28 ideas
| 6564 | To affirm 'p and not-p' is to have mislearned 'and' or 'not' [Quine] |
| Full Idea: To affirm a compound of the form 'p and not-p' is just to have mislearned one or both of these particles. | |
| From: Willard Quine (From Stimulus to Science [1995], p.23), quoted by Robert Fogelin - Walking the Tightrope of Reason Ch.1 | |
| A reaction: Quoted by Fogelin. This summarises the view of logic developed by the young Wittgenstein, that logical terms are 'operators', rather than referring terms. Of course the speaker may have a compartmentalised mind, or not understand 'p' properly. |
| 13070 | If definitions must be general, and general terms can't individuate, then Socrates can't be defined [Aquinas, by Cover/O'Leary-Hawthorne] |
| Full Idea: Socrates has no definition if definitions by their nature must be in purely general terms, and if no purely general terms can succeed in uniquely singling out this signated matter. | |
| From: report of Thomas Aquinas (De Ente et Essentia (Being and Essence) [1267], 23) by Cover,J/O'Leary-Hawthorne,J - Substance and Individuation in Leibniz 1.1.2 | |
| A reaction: There seem to be two models. That general terms actually individuate the matter of Socrates, or that they cross-reference to (so to speak) define Socrates 'by elimination', as the only individual that fits. But the latter is a poor definition. |
| 11197 | The definitions expressing identity are used to sort things [Aquinas] |
| Full Idea: What sorts things into their proper genus and species are the definitions that express what they are. | |
| From: Thomas Aquinas (De Ente et Essentia (Being and Essence) [1267], p.92) | |
| A reaction: This is straight from Aristotle, though Aristotle's view is a little more complex, I think. If the definitions 'express what they are', then definitions seem to specify the essence. |
| 18806 | Frege thought traditional categories had psychological and linguistic impurities [Frege, by Rumfitt] |
| Full Idea: Frege rejected the traditional categories as importing psychological and linguistic impurities into logic. | |
| From: report of Gottlob Frege (Function and Concept [1891]) by Ian Rumfitt - The Boundary Stones of Thought 1.2 | |
| A reaction: Resisting such impurities is the main motivation for making logic entirely symbolic, but it doesn't follow that the traditional categories have to be dropped. |
| 8490 | First-level functions have objects as arguments; second-level functions take functions as arguments [Frege] |
| Full Idea: Just as functions are fundamentally different from objects, so also functions whose arguments are and must be functions are fundamentally different from functions whose arguments are objects. The latter are first-level, the former second-level, functions. | |
| From: Gottlob Frege (Function and Concept [1891], p.38) | |
| A reaction: In 1884 he called it 'second-order'. This is the standard distinction between first- and second-order logic. The first quantifies over objects, the second over intensional entities such as properties and propositions. |
| 8492 | Relations are functions with two arguments [Frege] |
| Full Idea: Functions of one argument are concepts; functions of two arguments are relations. | |
| From: Gottlob Frege (Function and Concept [1891], p.39) | |
| A reaction: Nowadays we would say 'two or more'. Another interesting move in the aim of analytic philosophy to reduce the puzzling features of the world to mathematical logic. There is, of course, rather more to some relations than being two-argument functions. |
| 8487 | Arithmetic is a development of logic, so arithmetical symbolism must expand into logical symbolism [Frege] |
| Full Idea: I am of the opinion that arithmetic is a further development of logic, which leads to the requirement that the symbolic language of arithmetic must be expanded into a logical symbolism. | |
| From: Gottlob Frege (Function and Concept [1891], p.30) | |
| A reaction: This may the the one key idea at the heart of modern analytic philosophy (even though logicism may be a total mistake!). Logic and arithmetical foundations become the master of ontology, instead of the servant. The jury is out on the whole enterprise. |
| 11195 | If affirmative propositions express being, we affirm about what is absent [Aquinas] |
| Full Idea: If being is what makes propositions true, then anything we can express in an affirmative proposition, however unreal, is said to be; so lacks and absences are, since we say that absences are opposed to presences, and blindness exists in an eye. | |
| From: Thomas Aquinas (De Ente et Essentia (Being and Essence) [1267], p.92) | |
| A reaction: See Idea 11194 for the alternative Aristotelian approach to being, according to categories. Do absences and lacks have real essences, or causal properties? The absence of the sentry may cause the loss of the city. |
| 18899 | Frege takes the existence of horses to be part of their concept [Frege, by Sommers] |
| Full Idea: Frege regarded the existence of horses as a property of the concept 'horse'. | |
| From: report of Gottlob Frege (Function and Concept [1891]) by Fred Sommers - Intellectual Autobiography 'Realism' |
| 11201 | Properties have an incomplete essence, with definitions referring to their subject [Aquinas] |
| Full Idea: Incidental properties have an incomplete essence, and need to refer in their definitions to their subject, lying outside their own genus. | |
