72 ideas
| 19250 | Everything interesting should be recorded, with records that can be rearranged [Peirce] |
| Full Idea: Everything worth notice is worth recording; and those records should be so made that they can readily be arranged, and particularly so that they can be rearranged. | |
| From: Charles Sanders Peirce (Reasoning and the Logic of Things [1898], V) | |
| A reaction: Yet another epigraph for my project! Peirce must have had a study piled with labelled notes, and he would have adored this database, at least in its theory. |
| 19228 | Sciences concern existence, but philosophy also concerns potential existence [Peirce] |
| Full Idea: Philosophy differs from the special sciences in not confining itself to the reality of existence, but also to the reality of potential being. | |
| From: Charles Sanders Peirce (Reasoning and the Logic of Things [1898], I) | |
| A reaction: One might reply that sciences also concern potential being, if their output is universal generalisations (such as 'laws'). I take disposition and powers to be central to existence, which are hence of interest to sciences. |
| 19241 | An idea on its own isn't an idea, because they are continuous systems [Peirce] |
| Full Idea: There is no such thing as an absolutely detached idea. It would be no idea at all. For an idea is itself a continuous system. | |
| From: Charles Sanders Peirce (Reasoning and the Logic of Things [1898], III) | |
| A reaction: This is the new anti-epigraph for this database. This idea is part of Peirce's idea that relations are the central feature of our grasp of the world. |
| 19227 | Philosophy is a search for real truth [Peirce] |
| Full Idea: Philosophy differs from mathematics in being a search for real truth. | |
| From: Charles Sanders Peirce (Reasoning and the Logic of Things [1898], I) | |
| A reaction: This is important, coming from the founder of pragmatism, in rejecting the anti-realism which a lot of modern pragmatists seem to like. |
| 19218 | Metaphysics is pointless without exact modern logic [Peirce] |
| Full Idea: The metaphysician who is not prepared to grapple with the difficulties of modern exact logic had better put up his shutters and go out of the trade. | |
| From: Charles Sanders Peirce (Reasoning and the Logic of Things [1898], I) | |
| A reaction: This announcement comes before Russell proclaimed mathematical logic to be the heart of metaphysics (though it is contemporary with Frege's work, of which Peirce was unaware). It places Peirce firmly in the analytic tradition. |
| 19229 | Metaphysics is the science of both experience, and its general laws and types [Peirce] |
| Full Idea: Metaphysics is the science of being, not merely as given in physical experience, but of being in general, its laws and types. | |
| From: Charles Sanders Peirce (Reasoning and the Logic of Things [1898], I) | |
| A reaction: I agree with this. The question then is whether such a science is possible. Dogmatic empiricists think not. Explanatory empiricists (me) think it is. |
| 19219 | Metaphysical reasoning is simple enough, but the concepts are very hard [Peirce] |
| Full Idea: Metaphysical reasonings, such as they have hitherto been, have been simple enough for the most part. It is the metaphysical concepts which it is difficult to apprehend. | |
| From: Charles Sanders Peirce (Reasoning and the Logic of Things [1898], I) | |
| A reaction: Peirce is not, of course, saying that it is just conceptual, because for him science comes first. It is the woolly concepts that alienate some people from metaphysics. Metaphysicians should challenge the concepts they use much, much more! |
| 19231 | Metaphysics is turning into logic, and logic is becoming mathematics [Peirce] |
| Full Idea: Metaphysics is gradually and surely taking on the character of a logic. And finally seems destined to become more and more converted into mathematics. | |
| From: Charles Sanders Peirce (Reasoning and the Logic of Things [1898], I) | |
| A reaction: Remarkably prescient for 1898. I don't think Peirce knew of Frege (and certainly not when he wrote this). It shows that the revolution of Frege and Russell was in the air. It's there in Dedekind's writings. Peirce doesn't seem to be a logicist. |
| 17774 | Definitions make our intuitions mathematically useful [Mayberry] |
| Full Idea: Definition provides us with the means for converting our intuitions into mathematically usable concepts. | |
| From: John Mayberry (What Required for Foundation for Maths? [1994], p.405-1) |
| 17773 | Proof shows that it is true, but also why it must be true [Mayberry] |
| Full Idea: When you have proved something you know not only that it is true, but why it must be true. | |
| From: John Mayberry (What Required for Foundation for Maths? [1994], p.405-2) | |
| A reaction: Note the word 'must'. Presumably both the grounding and the necessitation of the truth are revealed. |
| 19247 | The one unpardonable offence in reasoning is to block the route to further truth [Peirce] |
| Full Idea: To set up a philosophy which barricades the road of further advance toward the truth is the one unpardonable offence in reasoning. | |
| From: Charles Sanders Peirce (Reasoning and the Logic of Things [1898], IV) | |
| A reaction: This is Popper's rather dubious objection to essentialism in science. Yet Popper tried to do the same thing with his account of induction. |
| 19246 | 'Holding for true' is either practical commitment, or provisional theory [Peirce] |
| Full Idea: Whether or not 'truth' has two meanings, I think 'holding for true' has two kinds. One is practical holding for true which alone is entitled to the name of Belief; the other is the acceptance of a proposition, which in pure science is always provisional. | |
| From: Charles Sanders Peirce (Reasoning and the Logic of Things [1898], IV) | |
| A reaction: The problem here seems to be that we can act on a proposition without wholly believing it, like walking across thin ice. |
| 17795 | Set theory can't be axiomatic, because it is needed to express the very notion of axiomatisation [Mayberry] |
