or reject A.
	From: Ian Rumfitt ("Yes" and "No" [2000], IV)
	A reaction: [compressed] This seems fairly anti-Fregean in spirit, because it looks at the psychology of how we learn 'not' as a way of clarifying what we mean by it, rather than just looking at its logical behaviour (and thus giving it a secondary role).

20. Action / A. Definition of Action / 1. Action Theory

20062	If a desire leads to a satisfactory result by an odd route, the causal theory looks wrong [Chisholm]
	Full Idea: If someone wants to kill his uncle to inherit a fortune, and having this desire makes him so agitated that he loses control of his car and kills a pedestrian, who turns out to be his uncle, the conditions of the causal theory seem to be satisfied.
	From: Roderick Chisholm (Freedom and Action [1966]), quoted by Rowland Stout - Action 6 'Deviant'
	A reaction: This line of argument has undermined all sorts of causal theories that were fashionable in the 1960s and 70s. Explanation should lead to understanding, but a deviant causal chain doesn't explain the outcome. The causal theory can be tightened.

20. Action / B. Preliminaries of Action / 2. Willed Action / c. Agent causation

20054	There has to be a brain event which is not caused by another event, but by the agent [Chisholm]
	Full Idea: There must be some event A, presumably some cerebral event, which is not caused by any other event, but by the agent.
	From: Roderick Chisholm (Freedom and Action [1966], p.20), quoted by Rowland Stout - Action 4 'Agent'
	A reaction: I'm afraid this thought strikes me as quaintly ridiculous. What kind of metaphysics can allow causation outside the natural nexus, yet occuring within the physical brain? This is a relic of religious dualism. Let it go.