25 ideas
| 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. |
| 21554 | Sets always exceed terms, so all the sets must exceed all the sets [Lackey] |
| Full Idea: Cantor proved that the number of sets in a collection of terms is larger than the number of terms. Hence Cantor's Paradox says the number of sets in the collection of all sets must be larger than the number of sets in the collection of all sets. | |
| From: Douglas Lackey (Intros to Russell's 'Essays in Analysis' [1973], p.127) | |
| A reaction: The sets must count as terms in the next iteration, but that is a normal application of the Power Set axiom. |
| 21553 | It seems that the ordinal number of all the ordinals must be bigger than itself [Lackey] |
| Full Idea: The ordinal series is well-ordered and thus has an ordinal number, and a series of ordinals to a given ordinal exceeds that ordinal by 1. So the series of all ordinals has an ordinal number that exceeds its own ordinal number by 1. | |
| From: Douglas Lackey (Intros to Russell's 'Essays in Analysis' [1973], p.127) | |
| A reaction: Formulated by Burali-Forti in 1897. |
| 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. |
| 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' |
| 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. |
| 23664 | Powers are quite distinct and simple, and so cannot be defined [Reid] |
| Full Idea: Power is a thing so much of its own kind, and so simple in its nature, as to admit of no logical definition. | |
| From: Thomas Reid (Essays on Active Powers 1: Active power [1788], 1) | |
| A reaction: True. And this makes Powers ideally suited for the role of primitives in a metaphysics of nature. |
| 23669 | Thinkers say that matter has intrinsic powers, but is also passive and acted upon [Reid] |
| Full Idea: Those philosophers who attribute to matter the power of gravitation, and other active powers, teach us, at the same time, that matter is a substance altogether inert, and merely passive; …that those powers are impressed on it by some external cause. | |
| From: Thomas Reid (Essays on Active Powers 1: Active power [1788], 6) | |
| A reaction: This shows the dilemma of the period, when 'laws of nature' were imposed on passive matter by God, and yet gravity and magnetism appeared as inherent properties of matter. |
| 23666 | It is obvious that there could not be a power without a subject which possesses it [Reid] |
| Full Idea: It is evident that a power is a quality, and cannot exist without a subject to which it belongs. That power may exist without any being or subject to which that power may be attributed, is an absurdity, shocking to every man of common understanding. | |
| From: Thomas Reid (Essays on Active Powers 1: Active power [1788], 1) | |
| A reaction: This is understandble in the 18th C, when free-floating powers were inconceivable, but now that we have fields and plasmas and whatnot, we can't rule out pure powers as basic. However, I incline to agree with Reid. Matter is active. |
| 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. |
| 23665 | Consciousness is the power of mind to know itself, and minds are grounded in powers [Reid] |
| Full Idea: Consciousness is that power of the mind by which it has an immediate knowledge of its own operations. …Every operation of the mind is the exertion of some power of the mind. | |
| From: Thomas Reid (Essays on Active Powers 1: Active power [1788], 1) | |
| A reaction: I strongly favour this account of the mind and consciousness in terms of powers, because they give the best basis for their dynamic nature, and seem to be primitives which terminate all of our explanations. Science identifies the powers for us. |
| 23668 | Our own nature attributes free determinations to our own will [Reid] |
| Full Idea: Every man is led by nature to attribute to himself the free determination of his own will, and to believe those events to be in his power which depend upon his will. | |
| From: Thomas Reid (Essays on Active Powers 1: Active power [1788], 5) | |
| A reaction: I'm happy to say we are all responsible for those actions which are caused by the conscious decisions of our own will (our mental decision mechanisms), but personally I would drop the word 'free', which adds nothing. We are not 'ultimately' responsible. |
| 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?' |
| 20051 | Reid said that agent causation is a unique type of causation [Reid, by Stout,R] |
| Full Idea: Thomas Reid said that an agent's causing something involves a fundamentally different kind of causation from inanimate causing. | |
| From: report of Thomas Reid (Essays on Active Powers 1: Active power [1788]) by Rowland Stout - Action 4 'Agent' | |
| A reaction: I'm afraid the great philosopher of common sense got it wrong on this one. Introducing a new type of causation into our account of nature is crazy. |
| 8383 | Day and night are constantly conjoined, but they don't cause one another [Reid, by Crane] |
| Full Idea: A famous example of Thomas Reid: day regularly follows night, and night regularly follows day. There is therefore a constant conjunction between night and day. But day does not cause night, nor does night cause day. | |
| From: report of Thomas Reid (Essays on Active Powers 1: Active power [1788]) by Tim Crane - Causation 1.2.2 | |
| A reaction: Not a fatal objection to Hume, of course, because in the complex real world there are huge numbers of nested constant conjunctions. Night and the rotation of the Earth are conjoined. But how do you tell which constant conjunctions are causal? |
| 23667 | Regular events don't imply a cause, without an innate conviction of universal causation [Reid] |
| Full Idea: A train of events following one another ever so regularly, could never lead us to the notion of a cause, if we had not, from our constitution, a conviction of the necessity of a cause for every event. | |
| From: Thomas Reid (Essays on Active Powers 1: Active power [1788], 5) | |
| A reaction: Presumably a theist like Reid must assume that the actions of God are freely chosen, rather than necessities. It's hard to see why this principle should be innate in us, and hard to see why it must thereby be true. A bit Kantian, this idea. |
| 23670 | Scientists don't know the cause of magnetism, and only discover its regulations [Reid] |
| Full Idea: A Newtonian philosopher …confesses his ignorance of the true cause of magnetic motion, and thinks that his business, as a philosopher, is only to find from experiment the laws by which it is regulated in all cases. | |
| From: Thomas Reid (Essays on Active Powers 1: Active power [1788], 6) | |
| A reaction: Since there is a 'true cause', that implies that the laws don't actively 'regulate' the magnetism, but only describe its regularity, which I think is the correct view of laws. |
| 23671 | Laws are rules for effects, but these need a cause; rules of navigation don't navigate [Reid] |
| Full Idea: The laws of nature are the rules according to which the effects are produced; but there must be a cause which operates according to these rules. The rules of navigation never navigated a ship. | |
| From: Thomas Reid (Essays on Active Powers 1: Active power [1788], 6) | |
| A reaction: Very nice. No enquirer should be satisfied with merely discovering patterns; the point is to explain the patterns. |
| 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. |