| From: Thomas Aquinas (De Ente et Essentia (Being and Essence) [1267], p.93) | |
| A reaction: These are 'incidental' properties, but it is a nice question whether properties have essences. Presumably they must have if they are universals, or platonic Forms. The notion of being 'strong' can be defined without specific examples. |
| 4028 | Frege allows either too few properties (as extensions) or too many (as predicates) [Mellor/Oliver on Frege] |
| Full Idea: Frege's theory of properties (which he calls 'concepts') yields too few properties, by identifying coextensive properties, and also too many, by letting every predicate express a property. | |
| From: comment on Gottlob Frege (Function and Concept [1891]) by DH Mellor / A Oliver - Introduction to 'Properties' §2 | |
| A reaction: Seems right; one extension may have two properties (have heart/kidneys), two predicates might express the same property. 'Cutting nature at the joints' covers properties as well as objects. |
| 11205 | If the form of 'human' contains 'many', Socrates isn't human; if it contains 'one', Socrates is Plato [Aquinas] |
| Full Idea: If (in the Platonic view) manyness was contained in humanness it could never be one as it is in Socrates, and if oneness was part of its definition then Socrates would be Plato and the nature couldn't be realised more than once. | |
| From: Thomas Aquinas (De Ente et Essentia (Being and Essence) [1267], p.100) | |
| A reaction: I suppose the reply is that since we are trying to explain one-over-many, then this unusual combination of both manyness and oneness is precisely what distinguishes forms from other ideas. |
| 8489 | The concept 'object' is too simple for analysis; unlike a function, it is an expression with no empty place [Frege] |
| Full Idea: I regard a regular definition of 'object' as impossible, since it is too simple to admit of logical analysis. Briefly: an object is anything that is not a function, so that an expression for it does not contain any empty place. | |
| From: Gottlob Frege (Function and Concept [1891], p.32) | |
| A reaction: Here is the core of the programme for deriving our ontology from our logic and language, followed through by Russell and Quine. Once we extend objects beyond the physical, it becomes incredibly hard to individuate them. |
| 13090 | The principle of diversity for corporeal substances is their matter [Aquinas, by Cover/O'Leary-Hawthorne] |
| Full Idea: In the view of Aquinas, while substantial form is the ultimate ground of identity and difference of angels, it is matter that provides a principle of diversity in the case of corporeal substances. | |
| From: report of Thomas Aquinas (De Ente et Essentia (Being and Essence) [1267]) by Cover,J/O'Leary-Hawthorne,J - Substance and Individuation in Leibniz 5.2.3 | |
| A reaction: This is at least as good a proposal as their apatial location. There is more chance of reidentifying matter than of precisely reidentifying a spatial location. Two indistinguishable spheres remain the classic problem case (of Max Black, Idea 10195) |
| 11202 | It is by having essence that things exist [Aquinas] |
| Full Idea: It is by having essence that things exist. | |
| From: Thomas Aquinas (De Ente et Essentia (Being and Essence) [1267], p.94) | |
| A reaction: Compare Idea 11199, which gives a fuller picture. This idea seems to suggest essence as the cause of existence, which sounds wrong. Perhaps essence is a necessary condition of existence, but it is necessary that nothing indeterminate can exist? |
| 11203 | Specific individual essence is defined by material, and generic essence is defined by form [Aquinas] |
| Full Idea: Specific essence differs from generic essence by being demarcated: individuals are demarcated within species by dimensionally defined material, but species within genus by a defining differentiation taken from the form. | |
| From: Thomas Aquinas (De Ente et Essentia (Being and Essence) [1267], p.95) | |
| A reaction: It clearly won't be enough to define an individual just to define its material and its shape. The material might also be essential to the genus, as when defining fire. Probably not very helpful. |
| 11200 | The definition of a physical object must include the material as well as the form [Aquinas] |
| Full Idea: Form alone cannot be a composite substance's essence. For a thing's essence is expressed by its definition, and unless the definition of a physical substance included both form and material, the definition wouldn't differ from mathematical objects. | |
| From: Thomas Aquinas (De Ente et Essentia (Being and Essence) [1267], p.93) | |
| A reaction: This is the sort of thoroughly sensible remark that you only get from the greatest philosophers. Minor philosophers fall in love with things like forms, and then try to use them to explain everything. |
| 11196 | Essence is something in common between the natures which sort things into categories [Aquinas] |
| Full Idea: Since being as belonging to a category expresses the 'isness' of things, and belongs to all ten Aristotelian categories, essence must be something all the natures that sort different beings into genera and species have in common. | |
| From: Thomas Aquinas (De Ente et Essentia (Being and Essence) [1267], p.92) | |
| A reaction: I like this because it is the essence which does the sorting, not the sorting which defines the essence (which seems to me to be a deep and widespread confusion). |
