26 ideas
| 12104 | All ideas must be understood historically [Comte] |
| Full Idea: No idea can be properly understood apart from its history. | |
| From: Auguste Comte (Intro to Positive Philosophy [1830], Ch.1) | |
| A reaction: This is somewhat dubious. Comte is preparing the ground for asserting positivism by rejecting out-of-date theology and metaphysics. The history is revealing, but can be misleading, when a meaning shifts. Try 'object' in logic. |
| 12105 | Our knowledge starts in theology, passes through metaphysics, and ends in positivism [Comte] |
| Full Idea: Our principal conceptions, each branch of our knowledge, passes in succession through three different theoretical states: the theological or fictitious state, the metaphysical or abstract state, and the scientific or positive state. | |
| From: Auguste Comte (Intro to Positive Philosophy [1830], Ch.1) | |
| A reaction: See Idea 5077 for the abstraction step. The idea that there is a 'law' here, as Comte thinks, is daft, but something of what he describes is undeniable. I suspect, though, that science rests on abstractions, so the last part is wrong. |
| 12112 | Metaphysics is just the oversubtle qualification of abstract names for phenomena [Comte] |
| Full Idea: The development of positivism was caused by the concept of metaphysical agents gradually becoming so empty through oversubtle qualification that all right-minded persons considered them to be only the abstract names of the phenomena in question. | |
| From: Auguste Comte (Intro to Positive Philosophy [1830], Ch.1) | |
| A reaction: I have quite a lot of sympathy with this thesis, but not couched in this negative way. I take abstraction to be essential to scientific thought, and wisdom to occur amongst the higher reaches of the abstractions. |
| 12106 | Positivism gives up absolute truth, and seeks phenomenal laws, by reason and observation [Comte] |
| Full Idea: In the positive state, the human mind, recognizing the impossibility of obtaining absolute truth, gives up the search for hidden and final causes. It endeavours to discover, by well-combined reasoning and observation, the actual laws of phenomena. | |
| From: Auguste Comte (Intro to Positive Philosophy [1830], Ch.1) | |
| A reaction: [compressed] Positivism attempted to turn the Humean regularity view of laws into a semi-religion. It is striking how pessimistic Comte was (as was Hume) about the chances of science revealing deep explanations. He would be astoundeds. |
| 12111 | Positivism is the final state of human intelligence [Comte] |
| Full Idea: The positive philosophy represents the true final state of human intelligence. | |
| From: Auguste Comte (Intro to Positive Philosophy [1830], Ch.1) | |
| A reaction: This is the sort of remark which made Comte notorious, and it looks a bit extravagant now, but the debate about his view is still ongoing. I am certainly sympathetic to his general drift. |
| 12114 | Science can drown in detail, so we need broad scientists (to keep out the metaphysicians) [Comte] |
| Full Idea: Getting lost in a mass of detail is the weak side of positivism, where partisans of theology and metaphysics may attack with some hope of success. ...We must train scientists who will consider all the different branches of positive science. | |
| From: Auguste Comte (Intro to Positive Philosophy [1830], Ch.1) | |
| A reaction: This would be Comte's answer now to those who claim there is still a role for metaphysics within the scientific world view. I would say that metaphysics not only takes an overview, but also deals with higher generalisations than Comte's general scientist. |
| 12116 | Only positivist philosophy can terminate modern social crises [Comte] |
| Full Idea: We may look upon the positive philosophy as constituting the only solid basis for the social reorganisation that must terminate the crisis in which the most civilized nations have found themselves for so long. | |
| From: Auguste Comte (Intro to Positive Philosophy [1830], Ch.1) | |
| A reaction: He is proposing not only to use positivist methods to solve social problems (he coined the word 'sociology'), but is also proposing that positivism itself should act as the unifying belief-system for future society. Science will be our religion. |
| 13886 | Later Frege held that definitions must fix a function's value for every possible argument [Frege, by Wright,C] |
| Full Idea: Frege later became fastidious about definitions, and demanded that they must provide for every possible case, and that no function is properly determined unless its value is fixed for every conceivable object as argument. | |
| From: report of Gottlob Frege (Grundgesetze der Arithmetik 2 (Basic Laws) [1903]) by Crispin Wright - Frege's Concept of Numbers as Objects 3.xiv | |
| A reaction: Presumably definitions come in degrees of completeness, but it seems harsh to describe a desire for the perfect definition as 'fastidious', especially if we are talking about mathematics, rather than defining 'happiness'. |
| 9845 | We can't define a word by defining an expression containing it, as the remaining parts are a problem [Frege] |
| Full Idea: Given the reference (bedeutung) of an expression and a part of it, obviously the reference of the remaining part is not always determined. So we may not define a symbol or word by defining an expression in which it occurs, whose remaining parts are known | |
