34 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 Comte is preparing the ground for asserting positivism by rejecting out-of-date theology and metaphysics.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. |
| 22270 | Frege changed philosophy by extending logic's ability to check the grounds of thinking [Potter on Frege] |
| Full Idea: Frege's 1879 logic transformed philosophy because it greatly expanded logic's reach - what thought can achieve unaided - and hence compelled a re-examination of everything previously said about the grounds of thought when logic gives out. | |
| From: comment on Gottlob Frege (Begriffsschrift [1879]) by Michael Potter - The Rise of Analytic Philosophy 1879-1930 Intro | |
| A reaction: I loved the gloss on logic as 'what thought can achieve unaided'. I largely see logic in terms of what is mechanically computable. |
| 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. |
| 8939 | We should not describe human laws of thought, but how to correctly track truth [Frege, by Fisher] |
| Full Idea: Frege disagree that logic should merely describe the laws of thought - how people actually did reason. Logic is essentially normative, not descriptive. We want the one logic which successfully tracks the truth. | |
| From: report of Gottlob Frege (Begriffsschrift [1879]) by Jennifer Fisher - On the Philosophy of Logic 1.III | |
| A reaction: This explains Frege's sustained attack on psychologism, and it also explains we he ended up as a platonist about logic - because he wanted its laws to be valid independently of human thinking. A step too far, perhaps. Brains are truth machines. |
| 4971 | I don't use 'subject' and 'predicate' in my way of representing a judgement [Frege] |
| Full Idea: A distinction of subject and predicate finds no place in my way of representing a judgement. | |
| From: Gottlob Frege (Begriffsschrift [1879], §03) | |
| A reaction: Perhaps this sentence could be taken as the beginning of modern analytical philosophy. The old view doesn't seem to me entirely redundant - merely replaced by a much more detailed analysis of what makes a 'subject' and what makes a 'predicate'. |
| 17745 | For Frege, 'All A's are B's' means that the concept A implies the concept B [Frege, by Walicki] |
| Full Idea: 'All A's are B's' meant for Frege that the concept A implies the concept B, or that to be A implies also to be B. Moreover this applies to arbitrary x which happens to be A. | |
| From: report of Gottlob Frege (Begriffsschrift [1879]) by Michal Walicki - Introduction to Mathematical Logic History D.2 | |
| A reaction: This seems to hit the renate/cordate problem. If all creatures with hearts also have kidneys, does that mean that being enhearted logically implies being kidneyfied? If all chimps are hairy, is that a logical requirement? Is inclusion implication? |
| 7728 | Frege has a judgement stroke (vertical, asserting or judging) and a content stroke (horizontal, expressing) [Frege, by Weiner] |
| Full Idea: Frege distinguished between asserting a proposition and expressing it, and he introduced the judgement stroke (a small vertical line, assertion) and the content stroke (a long horizontal line, expression) to represent them. | |
| From: report of Gottlob Frege (Begriffsschrift [1879]) by Joan Weiner - Frege Ch.3 | |
| A reaction: There are also strokes for conditional and denial. |
| 16881 | The laws of logic are boundless, so we want the few whose power contains the others [Frege] |
| Full Idea: Since in view of the boundless multitude of laws that can be enunciated we cannot list them all, we cannot achieve completeness except by searching out those that, by their power, contain all of them. | |
| From: Gottlob Frege (Begriffsschrift [1879], §13) | |
| A reaction: He refers to these laws in the previous sentence as the 'core'. His talk of 'power' is music to my ears, since it implies a direction of explanation. Burge says the power is that of defining other concepts. |
| 7622 | In 1879 Frege developed second order logic [Frege, by Putnam] |
| Full Idea: By 1879 Frege had discovered an algorithm, a mechanical proof procedure, that embraces what is today standard 'second order logic'. | |
| From: report of Gottlob Frege (Begriffsschrift [1879]) by Hilary Putnam - Reason, Truth and History Ch.5 | |
| A reaction: Note that Frege did more than introduce quantifiers, and the logic of predicates. |
| 7729 | Frege replaced Aristotle's subject/predicate form with function/argument form [Frege, by Weiner] |
| Full Idea: Frege's regimentation is based on the view of the simplest sort of statement as having, not subject/predicate form (as in Aristotle), but function/argument form. | |
| From: report of Gottlob Frege (Begriffsschrift [1879]) by Joan Weiner - Frege | |
| A reaction: This looks like being a crucial move into the modern world, where one piece of information is taken in and dealt with, as in computer procedures. Have educated people reorganised their minds along Fregean lines? |
| 9950 | A quantifier is a second-level predicate (which explains how it contributes to truth-conditions) [Frege, by George/Velleman] |
| Full Idea: The contribution of the quantifier to the truth conditions of sentences of which it is a part cannot be adequately explained if it is treated as other than a second-level predicate (for instance, if it is viewed as name). | |
| From: report of Gottlob Frege (Begriffsschrift [1879]) by A.George / D.J.Velleman - Philosophies of Mathematics Ch.2 | |
| A reaction: They suggest that this makes it something like a 'property of properties'. With this account it becomes plausible to think of numbers as quantifiers (since they do, after all, specify quantities). |
| 9991 | For Frege the variable ranges over all objects [Frege, by Tait] |
| Full Idea: For Frege the variable ranges over all objects. | |
| From: report of Gottlob Frege (Begriffsschrift [1879]) by William W. Tait - Frege versus Cantor and Dedekind XII | |
| A reaction: The point is that Frege had not yet seen the necessity to define the domain of quantification, and this leads him into various difficulties. |
