23 ideas
| 10688 | '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) |
| 18073 | Dummett says classical logic rests on meaning as truth, while intuitionist logic rests on assertability [Dummett, by Kitcher] |
| Full Idea: Dummett argues that classical logic depends on the choice of the concept of truth as central to the theory of meaning, while for the intuitionist the concept of assertability occupies this position. | |
| From: report of Michael Dummett (The philosophical basis of intuitionist logic [1973]) by Philip Kitcher - The Nature of Mathematical Knowledge 06.5 | |
| A reaction: Since I can assert any nonsense I choose, this presumably means 'warranted' assertability, which is tied to the concept of proof in mathematics. You can reason about falsehoods, or about uninterpreted variables. Can you 'assert' 'Fx'? |
| 10690 | 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. |
| 10691 | 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) |
| 10695 | 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. |
| 10689 | 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) |
| 19057 | Classical quantification is an infinite conjunction or disjunction - but you may not know all the instances [Dummett] |
| Full Idea: Classical quantification represents an infinite conjunction or disjunction, and the truth-value is determined by the infinite sum or product of the instances ....but this presupposes that all the instances already possess determinate truth-values. | |
| From: Michael Dummett (The philosophical basis of intuitionist logic [1973], p.246) | |
| A reaction: In the case of the universal quantifier, Dummett is doing no more than citing the classic empiricism objection to induction - that you can't make the universal claim if you don't know all the instances. The claim is still meaningful, though. |
| 15091 | Restrict 'logical truth' to formal logic, rather than including analytic and metaphysical truths [Shoemaker] |
| Full Idea: I favour restricting the term 'logical truth' to what logicians would count as such, excluding both analytic truths like 'Bachelors are unmarried' and Kripkean necessities like 'Gold is an element'. | |
| From: Sydney Shoemaker (Causal and Metaphysical Necessity [1998], I) | |
| A reaction: I agree. There is a tendency to splash the phrases 'logical truth' and 'logical necessity around in vague ways. I take them to strictly arise out of the requirements of formal systems of logic. |
| 10696 | 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. |
| 10693 | 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) |
| 10692 | 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) |
| 15095 | A property's causal features are essential, and only they fix its identity [Shoemaker] |
| Full Idea: The view I now favour says that the causal features of a property, both forward-looking and backward-looking, are essential to it. And it says that properties having the same causal features are identical. | |
| From: Sydney Shoemaker (Causal and Metaphysical Necessity [1998], III) | |
| A reaction: In this formulation we have essentialism about properties, as well as essentialism about the things which have the properties. |
| 15097 | I claim that a property has its causal features in all possible worlds [Shoemaker] |
| Full Idea: The controversial claim of my theory is that the causal features of properties are essential to them - are features that they have in all possible worlds. | |
| From: Sydney Shoemaker (Causal and Metaphysical Necessity [1998], III) | |
| A reaction: One problem is that a property can come in degrees, so what degree of the property is necessary to it? It is better to assign this claim to the fundamental properties (which are best called 'powers'). |
| 15094 | I now deny that properties are cluster of powers, and take causal properties as basic [Shoemaker] |
| Full Idea: I now reject the formulation of the causal theory which says that a property is a cluster of conditional powers. That has a reductionist flavour, which is a cheat. We need properties to explain conditional powers, so properties won't reduce. | |
| From: Sydney Shoemaker (Causal and Metaphysical Necessity [1998], III) | |
| A reaction: [compressed wording] I agree with Mumford and Anjum in preferring his earlier formulation. I think properties are broad messy things, whereas powers can be defined more precisely, and seem to have more stability in nature. |
| 15099 | If something is possible, but not nomologically possible, we need metaphysical possibility [Shoemaker] |
| Full Idea: If it is possible that there could be possible states of affairs that are not nomologically possible, don't we therefore need a notion of metaphysical possibility that outruns nomological possibility? | |
| From: Sydney Shoemaker (Causal and Metaphysical Necessity [1998], VI) | |
| A reaction: Shoemaker rejects this possibility (p.425). I sympathise. So there is 'natural' possibility (my preferred term), which is anything which stuff, if it exists, could do, and 'logical' possibility, which is anything that doesn't lead to contradiction. |
