Combining Texts

All the ideas for 'Logical Consequence', 'The Structure of Appearance' and 'Action, Intention and Reason'

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15 ideas

4. Formal Logic / A. Syllogistic Logic / 2. Syllogistic Logic
'Equivocation' is when terms do not mean the same thing in premises and conclusion [Beall/Restall]
     Full Idea: 'Equivocation' is when the terms do not mean the same thing in the premises and in the conclusion.
     From: JC Beall / G Restall (Logical Consequence [2005], Intro)
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / a. Sets as existing
Classes are a host of ethereal, platonic, pseudo entities [Goodman]
     Full Idea: I will not willingly use apparatus that peoples the world with a host of ethereal, platonic, pseudo entities.
     From: Nelson Goodman (The Structure of Appearance [1951], II.2), quoted by David Lewis - Parts of Classes 2.1
     A reaction: This represents the big gap that opened up with Goodman's former comrade in arms, Quine. Lewis quotes it in order to ask whether he means ethereal or platonic, as they are very different. I sympathise with Goodman.
4. Formal Logic / F. Set Theory ST / 8. Critique of Set Theory
Two objects can apparently make up quite distinct arrangements in sets [Goodman, by Burgess/Rosen]
     Full Idea: Goodman argues that the set or class {{a}},{a,b}} is supposed to be distinct from the set or class {{b},{a,b}}, even though both are ultimately constituted from the same a and b.
     From: report of Nelson Goodman (The Structure of Appearance [1951]) by JP Burgess / G Rosen - A Subject with No Object I.A.2.a
     A reaction: I'm with Goodman all the way here, even though it is deeply unfashionable, particularly in the circles I move in. If there are trillion grains of sand on a beach, how many sets are we supposed to be committed to?
4. Formal Logic / G. Formal Mereology / 1. Mereology
The counties of Utah, and the state, and its acres, are in no way different [Goodman]
     Full Idea: A class (counties of Utah) is different neither from the individual (state of Utah) that contains its members, nor from any other class (acres of Utah) whose members exhaust the whole. For nominalists, distinction of entity means distinction of content.
     From: Nelson Goodman (The Structure of Appearance [1951], p.26), quoted by Achille Varzi - Mereology 3.1
     A reaction: This is a nice credo for the nominalist version of mereology. You can still have a mereology that commits you to the wholes as well as the parts. Cf. Lewis in Idea 10660.
5. Theory of Logic / A. Overview of Logic / 4. Pure Logic
Formal logic is invariant under permutations, or devoid of content, or gives the norms for thought [Beall/Restall]
     Full Idea: Logic is purely formal either when it is invariant under permutation of object (Tarski), or when it has totally abstracted away from all contents, or it is the constitutive norms for thought.
     From: JC Beall / G Restall (Logical Consequence [2005], 2)
     A reaction: [compressed] The third account sounds rather woolly, and the second one sounds like a tricky operation, but the first one sounds clear and decisive, so I vote for Tarski.
5. Theory of Logic / B. Logical Consequence / 2. Types of Consequence
Logical consequence needs either proofs, or absence of counterexamples [Beall/Restall]
     Full Idea: Technical work on logical consequence has either focused on proofs, where validity is the existence of a proof of the conclusions from the premises, or on models, which focus on the absence of counterexamples.
     From: JC Beall / G Restall (Logical Consequence [2005], 3)
5. Theory of Logic / B. Logical Consequence / 4. Semantic Consequence |=
Logical consequence is either necessary truth preservation, or preservation based on interpretation [Beall/Restall]
     Full Idea: Two different views of logical consequence are necessary truth-preservation (based on modelling possible worlds; favoured by Realists), or truth-preservation based on the meanings of the logical vocabulary (differing in various models; for Anti-Realists).
     From: JC Beall / G Restall (Logical Consequence [2005], 2)
     A reaction: Thus Dummett prefers the second view, because the law of excluded middle is optional. My instincts are with the first one.
5. Theory of Logic / B. Logical Consequence / 8. Material Implication
A step is a 'material consequence' if we need contents as well as form [Beall/Restall]