| 10536 | Frege's domain for variables is all objects, but modern interpretations first fix the domain [Dummett on Frege] |
| Full Idea: For Frege there is no need to specify the domain of the individual variables, which is taken as the totality of all objects. This contrasts with the standard notion of an interpretation, which demands that we first fix the domain. | |
| From: comment on Gottlob Frege (Begriffsschrift [1879]) by Michael Dummett - Frege Philosophy of Language (2nd ed) Ch.14 | |
| A reaction: What intrigues me is how domains of quantification shift according to context in ordinary usage, even in mid-sentence. I ought to go through every idea in this database, specifying its domain of quantification. Any volunteers? |
| 7730 | Frege introduced quantifiers for generality [Frege, by Weiner] |
| Full Idea: In order to express generality, Frege introduced quantifier notation. | |
| From: report of Gottlob Frege (Begriffsschrift [1879]) by Joan Weiner - Frege | |
| A reaction: This is the birth of predicate logic, beloved of analytical philosophers (but of no apparent interest to phenomenalists, deconstructionists, existentialists?). Generality is what you get from induction (which is, of course, problematic). |
| 7742 | Frege reduced most quantifiers to 'everything' combined with 'not' [Frege, by McCullogh] |
| Full Idea: Frege treated 'everything' as basic, and suggested ways of recasting propositions containing other quantifiers so that this was the only one remaining. He recast 'something' as 'at least one thing', and defined this in terms of 'everything' and 'not'. | |
| From: report of Gottlob Frege (Begriffsschrift [1879]) by Gregory McCullogh - The Game of the Name 1.6 | |
| A reaction: Extreme parsimony seems highly desirable in logic as well as ontology, but it can lead to frustrations, especially over the crucial question of the existence of things quantified over. See Idea 6068. |
| 13824 | Proof theory began with Frege's definition of derivability [Frege, by Prawitz] |
| Full Idea: Frege's formal definition of derivability is perhaps the first investigation in general proof theory. | |
| From: report of Gottlob Frege (Begriffsschrift [1879]) by Dag Prawitz - Gentzen's Analysis of First-Order Proofs 2 n2 | |
| A reaction: In 'On General Proof Theory §1' Prawitz says "proof theory originated with Hilbert" in 1900. Presumably Frege offered a theory, and then Hilbert saw it as a general project. |
| 13609 | Frege produced axioms for logic, though that does not now seem the natural basis for logic [Frege, by Kaplan] |
| Full Idea: Frege's work supplied a set of axioms for logic itself, at least partly because it was a well-known way of presenting the foundations in other disciplines, especially mathematics, but it does not nowadays strike us as natural for logic. | |
| From: report of Gottlob Frege (Begriffsschrift [1879]) by David Kaplan - Dthat 5.1 | |
| A reaction: What Bostock has in mind is the so-called 'natural' deduction systems, which base logic on rules of entailment, rather than on a set of truths. The axiomatic approach uses a set of truths, plus the idea of possible contradictions. |
| 17855 | It may be possible to define induction in terms of the ancestral relation [Frege, by Wright,C] |
| Full Idea: Frege's account of the ancestral has made it possible, in effect, to define the natural numbers as entities for which induction holds. | |
| From: report of Gottlob Frege (Begriffsschrift [1879]) by Crispin Wright - Frege's Concept of Numbers as Objects 4.xix | |
| A reaction: This is the opposite of the approach in the Peano Axioms, where induction is used to define the natural numbers. |
| 10607 | Frege's logic has a hierarchy of object, property, property-of-property etc. [Frege, by Smith,P] |
| Full Idea: Frege's general logical system involves a type hierarchy, distinguishing objects from properties from properties-of-properties etc., with every item belonging to a determinate level. | |
| From: report of Gottlob Frege (Begriffsschrift [1879]) by Peter Smith - Intro to Gödel's Theorems 14.1 | |
| A reaction: The Theory of Types went on to apply this hierarchy to classes, where Frege's disastrous Basic Law V flattens the hierarchy of classes, putting them on the same level (Smith p.119) |
| 11008 | Existence is not a first-order property, but the instantiation of a property [Frege, by Read] |
| Full Idea: When Kant said that existence was not a property, what he meant was, according to Frege, that existence is not a first-order property - it is not a property of individuals but a property of properties, that the property has an instance. | |
| From: report of Gottlob Frege (Begriffsschrift [1879]) by Stephen Read - Thinking About Logic Ch.5 |
| 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. |
| 22280 | Frege's account was top-down and decompositional, not bottom-up and compositional [Frege, by Potter] |
| Full Idea: Frege's account was top-down, not bottom-up: he aimed to decompose and discern function-argument structure in already existing sentences, not to explain how those sentences acquired their meanings in the first place. | |
| From: report of Gottlob Frege (Begriffsschrift [1879]) by Michael Potter - The Rise of Analytic Philosophy 1879-1930 03 'Func' | |
| A reaction: This goes with the holistic account of meaning, which leads to Quine's gavagai and Kuhn's obfuscation of science. I recommend compositionality for everthing. |
| 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. |
| 7741 | The predicate 'exists' is actually a natural language expression for a quantifier [Frege, by Weiner] |
| Full Idea: On Frege's logical analysis, the predicate 'exists' is actually a natural language expression for a quantifier. | |
| From: report of Gottlob Frege (Begriffsschrift [1879]) by Joan Weiner - Frege Ch.8 | |
| A reaction: However see Idea 6067, for McGinn's alternative view of quantifiers. In the normal conventions of predicate logic it may be that existence is treated as a quantifier, but that is not the same as saying that existence just IS a quantifier. |