| 15101 | Once you give up necessity as a priori, causal necessity becomes the main type of necessity [Shoemaker] |
| Full Idea: Once the obstacle of the deeply rooted conviction that necessary truths should be knowable a priori is removed, ...causal necessity is (pretheoretically) the very paradigm of necessity, in ordinary usage and in dictionaries. | |
| From: Sydney Shoemaker (Causal and Metaphysical Necessity [1998], VII) | |
| A reaction: The a priori route seems to lead to logical necessity, just by doing a priori logic, and also to metaphysical necessity, by some sort of intuitive vision. This is a powerful idea of Shoemaker's (implied, of course, in Kripke). |
| 15098 | Empirical evidence shows that imagining a phenomenon can show it is possible [Shoemaker] |
| Full Idea: We have abundant empirical evidence that when we can imagine some phenomenal situation, e.g., imagine things appearing certain ways, such a situation could actually exist. | |
| From: Sydney Shoemaker (Causal and Metaphysical Necessity [1998], VI) | |
| A reaction: There seem to be good reasons for holding the opposite view too. We can imagine gold appearing to be all sorts of colours, but that doesn't make it possible. What does empirical evidence really tell us here? |
| 15100 | Imagination reveals conceptual possibility, where descriptions avoid contradiction or incoherence [Shoemaker] |
| Full Idea: Imaginability can give us access to conceptual possibility, when we come to believe situations to be conceptually possible by reflecting on their descriptions and seeing no contradiction or incoherence. | |
| From: Sydney Shoemaker (Causal and Metaphysical Necessity [1998], VI) | |
| A reaction: If take the absence of contradiction to indicate 'logical' possibility, but the absence of incoherence is more interesting, even if it is a bit vague. He is talking of 'situations', which I take to be features of reality. A priori synthetic? |
| 15096 | 'Grue' only has causal features because of its relation to green [Shoemaker] |
| Full Idea: Perhaps 'grue' has causal features, but only derivatively, in virtue of its relation to green. | |
| From: Sydney Shoemaker (Causal and Metaphysical Necessity [1998], III) | |
| A reaction: I take grue to be a behaviour, and not a property at all. The problem only arises because the notion of a 'property' became too lax. Presumably Shoemaker should also mention blue in his account. |
| 19055 | Stating a sentence's truth-conditions is just paraphrasing the sentence [Dummett] |
| Full Idea: An ability to state the condition for the truth of a sentence is, in effect, no more than an ability to express the content of the sentence in other words. | |
| From: Michael Dummett (The philosophical basis of intuitionist logic [1973], p.224) | |
| A reaction: Alternatively, if you give something other than a paraphrase of the sentence as its meaning (such as a proof of its truth), then you seem to have departed from your target sentence. Can we reduce and eliminate our sentences in this way? |
| 19056 | If a sentence is effectively undecidable, we can never know its truth conditions [Dummett] |
| Full Idea: If a sentence is effectively undecidable, the condition which must obtain for it to be true is not one which we are capable of recognising whenever it obtains, or of getting ourselves in a position to do so. | |
| From: Michael Dummett (The philosophical basis of intuitionist logic [1973], p.225) | |
| A reaction: The instances of 'undecidable' sentences are most clearly seen in mathematics, such as the Continuum Hypothesis or Goldbach's Conjecture, or anything involving vast infinite cardinals. But do you need precise truth-conditions for meaning? |
| 19054 | Meaning as use puts use beyond criticism, and needs a holistic view of language [Dummett] |
| Full Idea: If use constitutes meaning, it might seem that use is beyond criticism. ....But such an attitude can, ultimately, be supported onlly by the adoption of a holistic view of language. | |
| From: Michael Dummett (The philosophical basis of intuitionist logic [1973], p.218) | |
| A reaction: Dummett goes on to say that the rejection of the holistic view of mathematical meaning leads to his preference for intuitionistic logic. |
| 15093 | We might say laws are necessary by combining causal properties with Armstrong-Dretske-Tooley laws [Shoemaker] |
| Full Idea: One way to get the conclusion that laws are necessary is to combine my view of properties with the view of Armstrong, Dretske and Tooley, that laws are, or assert, relations between properties. | |
| From: Sydney Shoemaker (Causal and Metaphysical Necessity [1998], I) | |
| A reaction: This is interesting, because Armstrong in particular wants the necessity to arise from relations between properties as universals, but if we define properties causally, and make them necessary, we might get the same result without universals. |