24 ideas
| 9108 | From an impossibility anything follows [William of Ockham] |
| Full Idea: From an impossibility anything follows ('quod ex impossibili sequitur quodlibet'). | |
| From: William of Ockham (Summa totius logicae [1323], III.c.xxxvi) | |
| A reaction: The hallmark of a true logician, I suspect, is that this opinion is really meaningful and important to them. They yearn to follow the logic wherever it leads. Common sense would seem to say that absolutely nothing follows from an impossibility. |
| 9107 | A proposition is true if its subject and predicate stand for the same thing [William of Ockham] |
| Full Idea: If in the proposition 'This is an angel' subject and predicate stand for the same thing, the proposition is true. | |
| From: William of Ockham (Summa totius logicae [1323], II.c.ii) | |
| A reaction: An interesting statement of what looks like a correspondence theory, employing the idea that both the subject and the predicate have a reference. I think Frege would say that 'x is an angel' is unsaturated, and so lacks reference. |
| 16300 | Ockham had an early axiomatic account of truth [William of Ockham, by Halbach] |
| Full Idea: Theories structurally very similar to axiomatic compositional theories of truth can be found in Ockham's 'Summa Logicae'. | |
| From: report of William of Ockham (Summa totius logicae [1323]) by Volker Halbach - Axiomatic Theories of Truth 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. |
| 9106 | The word 'every' only signifies when added to a term such as 'man', referring to all men [William of Ockham] |
| Full Idea: The syncategorematic word 'every' does not signify any fixed thing, but when added to 'man' it makes the term 'man' stand for all men actually. | |
| From: William of Ockham (Summa totius logicae [1323], I.c.iv) | |
| A reaction: Although quantifiers may have become a part of formal logic with Frege, their importance is seen from Aristotle onwards, and it is clearly a key part of William's understanding of logic. |
| 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. |
| 9113 | Just as unity is not a property of a single thing, so numbers are not properties of many things [William of Ockham] |
| Full Idea: Number is nothing but the actual numbered things themselves. Hence just as unity is not an accident added to the thing which is one, so number is not an accident of the things which are numbered. | |
| From: William of Ockham (Summa totius logicae [1323], I.c.xliv) | |
| A reaction: [William does not necessarily agree with this view] It strikes me as a key point here that any account of the numbers had better work for 'one', though 'zero' might be treated differently. Some people seem to think unity is a property of things. |
| 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. |
| 9110 | The words 'thing' and 'to be' assert the same idea, as a noun and as a verb [William of Ockham] |
| Full Idea: The words 'thing' and 'to be' (esse) signify one and the same thing, but the one in the manner of a noun and the other in the manner of a verb. | |
| From: William of Ockham (Summa totius logicae [1323], III,II,c,xxvii) | |
| A reaction: Well said - as you would expect from a thoroughgoing nominalist. I would have thought that this was the last word on the subject of Being, thus rendering any need for me to read Heidegger quite superfluous. Or am I missing something? |
| 15388 | Universals are single things, and only universal in what they signify [William of Ockham] |
| Full Idea: Every universal is one particular thing and it is not a universal except in its signification, in its signifying many thing. | |
| From: William of Ockham (Summa totius logicae [1323]), quoted by Claude Panaccio - Medieval Problem of Universals 'William' | |
| A reaction: Sounds as if William might have liked tropes. It seems to leave the problem unanswered (the 'ostrich' problem?). How are they able to signify in this universal way, if each thing is just distinct and particular? |
| 9109 | If essence and existence were two things, one could exist without the other, which is impossible [William of Ockham] |
| Full Idea: If essence and existence were two things, then no contradiction would be involved if God preserved the essence of a thing in the world without its existence, or vice versa, its existence without its essence; both of which are impossible. | |
| From: William of Ockham (Summa totius logicae [1323], III,II,c,xxvii) | |
| A reaction: Not that William is using the concept of a supreme mind as a tool in argument. His denial of essence as something separable is presumably his denial of the Aristotelian view of universals, as well as of the Platonic view. |