| From: Gottlob Frege (Grundgesetze der Arithmetik 2 (Basic Laws) [1903], §66) | |
| A reaction: Dummett cites this as Frege's rejection of contextual definitions, which he had employed in the Grundlagen. I take it not so much that they are wrong, as that Frege decided to set the bar a bit higher. |
| 10019 | Only what is logically complex can be defined; what is simple must be pointed to [Frege] |
| Full Idea: Only what is logically complex can be defined; what is simple can only be pointed to. | |
| From: Gottlob Frege (Grundgesetze der Arithmetik 2 (Basic Laws) [1903], §180), quoted by Harold Hodes - Logicism and Ontological Commits. of Arithmetic p.137 | |
| A reaction: Frege presumably has in mind his treasured abstract objects, such as cardinal numbers. It is hard to see how you could 'point to' anything in the phenomenal world that had atomic simplicity. Hodes calls this a 'desperate Kantian move'. |
| 9886 | Cardinals say how many, and reals give measurements compared to a unit quantity [Frege] |
| Full Idea: The cardinals and the reals are completely disjoint domains. The cardinal numbers answer the question 'How many objects of a given kind are there?', but the real numbers are for measurement, saying how large a quantity is compared to a unit quantity. | |
| From: Gottlob Frege (Grundgesetze der Arithmetik 2 (Basic Laws) [1903], §157), quoted by Michael Dummett - Frege philosophy of mathematics Ch.19 | |
| A reaction: We might say that cardinals are digital and reals are analogue. Frege is unusual in totally separating them. They map onto one another, after all. Cardinals look like special cases of reals. Reals are dreams about the gaps between cardinals. |
| 9889 | Real numbers are ratios of quantities [Frege, by Dummett] |
| Full Idea: Frege fixed on construing real numbers as ratios of quantities (in agreement with Newton). | |
| From: report of Gottlob Frege (Grundgesetze der Arithmetik 2 (Basic Laws) [1903]) by Michael Dummett - Frege philosophy of mathematics Ch.20 | |
| A reaction: If 3/4 is the same real number as 6/8, which is the correct ratio? Why doesn't the square root of 9/16 also express it? Why should irrationals be so utterly different from rationals? In what sense are they both 'numbers'? |
| 19406 | I strongly believe in the actual infinite, which indicates the perfections of its author [Leibniz] |
| Full Idea: I am so much for the actual infinite that instead of admitting that nature abhors it, as is commonly said, I hold that it affects nature everywhere in order to indicate the perfections of its author. | |
| From: Gottfried Leibniz (Reply to Foucher [1693], p.99) | |
| A reaction: I would have thought that, for Leibniz, while infinities indicate the perfections of their author, that is not the reason why they exist. God wasn't, presumably, showing off. Leibniz does not think we can actually know these infinities. |
| 10020 | Frege's biggest error is in not accounting for the senses of number terms [Hodes on Frege] |
| Full Idea: The inconsistency of Grundgesetze was only a minor flaw. Its fundamental flaw was its inability to account for the way in which the senses of number terms are determined. It leaves the reference-magnetic nature of the standard numberer a mystery. | |
| From: comment on Gottlob Frege (Grundgesetze der Arithmetik 2 (Basic Laws) [1903]) by Harold Hodes - Logicism and Ontological Commits. of Arithmetic p.139 | |
| A reaction: A point also made by Hofweber. As a logician, Frege was only concerned with the inferential role of number terms, and he felt he had captured their logical form, but it is when you come to look at numbers in natural language that he seem in trouble. |
| 10553 | A number is a class of classes of the same cardinality [Frege, by Dummett] |
| Full Idea: For Frege, in 'Grundgesetze', a number is a class of classes of the same cardinality. | |
| From: report of Gottlob Frege (Grundgesetze der Arithmetik 2 (Basic Laws) [1903]) by Michael Dummett - Frege Philosophy of Language (2nd ed) Ch.14 |
| 9887 | Formalism misunderstands applications, metatheory, and infinity [Frege, by Dummett] |
| Full Idea: Frege's three main objections to radical formalism are that it cannot account for the application of mathematics, that it confuses a formal theory with its metatheory, and it cannot explain an infinite sequence. | |
| From: report of Gottlob Frege (Grundgesetze der Arithmetik 2 (Basic Laws) [1903], §86-137) by Michael Dummett - Frege philosophy of mathematics | |
| A reaction: The application is because we don't design maths randomly, but to be useful. The third objection might be dealt with by potential infinities (from formal rules). The second objection sounds promising. |
| 8751 | Only applicability raises arithmetic from a game to a science [Frege] |
| Full Idea: It is applicability alone which elevates arithmetic from a game to the rank of a science. | |
| From: Gottlob Frege (Grundgesetze der Arithmetik 2 (Basic Laws) [1903], §91), quoted by Stewart Shapiro - Thinking About Mathematics 6.1.2 | |
| A reaction: This is the basic objection to Formalism. It invites the question of why it is applicable, which platonists like Frege don't seem to answer (though Plato himself has reality modelled on the Forms). This is why I like structuralism. |