     Full Idea: A logical step is a 'material consequence' and not a formal one, if we need the contents as well as the structure or form.
     From: JC Beall / G Restall (Logical Consequence [2005], 2)
5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
A 'logical truth' (or 'tautology', or 'theorem') follows from empty premises [Beall/Restall]
     Full Idea: If a conclusion follows from an empty collection of premises, it is true by logic alone, and is a 'logical truth' (sometimes a 'tautology'), or, in the proof-centred approach, 'theorems'.
     From: JC Beall / G Restall (Logical Consequence [2005], 4)
     A reaction: These truths are written as following from the empty set Φ. They are just implications derived from the axioms and the rules.
5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
Models are mathematical structures which interpret the non-logical primitives [Beall/Restall]
     Full Idea: Models are abstract mathematical structures that provide possible interpretations for each of the non-logical primitives in a formal language.
     From: JC Beall / G Restall (Logical Consequence [2005], 3)
6. Mathematics / B. Foundations for Mathematics / 2. Proof in Mathematics
Hilbert proofs have simple rules and complex axioms, and natural deduction is the opposite [Beall/Restall]
     Full Idea: There are many proof-systems, the main being Hilbert proofs (with simple rules and complex axioms), or natural deduction systems (with few axioms and many rules, and the rules constitute the meaning of the connectives).
     From: JC Beall / G Restall (Logical Consequence [2005], 3)
8. Modes of Existence / E. Nominalism / 2. Resemblance Nominalism
If all and only red things were round things, we would need to specify the 'respect' of the resemblance [Goodman, by Macdonald,C]
     Full Idea: According to Goodman's 'companionship difficulty', resemblance nominalism has a problem if, say, all and only the red things were the round things, because we cannot distinguish the two different respects in which the things resemble one another.
     From: report of Nelson Goodman (The Structure of Appearance [1951]) by Cynthia Macdonald - Varieties of Things Ch.6
     A reaction: Goodman opts for extreme linguististic nominalism in response to this (Idea 7952), whereas Russell opts for a sort of Platonism (4441). The current idea gives Russell a further problem, of needing a universal of the respect of the resemblance.
Without respects of resemblance, we would collect blue book, blue pen, red pen, red clock together [Goodman, by Macdonald,C]
     Full Idea: Goodman's 'imperfect community' problem for Resemblance Nominalism says that without mention of respects in which things resemble, we end up with a heterogeneous collection with nothing wholly in common (blue book, blue pen, red pen, red clock).
     From: report of Nelson Goodman (The Structure of Appearance [1951]) by Cynthia Macdonald - Varieties of Things Ch.6
     A reaction: This suggests Wittgenstein's 'family' resemblance as a way out (Idea 4141), but a blue book and a red clock seem totally unrelated. Nice objection! At this point we start to think that the tropes resemble, rather than the objects.
8. Modes of Existence / E. Nominalism / 3. Predicate Nominalism
If we apply the same word to different things, it is only because we are willing to do so [Goodman, by Macdonald,C]
     Full Idea: Predicate nominalism is the view that what all things to which the same word applies have in common is simply our willingness to apply the same word to them.
     From: report of Nelson Goodman (The Structure of Appearance [1951], Ch.6) by Cynthia Macdonald - Varieties of Things
     A reaction: This is Goodman's 'extreme nominalist' position. This seems also to be an anti-realist position, as it denies any 'joints' to nature (Idea 7953). It strikes me as daft. WHY are we willing to apply words in certain ways?
20. Action / C. Motives for Action / 3. Acting on Reason / c. Reasons as causes
Actions are not mere effects of reasons, but are under their control [Audi,R]
     Full Idea: An action for a reason is one that is, in a special way, under the control of reason. It is a response to, not a mere effect of, a reason.
     From: Robert Audi (Action, Intention and Reason [1992], p.177), quoted by Rowland Stout - Action 6 'Alien'
     A reaction: This modifies Davidson's 'reasons are causes'. Audi has a deviant causal chain which causes trouble for his idea, but Stout says he is right to focus on causal 'processes' (an Aristotelian idea) rather than causal 'chains'.