24 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. |
12710 | As well as extension, bodies contain powers [Leibniz] |
Full Idea: Over and above what can be deduced from extension, we must add and recognise in bodies certain notions or forms that are immaterial, so to speak, or independent of extension, which you can call powers [potentia], by which speed is adjusted to magnitude. | |
From: Gottfried Leibniz (De Natura Corporis [1678], A6.4.1980), quoted by Daniel Garber - Leibniz:Body,Substance,Monad 3 | |
A reaction: He boldly asserts that the powers are 'immaterial', but is then forced to qualify it (as he often does) with 'so to speak'. The notion that bodies just have extension (occupy space) comes from Descartes, and is firmly opposed by Leibniz. |
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. |
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?' |
21075 | The state of nature always involves the threat of war [Kant] |
Full Idea: The state of nature is a state of war. For even if it does not involve active hostilities, it involves a constant threat of their breaking out. | |
From: Immanuel Kant (Perpetual Peace [1795], 2) | |
A reaction: Kant is siding with Hobbes against Rousseau, despite Rousseau's claim that Hobbes's pessimism concerns a more advanced situation that the true (and peaceful) state of nature. |
20569 | Kant made the social contract international and cosmopolitan [Kant, by Oksala] |
Full Idea: Kant developed the social contract theory into an international and cosmopolitan idea. | |
From: report of Immanuel Kant (Perpetual Peace [1795]) by Johanna Oksala - Political Philosophy: all that matters Ch.6 | |
A reaction: That is, the contract both operates between states, and rises above them. I found this idea rather thrilling when I first met it (listening to Onora O'Neill). But then I remain a child of the Englightenment. |
21079 | The a priori general will of a people shows what is right [Kant] |
Full Idea: It is precisely the general will as it is given a priori, within a single people or in the mutual relationships of various peoples, which alone determines what is right among men. | |
From: Immanuel Kant (Perpetual Peace [1795], App 1) | |
A reaction: The clearest quotation for showing Kant's debt to Rousseau. Why should Rousseau bother to have a real assembly of the people, if the General Will can be worked out a priori? Indeed, the a priori version must be deemed superior to any meeting. |
21077 | Each nation should, from self-interest, join an international security constitution [Kant] |
Full Idea: Each nation, for the sake of its own security, can and ought to demand of the others that they should enter along with it into a constitution, similar to the civil one, within which the rights of each could be secured. | |
From: Immanuel Kant (Perpetual Peace [1795], 2.2nd) | |
A reaction: Not sure how close the United Nations takes us to this. You have to admire Kant for this one. |
21078 | A constitution must always be improved when necessary [Kant] |
Full Idea: Changes for the better are necessary, in order that the constitution may constantly approach the optimum end prescribed by laws of right. | |
From: Immanuel Kant (Perpetual Peace [1795], App 1) | |
A reaction: This should be a clause in every constitution. It is crazy to feel trapped by a misjudgement or outdated view of your ancestors. |
21076 | Equality is where you cannot impose a legal obligation you yourself wouldn't endure [Kant] |
Full Idea: Rightful equality within a state is a relationship among citizens where no-one can put anyone else under a legal obligation without submitting simultaneously to a law which requires that he can be put under the same kind of obligation by the other person. | |
From: Immanuel Kant (Perpetual Peace [1795], 2.1st n) | |
A reaction: This appears only to be legal equality, rather than political or economic or social equality. |
20570 | There is now a growing universal community, and violations of rights are felt everywhere [Kant] |
Full Idea: The peoples of the earth have entered in varying degrees into a universal community, and it has developed to the point where a violation of rights in one part of the world is felt everywhere. | |
From: Immanuel Kant (Perpetual Peace [1795], 'Third') | |
A reaction: I hope slavery was at the forefront of his mind when he wrote that. It is only in very recent times (since about 1960?) that major violations of rights are felt to matter to the whole human race. A long way to go, though. |
20571 | There are political and inter-national rights, but also universal cosmopolitan rights [Kant] |
Full Idea: The idea of a cosmopolitan right is not fantastic and overstrained; it is a necessary complement to the unwritten code of political and international right, transforming it into a universal right of humanity. | |
From: Immanuel Kant (Perpetual Peace [1795], 'Third') | |
A reaction: The interesting thought is that there are no 'natural rights', but there can be universal rights insofar as there exists a universal community. See the UN Declaration of Human Rights c.1948. |
21073 | Hiring soldiers is to use them as instruments, ignoring their personal rights [Kant] |
Full Idea: The hiring of men to kill or be killed seems to mean using them as mere machines and insturments in the hands of someone else (the state), which cannot easily be reconciled with the rights of man in one's own person. | |
From: Immanuel Kant (Perpetual Peace [1795], 1.3) | |
A reaction: Kant was not a pacificist, though this makes him sound like one. Some men go off to war with enthusiasm, and then regret it. Exploitation of rational beings may be the worst sin in Kant's Enlightenment world. |
21074 | Some trust in the enemy is needed during wartime, or peace would be impossible [Kant] |
Full Idea: It must remain possible, even in wartime, to have some sort of trust in the attitude of the enemy, otherwise peace could not be concluded and the hostilities would turn into a war of extermination. | |
From: Immanuel Kant (Perpetual Peace [1795], 1.6) | |
A reaction: Consider the 'unconditional surrender' approach to the Nazis in 1944, and the peace of May 1945, made with very different Germans. How do you make peace with an enemy you cannot trust? |
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. |