21 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 Comte is preparing the ground for asserting positivism by rejecting out-of-date theology and metaphysics.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. |
| 17610 | The Axiom of Choice paradoxically allows decomposing a sphere into two identical spheres [Maddy] |
| Full Idea: One feature of the Axiom of Choice that troubled many mathematicians was the so-called Banach-Tarski paradox: using the Axiom, a sphere can be decomposed into finitely many parts and those parts reassembled into two spheres the same size as the original. | |
| From: Penelope Maddy (Defending the Axioms [2011], 1.3) | |
| A reaction: (The key is that the parts are non-measurable). To an outsider it is puzzling that the Axiom has been universally accepted, even though it produces such a result. Someone can explain that, I'm sure. |
| 17620 | Critics of if-thenism say that not all starting points, even consistent ones, are worth studying [Maddy] |
| Full Idea: If-thenism denies that mathematics is in the business of discovering truths about abstracta. ...[their opponents] obviously don't regard any starting point, even a consistent one, as equally worthy of investigation. | |
| From: Penelope Maddy (Defending the Axioms [2011], 3.3) | |
| A reaction: I have some sympathy with if-thenism, in that you can obviously study the implications of any 'if' you like, but deep down I agree with the critics. |
| 17605 | Hilbert's geometry and Dedekind's real numbers were role models for axiomatization [Maddy] |
| Full Idea: At the end of the nineteenth century there was a renewed emphasis on rigor, the central tool of which was axiomatization, along the lines of Hilbert's axioms for geometry and Dedekind's axioms for real numbers. | |
| From: Penelope Maddy (Defending the Axioms [2011], 1.3) |
| 17625 | If two mathematical themes coincide, that suggest a single deep truth [Maddy] |
| Full Idea: The fact that two apparently fruitful mathematical themes turn out to coincide makes it all the more likely that they're tracking a genuine strain of mathematical depth. | |
| From: Penelope Maddy (Defending the Axioms [2011], 5.3ii) |
| 17615 | Every infinite set of reals is either countable or of the same size as the full set of reals [Maddy] |
| Full Idea: One form of the Continuum Hypothesis is the claim that every infinite set of reals is either countable or of the same size as the full set of reals. | |
| From: Penelope Maddy (Defending the Axioms [2011], 2.4 n40) |
| 17618 | Set-theory tracks the contours of mathematical depth and fruitfulness [Maddy] |
| Full Idea: Our set-theoretic methods track the underlying contours of mathematical depth. ...What sets are, most fundamentally, is markers for these contours ...they are maximally effective trackers of certain trains of mathematical fruitfulness. | |
| From: Penelope Maddy (Defending the Axioms [2011], 3.4) | |
| A reaction: This seems to make it more like a map of mathematics than the actual essence of mathematics. |
| 17614 | The connection of arithmetic to perception has been idealised away in modern infinitary mathematics [Maddy] |
| Full Idea: Ordinary perceptual cognition is most likely involved in our grasp of elementary arithmetic, but ...this connection to the physical world has long since been idealized away in the infinitary structures of contemporary pure mathematics. | |
| From: Penelope Maddy (Defending the Axioms [2011], 2.3) | |
| A reaction: Despite this, Maddy's quest is for a 'naturalistic' account of mathematics. She ends up defending 'objectivity' (and invoking Tyler Burge), rather than even modest realism. You can't 'idealise away' the counting of objects. I blame Cantor. |
| 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. |
| 468 | Musical performance can reveal a range of virtues [Damon of Ath.] |
| Full Idea: In singing and playing the lyre, a boy will be likely to reveal not only courage and moderation, but also justice. | |
| From: Damon (fragments/reports [c.460 BCE], B4), quoted by (who?) - where? |
| 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. |