20 ideas
| 23122 | Montaigne was the founding father of liberalism [Montaigne, by Gopnik] |
| Full Idea: The first liberal, the founding father if we have one, is the great sixteenth century French essayist Michel de Montaigne. | |
| From: report of Michel de Montaigne (On Cruelty [1580]) by Adam Gopnik - A Thousand Small Sanities 1 | |
| A reaction: He says this not on the basis of his politicies or achievements, but his general attitudes and values. It may be another hundred years before we can identify another obvious liberal (Locke?). |
| 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. |
| 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. |
| 12184 | Logical necessity overrules all other necessities [McFetridge] |
| Full Idea: If it is logically necessary that if p then q, then there is no other sense of 'necessary' in which it is not necessary that if p then q. | |
| From: Ian McFetridge (Logical Necessity: Some Issues [1986], §1) | |
| A reaction: The thesis which McFetridge proposes to defend. The obvious rival would be metaphysical necessity, and the rival claim would presumably be that things are only logically necessary if that is entailed by a metaphysical necessity. Metaphysics drives logic. |
| 15083 | The fundamental case of logical necessity is the valid conclusion of an inference [McFetridge, by Hale] |
| Full Idea: McFetridge's conception of logical necessity is one which sees the concept as receiving its fundamental exemplification in the connection between the premiss and conclusion of a deductively valid inference. | |
| From: report of Ian McFetridge (Logical Necessity: Some Issues [1986]) by Bob Hale - Absolute Necessities 2 | |
| A reaction: This would mean that p could be logically necessary but false (if it was a valid argument from false premisses). What if it was a valid inference in a dodgy logical system (including 'tonk', for example)? |
| 15084 | In the McFetridge view, logical necessity means a consequent must be true if the antecedent is [McFetridge, by Hale] |
| Full Idea: McFetridge's view proves that if the conditional corresponding to a valid inference is logically necessary, then there is no sense in which it is possible that its antecedent be true but its consequent false. ..This result generalises to any statement. | |
| From: report of Ian McFetridge (Logical Necessity: Some Issues [1986]) by Bob Hale - Absolute Necessities 2 | |
| A reaction: I am becoming puzzled by Hale's assertion that logical necessity is 'absolute', while resting his case on a conditional. Are we interested in the necessity of the inference, or the necessity of the consequent? |
| 12180 | Logical necessity requires that a valid argument be necessary [McFetridge] |
| Full Idea: There will be a legitimate notion of 'logical' necessity only if there is a notion of necessity which attaches to the claim, concerning a deductively valid argument, that if the premisses are true then so is the conclusion. | |
| From: Ian McFetridge (Logical Necessity: Some Issues [1986], §1) | |
| A reaction: He quotes Aristotle's Idea 11148 in support. Is this resting a stronger idea on a weaker one? Or is it the wrong way round? We endorse validity because we see the necessity; we don't endorse necessity because we see 'validity'. |
| 12181 | Traditionally, logical necessity is the strongest, and entails any other necessities [McFetridge] |
| Full Idea: The traditional crucial assumption is that logical necessity is the strongest notion of necessity. If it is logically necessary that p, then it is necessary that p in any other use of the notion of necessity there may be (physically, practically etc.). | |
| From: Ian McFetridge (Logical Necessity: Some Issues [1986], §1) | |
| A reaction: Sounds right. We might say it is physically necessary simply because it is logically necessary, and even that it is metaphysically necessary because it is logically necessary (required by logic). Logical possibility is hence the weakest kind? |
| 12183 | It is only logical necessity if there is absolutely no sense in which it could be false [McFetridge] |
| Full Idea: Is there any sense in which, despite an ascription of necessity to p, it is held that not-p is possible? If there is, then the original claim then it was necessary is not a claim of 'logical' necessity (which is the strongest necessity). | |
| From: Ian McFetridge (Logical Necessity: Some Issues [1986], §1) | |
| A reaction: See Idea 12181, which leads up to this proposed "test" for logical necessity. McFetridge has already put epistemic ('for all I know') possibility to one side. □p→¬◊¬p is the standard reading of necessity. His word 'sense' bears the burden. |
| 12192 | The mark of logical necessity is deduction from any suppositions whatever [McFetridge] |
| Full Idea: The manifestation of the belief that a mode of inference is logically necessarily truth-preserving is the preparedness to employ that mode of inference in reasoning from any set of suppositions whatsoever. | |
| From: Ian McFetridge (Logical Necessity: Some Issues [1986], §4) | |
| A reaction: He rests this on the idea of 'cotenability' of the two sides of a counterfactual (in Mill, Goodman and Lewis). There seems, at first blush, to be a problem of the relevance of the presuppositions. |
| 12182 | We assert epistemic possibility without commitment to logical possibility [McFetridge] |
| Full Idea: Time- and person-relative epistemic possibility can be asserted even when logical possibility cannot, such as undecided mathematical propositions. 'It may be that p' just comes to 'For all I know, not-p'. | |
| From: Ian McFetridge (Logical Necessity: Some Issues [1986], §1) | |
| A reaction: If it is possible 'for all I know', then it could be actual for all I know, and if we accept that it might be actual, we could hardly deny that it is logically possible. Logical and epistemic possibilities of mathematical p stand or fall together. |
| 12187 | Objectual modal realists believe in possible worlds; non-objectual ones rest it on the actual world [McFetridge] |
| Full Idea: The 'objectual modal realist' holds that what makes modal beliefs true are certain modal objects, typically 'possible worlds'. ..The 'non-objectual modal realist' says modal judgements are made true by how things stand with respect to this world. | |
| From: Ian McFetridge (Logical Necessity: Some Issues [1986], §2) | |
| A reaction: I am an enthusiastic 'non-objectual modal realist'. I accept the argument that real possible worlds have no relevance to the actual world, and explain nothing (see Jubien). The possibilities reside in the 'powers' of this world. See Molnar on powers. |
| 12186 | Modal realists hold that necessities and possibilities are part of the totality of facts [McFetridge] |
| Full Idea: The 'modal realist' holds that part of the totality of what is the case, the totality of facts, are such things as that certain events could have happened, certain propositions are necessarily true, if this happened then that would have been the case. | |
| From: Ian McFetridge (Logical Necessity: Some Issues [1986], §2) | |
| A reaction: I am an enthusiastic modal realist. If the aim of philosophy is 'to understand' (and I take that to be the master idea of the subject) then no understanding is possible which excludes the possibilities and necessities in things. |
| 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. |