19 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 |
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. |
10631 | If 'x is heterological' iff it does not apply to itself, then 'heterological' is heterological if it isn't heterological [Hale/Wright] |
Full Idea: If we stipulate that 'x is heterological' iff it does not apply to itself, we speedily arrive at the contradiction that 'heterological' is itself heterological just in case it is not. | |
From: B Hale / C Wright (Intro to 'The Reason's Proper Study' [2001], 3.2) |
10624 | The incompletability of formal arithmetic reveals that logic also cannot be completely characterized [Hale/Wright] |
Full Idea: The incompletability of formal arithmetic reveals, not arithmetical truths which are not truths of logic, but that logical truth likewise defies complete deductive characterization. ...Gödel's result has no specific bearing on the logicist project. | |
From: B Hale / C Wright (Intro to 'The Reason's Proper Study' [2001], §2 n5) | |
A reaction: This is the key defence against the claim that Gödel's First Theorem demolished logicism. |
10629 | If structures are relative, this undermines truth-value and objectivity [Hale/Wright] |
Full Idea: The relativization of ontology to theory in structuralism can't avoid carrying with it a relativization of truth-value, which would compromise the objectivity which structuralists wish to claim for mathematics. | |
From: B Hale / C Wright (Intro to 'The Reason's Proper Study' [2001], 3.2 n26) | |
A reaction: This is the attraction of structures which grow out of the physical world, where truth-value is presumably not in dispute. |
10628 | The structural view of numbers doesn't fit their usage outside arithmetical contexts [Hale/Wright] |
Full Idea: It is not clear how the view that natural numbers are purely intra-structural 'objects' can be squared with the widespread use of numerals outside purely arithmetical contexts. | |
From: B Hale / C Wright (Intro to 'The Reason's Proper Study' [2001], 3.2 n26) | |
A reaction: I don't understand this objection. If they refer to quantity, they are implicitly cardinal. If they name things in a sequence they are implicitly ordinal. All users of numbers have a grasp of the basic structure. |
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. |
10622 | The neo-Fregean is more optimistic than Frege about contextual definitions of numbers [Hale/Wright] |
Full Idea: The neo-Fregean takes a more optimistic view than Frege of the prospects for the kind of contextual explanation of the fundamental concepts of arithmetic and analysis (cardinals and reals), which he rejected in 'Grundlagen' 60-68. | |
From: B Hale / C Wright (Intro to 'The Reason's Proper Study' [2001], §1) |
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? |
10626 | Objects just are what singular terms refer to [Hale/Wright] |
Full Idea: Objects, as distinct from entities of other types (properties, relations or, more generally, functions of different types and levels), just are what (actual or possible) singular terms refer to. | |
From: B Hale / C Wright (Intro to 'The Reason's Proper Study' [2001], 3.1) | |
A reaction: I find this view very bizarre and hard to cope with. It seems either to preposterously accept the implications of the way we speak into our ontology ('sakes'?), or preposterously bend the word 'object' away from its normal meaning. |
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. |
10630 | Abstracted objects are not mental creations, but depend on equivalence between given entities [Hale/Wright] |
Full Idea: The new kind of abstract objects are not creations of the human mind. ...The existence of such objects depends upon whether or not the relevant equivalence relation holds among the entities of the presupposed kind. | |
From: B Hale / C Wright (Intro to 'The Reason's Proper Study' [2001], 3.2) | |
A reaction: It seems odd that we no longer have any choice about what abstract objects we use, and that we can't evade them if the objects exist, and can't have them if the objects don't exist - and presumably destruction of the objects kills the concept? |
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. |
10627 | Many conceptual truths ('yellow is extended') are not analytic, as derived from logic and definitions [Hale/Wright] |
Full Idea: There are many statements which are plausibly viewed as conceptual truths (such as 'what is yellow is extended') which do not qualify as analytic under Frege's definition (as provable using only logical laws and definitions). | |
From: B Hale / C Wright (Intro to 'The Reason's Proper Study' [2001], 3.2) | |
A reaction: Presumably this is because the early assumptions of Frege were mathematical and logical, and he was trying to get away from Kant. That yellow is extended is a truth for non-linguistic beings. |
13304 | Learned men gain more in one day than others do in a lifetime [Posidonius] |
Full Idea: In a single day there lies open to men of learning more than there ever does to the unenlightened in the longest of lifetimes. | |
From: Posidonius (fragments/reports [c.95 BCE]), quoted by Seneca the Younger - Letters from a Stoic 078 | |
A reaction: These remarks endorsing the infinite superiority of the educated to the uneducated seem to have been popular in late antiquity. It tends to be the religions which discourage great learning, especially in their emphasis on a single book. |
20820 | Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus] |
Full Idea: Posidonius defined time thus: it is an interval of motion, or the measure of speed and slowness. | |
From: report of Posidonius (fragments/reports [c.95 BCE]) by John Stobaeus - Anthology 1.08.42 | |
A reaction: Hm. Can we define motion or speed without alluding to time? Looks like we have to define them as a conjoined pair, which means we cannot fully understand either of them. |