| 9891 | The first demand of logic is of a sharp boundary [Frege] |
| Full Idea: The first demand of logic is of a sharp boundary. | |
| From: Gottlob Frege (Grundgesetze der Arithmetik 2 (Basic Laws) [1903], §160), quoted by Michael Dummett - Frege philosophy of mathematics Ch.22 | |
| A reaction: Nothing I have read about vagueness has made me doubt Frege's view of this, although precisification might allow you to do logic with vague concepts without having to finally settle where the actual boundaries are. |
| 12108 | All real knowledge rests on observed facts [Comte] |
| Full Idea: All competent thinkers agree with Bacon that there can be no real knowledge except that which rests upon observed facts. | |
| From: Auguste Comte (Intro to Positive Philosophy [1830], Ch.1) | |
| A reaction: Are there any unobservable facts? If so, can we know them? The only plausible route is to add 'best explanation' to the positivist armoury. With positivism, empiricism became - for a while - a quasi-religion. |
| 12109 | We must observe in order to form theories, but connected observations need prior theories [Comte] |
| Full Idea: There is a difficulty: the human mind had to observe in order to form real theories; and yet it had to form theories of some sort before it could apply itself to a connected series of observations. | |
| From: Auguste Comte (Intro to Positive Philosophy [1830], Ch.1) | |
| A reaction: Comte's view is that we get started by forming a silly theory (religion), and then refine the theory once the observations get going. Note that Comte has sort of anticipated the Quine-Duhem thesis. |
| 12107 | Positivism explains facts by connecting particular phenomena with general facts [Comte] |
| Full Idea: In positivism the explanation of facts consists only in the connection established between different particular phenomena and some general facts, the number of which the progress of science tends more and more to diminish. | |
| From: Auguste Comte (Intro to Positive Philosophy [1830], Ch.1) | |
| A reaction: This seems to be the ancestor of Hempel's more precisely formulated 'covering law' account, which became very fashionably, and now seems fairly discredited. It is just a fancy version of Humeanism about laws. |
| 12115 | Introspection is pure illusion; we can obviously observe everything except ourselves [Comte] |
| Full Idea: The pretended direct contemplation of the mind by itself is a pure illusion. ...It is clear that, by an inevitable necessity, the human mind can observe all phenomena directly, except its own. | |
| From: Auguste Comte (Intro to Positive Philosophy [1830], Ch.1) | |
| A reaction: I recently heard of a university psychology department which was seeking skilled introspectors to help with their researches. I take introspection to be very difficult, but partially possible. Read Proust. |
| 9890 | The modern account of real numbers detaches a ratio from its geometrical origins [Frege] |
| Full Idea: From geometry we retain the interpretation of a real number as a ratio of quantities or measurement-number; but in more recent times we detach it from geometrical quantities, and from all particular types of quantity. | |
| From: Gottlob Frege (Grundgesetze der Arithmetik 2 (Basic Laws) [1903], §159), quoted by Michael Dummett - Frege philosophy of mathematics | |
| A reaction: Dummett glosses the 'recent' version as by Cantor and Dedekind in 1872. This use of 'detach' seems to me startlingly like the sort of psychological abstractionism which Frege was so desperate to avoid. |
| 11846 | If we abstract the difference between two houses, they don't become the same house [Frege] |
| Full Idea: If abstracting from the difference between my house and my neighbour's, I were to regard both houses as mine, the defect of the abstraction would soon be made clear. It may, though, be possible to obtain a concept by means of abstraction... | |
| From: Gottlob Frege (Grundgesetze der Arithmetik 2 (Basic Laws) [1903], §99) | |
| A reaction: Note the important concession at the end, which shows Frege could never deny the abstraction process, despite all the modern protests by Geach and Dummett that he totally rejected it. |
| 12113 | The search for first or final causes is futile [Comte] |
| Full Idea: We regard the search after what are called causes, whether first or final, as absolutely inaccessible and unmeaning. | |
| From: Auguste Comte (Intro to Positive Philosophy [1830], Ch.1) | |
| A reaction: This remark lies behind Russell's rejection of the notion of cause in scientific thinking. Personally it seems to me indispensable, even if we accept that the pursuit of 'final' causes is fairly hopeless. We don't know where the quest will lead. |
| 12110 | We can never know origins, purposes or inner natures [Comte] |
| Full Idea: The inner nature of objects, or the origin and purpose of all phenomena, are the most insoluble questions. | |
| From: Auguste Comte (Intro to Positive Philosophy [1830], Ch.1) | |
| A reaction: I take it that this Humean pessimism about science ever penetrating below the surface is precisely what is challenged by modern science, and that 'scientific essentialism' is catching up with what has happened. 'Inner' is knowable, bottom level isn't. |