| 11208 | A simple substance is its own essence [Aquinas] |
| Full Idea: A simple substance is its own essence. | |
| From: Thomas Aquinas (De Ente et Essentia (Being and Essence) [1267], p.103) | |
| A reaction: Aquinas takes complex substances to have their essences in various ways, but this thought is the basis of all essence. Presumably the Greek word 'ousia' names the key ingredient. |
| 11198 | Definition of essence makes things understandable [Aquinas] |
| Full Idea: It is definition of essence that makes things understandable. | |
| From: Thomas Aquinas (De Ente et Essentia (Being and Essence) [1267], p.92) | |
| A reaction: The aim of philosophy is understanding, which is achieved by successful explanation. I totally agree with this Aristotelian view, so neatly summarised by Aquinas. |
| 9947 | Concepts are the ontological counterparts of predicative expressions [Frege, by George/Velleman] |
| Full Idea: Concepts, for Frege, are the ontological counterparts of predicative expressions. | |
| From: report of Gottlob Frege (Function and Concept [1891]) by A.George / D.J.Velleman - Philosophies of Mathematics Ch.2 | |
| A reaction: That sounds awfully like what many philosophers call 'universals'. Frege, as a platonist (at least about numbers), I would take to be in sympathy with that. At least we can say that concepts seem to be properties. |
| 10319 | An assertion about the concept 'horse' must indirectly speak of an object [Frege, by Hale] |
| Full Idea: Frege had a notorious difficulty over the concept 'horse', when he suggests that if we wish to assert something about a concept, we are obliged to proceed indirectly by speaking of an object that represents it. | |
| From: report of Gottlob Frege (Function and Concept [1891], Ch.2.II) by Bob Hale - Abstract Objects | |
| A reaction: This sounds like the thin end of a wedge. The great champion of objects is forced to accept them here as a façon de parler, when elsewhere they have ontological status. |
| 8488 | A concept is a function whose value is always a truth-value [Frege] |
| Full Idea: A concept in logic is closely connected with what we call a function. Indeed, we may say at once: a concept is a function whose value is always a truth-value. ..I give the name 'function' to what is meant by the 'unsaturated' part. | |
| From: Gottlob Frege (Function and Concept [1891], p.30) | |
| A reaction: So a function becomes a concept when the variable takes a value. Problems arise when the value is vague, or the truth-value is indeterminable. |
| 9948 | Unlike objects, concepts are inherently incomplete [Frege, by George/Velleman] |
| Full Idea: For Frege, concepts differ from objects in being inherently incomplete in nature. | |
| From: report of Gottlob Frege (Function and Concept [1891]) by A.George / D.J.Velleman - Philosophies of Mathematics Ch.2 | |
| A reaction: This is because they are 'unsaturated', needing a quantified variable to complete the sentence. This could be a pointer towards Quine's view of properties, as simply an intrinsic feature of predication about objects, with no separate identity. |
| 4972 | I may regard a thought about Phosphorus as true, and the same thought about Hesperus as false [Frege] |
| Full Idea: From sameness of meaning there does not follow sameness of thought expressed. A fact about the Morning Star may express something different from a fact about the Evening Star, as someone may regard one as true and the other false. | |
| From: Gottlob Frege (Function and Concept [1891], p.14) | |
| A reaction: This all gets clearer if we distinguish internalist and externalist theories of content. Why take sides on this? Why not just ask 'what is in the speaker's head?', 'what does the sentence mean in the community?', and 'what is the corresponding situation?' |
| 11206 | The mind constructs complete attributions, based on the unified elements of the real world [Aquinas] |
| Full Idea: Attribution is something mind brings to completion by constructing propositional connections and disconnections, basing itself on real-world unity possessed by the things being attributed to one another. | |
| From: Thomas Aquinas (De Ente et Essentia (Being and Essence) [1267], p.102) | |
| A reaction: This compromise story seems to me to be exactly right. I take it that we respond to the real joints of nature, but using thought and language which is riddled with convention. |
| 11207 | A cause can exist without its effect, but the effect cannot exist without its cause [Aquinas] |
| Full Idea: When things are so related that one causes the other to exist, the cause can exist without what it causes but not vice versa. | |
| From: Thomas Aquinas (De Ente et Essentia (Being and Essence) [1267], p.103) | |
| A reaction: This is open to question, if causes are supposed to be sufficient for effects. Presumably Aquinas would support the view that if the cause had not been, the effect would not have happened. But the current idea indicates the priority relation. |
| 8491 | The Ontological Argument fallaciously treats existence as a first-level concept [Frege] |
| Full Idea: The ontological proof of God's existence suffers from the fallacy of treating existence as a first-level concept. | |
| From: Gottlob Frege (Function and Concept [1891], p.38 n) | |
| A reaction: [See Idea 8490 for first- and second-order functions] This is usually summarised as the idea that existence is a quantifier rather than a predicate. |