| 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. |
| 6417 | In 1921 Russell abandoned sense-data, and the gap between sensation and object [Russell, by Grayling] |
| Full Idea: In 'The Analysis of Mind' Russell gave up talk of 'sense-data', and ceased to distinguish between the act of sensing and what is sensed. | |
| From: report of Bertrand Russell (The Analysis of Mind [1921]) by A.C. Grayling - Russell Ch.2 | |
| A reaction: This seems to lead towards the modern 'adverbial' account of sensing, where I don't sense 'data', but where qualia (such as redness) are our particular mode of directly perceiving objects, where insects might directly perceive them in a different mode. |
| 6474 | Seeing is not in itself knowledge, but is separate from what is seen, such as a patch of colour [Russell] |
| Full Idea: Undeniably, knowledge comes through seeing, but it is a mistake to regard the mere seeing itself as knowledge; if we are so to regard it, we must distinguish the seeing from what is seen; a patch of colour is one thing, and our seeing it is another. | |
| From: Bertrand Russell (The Analysis of Mind [1921], Lec. VIII) | |
| A reaction: This is Russell's 1921 explanation of why he adopted sense-data (but he rejects them later in this paragraph). This gives a simplistic impression of what he intended, which has three components: the object, the 'sensibile', and the sense-datum. |
| 6476 | We cannot assume that the subject actually exists, so we cannot distinguish sensations from sense-data [Russell] |
| Full Idea: If we are to avoid a perfectly gratuitous assumption, we must dispense with the subject as one of the actual ingredients of the world; but when we do this, the possibility of distinguishing the sensation from the sense-datum vanishes. | |
| From: Bertrand Russell (The Analysis of Mind [1921], Lec. VIII) | |
| A reaction: This is the reason why Russell himself rejected sense-data. It is more normal, I think, to reject them simply as being superfluous. If the subject can simply perceive the sense-data, why can't they just perceive the object more directly? |
| 2792 | It is possible the world came into existence five minutes ago, complete with false memories [Russell] |
| Full Idea: There is no logical impossibility in the hypothesis that the world sprang into being five minutes ago, exactly as it then was, with a population that "remembered" a wholly unreal past. | |
| From: Bertrand Russell (The Analysis of Mind [1921], p.159) | |
| A reaction: One of the great sceptical arguments! At a stroke it undermines forever any dreams that memories are totally certain. This is an extra scepticism, which arises if you decide that current experience IS totally certain. |
| 22326 | Knowledge needs more than a sensitive response; the response must also be appropriate [Russell] |
| Full Idea: Accuracy of response to stimulus does not alone show knowledge, but must be reinforced by appropriateness, i.e. suitability of realising one's purpose. | |
| From: Bertrand Russell (The Analysis of Mind [1921], p.261), quoted by Michael Potter - The Rise of Analytic Philosophy 1879-1930 66 'Rel' | |
| A reaction: The aim of 'realising one's purpose' puts a very pragmatist spin on this. The point is a good one, and seems to apply particularly to Nozick's accurate 'tracking' account of knowledge. |
| 6475 | In perception, the self is just a logical fiction demanded by grammar [Russell] |
| Full Idea: In perception, the idea of the subject appears to be a logical fiction, like mathematical points and instants; it is introduced, not because observation reveals it, but because it is linguistically convenient and apparently demanded by grammar. | |
| From: Bertrand Russell (The Analysis of Mind [1921], Lec. VIII) | |
| A reaction: In 1912, Russell had felt that both the Cogito, and the experience of meta-thought, had confirmed the existence of a non-permanent ego, but here he offers a Humean rejection. His notion of a 'logical fiction' is behaviouristic. I believe in the Self. |
| 9105 | Some concepts for propositions exist only in the mind, and in no language [William of Ockham] |
| Full Idea: Conceptual terms and the propositions formed by them are those mental words which do not belong to any language; they remain only in the mind and cannot be uttered exteriorly, though signs subordinated to these can be exteriorly uttered. | |
| From: William of Ockham (Summa totius logicae [1323], I.c.i) | |
| A reaction: [He cites Augustine] A glimmer of the idea of Mentalese, and is probably an integral part of any commitment to propositions. Quine would hate it, but I like it. Logicians seem to dislike anything that cannot be articulated, but brains are like that. |