22 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. |
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. |
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. |
6230 | If the soul were a tabula rasa, with no innate ideas, there could be no moral goodness or justice [Cudworth] |
Full Idea: The soul is not a mere rasa tabula, a naked and passive thing, with no innate furniture of its own, nor any thing in it, but what was impressed upon it without; for then there could not possibly be any such thing as moral good and evil, just and unjust. | |
From: Ralph Cudworth (On Eternal and Immutable Morality [1688], Bk IV Ch 6.4) | |
A reaction: He goes on to quote Hobbes saying there is no good in objects themselves. I don't see why we must have an innate moral capacity, provided that we have a capacity to make judgements. |
6228 | Senses cannot judge one another, so what judges senses cannot be a sense, but must be superior [Cudworth] |
Full Idea: The sight cannot judge of sounds, nor the hearing of light and colours; wherefore that which judges of all the senses and their several objects, cannot be itself any sense, but something of a superior nature. | |
From: Ralph Cudworth (On Eternal and Immutable Morality [1688], Ch.II.VI.1) | |
A reaction: How nice to find a seventeenth century English writer rebelling against empiricism! |
6229 | Sense is fixed in the material form, and so can't grasp abstract universals [Cudworth] |
Full Idea: Sense which lies flat and grovelling in the individuals, and is stupidly fixed in the material form, is not able to rise up or ascend to an abstract universal notion. | |
From: Ralph Cudworth (On Eternal and Immutable Morality [1688], Ch.III.III.2) | |
A reaction: This still strikes me as being one of the biggest problems with reductive physicalism, that a lump of meat in your head can grasp abstractions (whatever they are) and universal concepts. Personally I am a physicalist, but it is weird. |
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?' |
6227 | Keeping promises and contracts is an obligation of natural justice [Cudworth] |
Full Idea: To keep faith and perform covenants is that which natural justice obligeth to absolutely. | |
From: Ralph Cudworth (On Eternal and Immutable Morality [1688], Ch.II.4) | |
A reaction: A nice example of an absolute moral intuition, but one which can clearly be challenged. Covenants (contracts) wouldn't work unless everyone showed intense commitment to keeping them, even beyond the grave, and we all benefit from good contracts. |
7453 | Galen's medicine followed the mean; each illness was balanced by opposite treatment [Galen, by Hacking] |
Full Idea: Galen ran medicine on the principle of the mean; afflictions must be treated by contraries; hot diseases deserve cold medicine and moist illnesses want drying agents. (Paracelsus rebelled, treating through similarity). | |
From: report of Galen (On Medical Experience [c.169]) by Ian Hacking - The Emergence of Probability Ch.5 | |
A reaction: This must be inherited from Aristotle, with the aim of virtue for the body, as Aristotle wanted virtue for the psuché. In some areas Galen is probably right, that natural balance is the aim, as in bodily temperature control. |
6225 | Obligation to obey all positive laws is older than all laws [Cudworth] |
Full Idea: Obligation to obey all positive laws is older than all laws. | |
From: Ralph Cudworth (On Eternal and Immutable Morality [1688], Ch.II.3) | |
A reaction: Clearly villains can pass wicked laws, so there can't be an obligation to obey all laws (even if they are 'positive', which seems to beg the question). Nevertheless this is a good reason why laws cannot be the grounding of morality. |
6224 | An omnipotent will cannot make two things equal or alike if they aren't [Cudworth] |
Full Idea: Omnipotent will cannot make things like or equal one to another, without the natures of likeness and equality. | |
From: Ralph Cudworth (On Eternal and Immutable Morality [1688], Ch.II.I) | |
A reaction: This is one of the many classic 'paradoxes of omnipotence'. The best strategy is to define omnipotence as 'being able to do everything which it is possible to do'. Anything beyond that is inviting paradoxical disaster. |
6223 | If the will and pleasure of God controls justice, then anything wicked or unjust would become good if God commanded it [Cudworth] |
Full Idea: If the arbitrary will and pleasure of God is the first and only rule of good and justice, it follows that nothing can be so grossly wicked or unjust but if it were commanded by this omnipotent Deity, it must forthwith become holy, just and righteous. | |
From: Ralph Cudworth (On Eternal and Immutable Morality [1688], Ch.I.I.5) | |
A reaction: This is the strong (Platonic) answer to the Euthyphro Question (Idea 336). One answer is that God would not command in such a way - but why not? We may say that God and goodness merge into one, but we are interested in ultimate authority. |
6226 | The requirement that God must be obeyed must precede any authority of God's commands [Cudworth] |
Full Idea: If it were not morally good and just in its own nature before any positive command of God, that God should be obeyed by his creatures, the bare will of God himself could not beget any obligation upon anyone. | |
From: Ralph Cudworth (On Eternal and Immutable Morality [1688], Ch.II.3) | |
A reaction: This strikes me as a self-evident truth, and a big problem for anyone who wants to make God the source of morality. You don't have to accept anyone's authority just because they are powerful or clever (though they do bestow a certain natural authority!). |
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. |