15 ideas
| 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'? |
| 16728 | Logicians acknowledge too few things, while others acknowledge too many [Fitzralph] |
| Full Idea: Those who have been well trained in logic err in recognising too few things, whereas others who are ignorant of logic ascribe to every statement a new entity, postulating more entities than God has ever established as real. | |
| From: Richard Fitzralph (Sentences [1328], II.1.2), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 22.3 |
| 18739 | Three stages of philosophical logic: syntactic (1905-55), possible worlds (1963-85), widening (1990-) [Horsten/Pettigrew] |
| Full Idea: Three periods can be distinguished in philosophical logic: the syntactic stage, from Russell's definite descriptions to the 1950s, the dominance of possible world semantics from the 50s to 80s, and a current widening of the subject. | |
| From: Horsten,L/Pettigrew,R (Mathematical Methods in Philosophy [2014], 1) | |
| A reaction: [compressed] I've read elsewhere that the arrival of Tarski's account of truth in 1933, taking things beyond the syntactic, was also a landmark. |
| 18741 | Logical formalization makes concepts precise, and also shows their interrelation [Horsten/Pettigrew] |
| Full Idea: Logical formalization forces the investigator to make the central philosophical concepts precise. It can also show how some philosophical concepts and objects can be defined in terms of others. | |
| From: Horsten,L/Pettigrew,R (Mathematical Methods in Philosophy [2014], 2) | |
| A reaction: This is the main rationale of the highly formal and mathematical approach to such things. The downside is when you impose 'precision' on language that was never intended to be precise. |
| 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. |
| 18744 | Models are sets with functions and relations, and truth built up from the components [Horsten/Pettigrew] |
| Full Idea: A (logical) model is a set with functions and relations defined on it that specify the denotation of the non-logical vocabulary. A series of recursive clauses explicate how truth values of complex sentences are compositionally determined from the parts. | |
| From: Horsten,L/Pettigrew,R (Mathematical Methods in Philosophy [2014], 3) | |
| A reaction: See the ideas on 'Functions in logic' and 'Relations in logic' (in the alphabetical list) to expand this important idea. |
| 18740 | If 'exist' doesn't express a property, we can hardly ask for its essence [Horsten/Pettigrew] |
| Full Idea: If there is indeed no property of existence that is expressed by the word 'exist', then it makes no sense to ask for its essence. | |
| From: Horsten,L/Pettigrew,R (Mathematical Methods in Philosophy [2014], 2) | |
| A reaction: As far as I can tell, this was exactly Aristotle's conclusion, so he skirted round the question of 'being qua being', and focused on the nature of objects instead. Grand continental talk of 'Being' doesn't sound very interesting. |
| 18745 | A Tarskian model can be seen as a possible state of affairs [Horsten/Pettigrew] |
| Full Idea: A Tarskian model can in a sense be seen as a model of a possible state of affairs. | |
| From: Horsten,L/Pettigrew,R (Mathematical Methods in Philosophy [2014], 3) | |
| A reaction: I include this remark to show how possible worlds semantics built on the arrival of model theory. |
| 18747 | The 'spheres model' was added to possible worlds, to cope with counterfactuals [Horsten/Pettigrew] |
| Full Idea: The notion of a possible worlds model was extended (resulting in the concept of a 'spheres model') in order to obtain a satisfactory logical treatment of counterfactual conditional sentences. | |
| From: Horsten,L/Pettigrew,R (Mathematical Methods in Philosophy [2014], 4) | |
| A reaction: Thus we add 'centred' worlds, and an 'actual' world, to the loose original model. It is important to remember when we discuss 'close' worlds that we are then committed to these presuppositions. |
| 18748 | Epistemic logic introduced impossible worlds [Horsten/Pettigrew] |
| Full Idea: The idea of 'impossible worlds' was introduced into epistemic logic. | |
| From: Horsten,L/Pettigrew,R (Mathematical Methods in Philosophy [2014], 4) | |
| A reaction: Nathan Salmon seems interested in their role in metaphysics (presumably in relation to Meinongian impossible objects, like circular squares, which must necessarily be circular). |
| 18746 | Possible worlds models contain sets of possible worlds; this is a large metaphysical commitment [Horsten/Pettigrew] |
| Full Idea: Each possible worlds model contains a set of possible worlds. For this reason, possible worlds semantics is often charged with smuggling in heavy metaphysical commitments. | |
| From: Horsten,L/Pettigrew,R (Mathematical Methods in Philosophy [2014], 3) | |
| A reaction: To a beginner it looks very odd that you should try to explain possibility by constructing a model of it in terms of 'possible' worlds. |
| 18750 | Using possible worlds for knowledge and morality may be a step too far [Horsten/Pettigrew] |
| Full Idea: When the possible worlds semantics were further extended to model notions of knowledge and of moral obligation, the application was beginning to look distinctly forced and artificial. | |
| From: Horsten,L/Pettigrew,R (Mathematical Methods in Philosophy [2014], 5) | |
| A reaction: They accept lots of successes in modelling necessity and time. |
| 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. |