| Full Idea: Set theory cannot be an axiomatic theory, because the very notion of an axiomatic theory makes no sense without it. | |
| From: John Mayberry (What Required for Foundation for Maths? [1994], p.413-2) | |
| A reaction: This will come as a surprise to Penelope Maddy, who battles with ways to accept the set theory axioms as the foundation of mathematics. Mayberry says that the basic set theory required is much more simple and intuitive. |
| 17796 | There is a semi-categorical axiomatisation of set-theory [Mayberry] |
| Full Idea: We can give a semi-categorical axiomatisation of set-theory (all that remains undetermined is the size of the set of urelements and the length of the sequence of ordinals). The system is second-order in formalisation. | |
| From: John Mayberry (What Required for Foundation for Maths? [1994], p.413-2) | |
| A reaction: I gather this means the models may not be isomorphic to one another (because they differ in size), but can be shown to isomorphic to some third ingredient. I think. Mayberry says this shows there is no such thing as non-Cantorian set theory. |
| 17800 | The misnamed Axiom of Infinity says the natural numbers are finite in size [Mayberry] |
| Full Idea: The (misnamed!) Axiom of Infinity expresses Cantor's fundamental assumption that the species of natural numbers is finite in size. | |
| From: John Mayberry (What Required for Foundation for Maths? [1994], p.414-2) |
| 17801 | The set hierarchy doesn't rely on the dubious notion of 'generating' them [Mayberry] |
| Full Idea: The idea of 'generating' sets is only a metaphor - the existence of the hierarchy is established without appealing to such dubious notions. | |
| From: John Mayberry (What Required for Foundation for Maths? [1994], p.414-2) | |
| A reaction: Presumably there can be a 'dependence' or 'determination' relation which does not involve actual generation. |
| 17803 | Limitation of size is part of the very conception of a set [Mayberry] |
| Full Idea: Our very notion of a set is that of an extensional plurality limited in size. | |
| From: John Mayberry (What Required for Foundation for Maths? [1994], p.415-2) |
| 17786 | The mainstream of modern logic sees it as a branch of mathematics [Mayberry] |
| Full Idea: In the mainstream tradition of modern logic, beginning with Boole, Peirce and Schröder, descending through Löwenheim and Skolem to reach maturity with Tarski and his school ...saw logic as a branch of mathematics. | |
| From: John Mayberry (What Required for Foundation for Maths? [1994], p.410-1) | |
| A reaction: [The lesser tradition, of Frege and Russell, says mathematics is a branch of logic]. Mayberry says the Fregean tradition 'has almost died out'. |
| 17788 | First-order logic only has its main theorems because it is so weak [Mayberry] |
| Full Idea: First-order logic is very weak, but therein lies its strength. Its principle tools (Compactness, Completeness, Löwenheim-Skolem Theorems) can be established only because it is too weak to axiomatize either arithmetic or analysis. | |
| From: John Mayberry (What Required for Foundation for Maths? [1994], p.411-2) | |
| A reaction: He adds the proviso that this is 'unless we are dealing with structures on whose size we have placed an explicit, finite bound' (p.412-1). |
| 17791 | Only second-order logic can capture mathematical structure up to isomorphism [Mayberry] |
| Full Idea: Second-order logic is a powerful tool of definition: by means of it alone we can capture mathematical structure up to isomorphism using simple axiom systems. | |
| From: John Mayberry (What Required for Foundation for Maths? [1994], p.412-1) |
| 19237 | Deduction is true when the premises facts necessarily make the conclusion fact true [Peirce] |
| Full Idea: The question of whether a deductive argument is true or not is simply the question whether or not the facts stated in the premises could be true in any sort of universe no matter what be true without the fact stated in the conclusion being true likewise. | |
| From: Charles Sanders Peirce (Reasoning and the Logic of Things [1898], III) | |
| A reaction: A remarkably modern account, fitting the normal modern view of semantic consequence, and expressing the necessity in the validity in terms of something close to possible worlds. |
| 19256 | Our research always hopes that reality embodies the logic we are employing [Peirce] |
| Full Idea: Every attempt to understand anything at least hopes that the very objects of study themselves are subject to a logic more or less identical with that which we employ. | |
| From: Charles Sanders Peirce (Reasoning and the Logic of Things [1898], VIII) | |
| A reaction: The idea that external objects might be subject to a logic has become very unfashionable since Frege, but I love the idea. I'm inclined to think that we derive our logic from the world, so I'm a bit more confident that Peirce. |
| 19238 | The logic of relatives relies on objects built of any relations (rather than on classes) [Peirce] |
| Full Idea: In the place of the class ...the logic of relatives considers the system, which is composed of objects brought together by any kind of relations whatsoever. | |
| From: Charles Sanders Peirce (Reasoning and the Logic of Things [1898], III) | |
| A reaction: Peirce's logic of relations might support the purely structural view of reality defended by Ladyman and Ross. Modern logic standardly expresses its semantics in terms of set theory. Peirce pioneered relations in logic. |
| 17787 | Big logic has one fixed domain, but standard logic has a domain for each interpretation [Mayberry] |
| Full Idea: The 'logica magna' [of the Fregean tradition] has quantifiers ranging over a fixed domain, namely everything there is. In the Boolean tradition the domains differ from interpretation to interpretation. | |
| From: John Mayberry (What Required for Foundation for Maths? [1994], p.410-2) | |
| A reaction: Modal logic displays both approaches, with different systems for global and local domains. |
| 17790 | No Löwenheim-Skolem logic can axiomatise real analysis [Mayberry] |
| Full Idea: No logic which can axiomatize real analysis can have the Löwenheim-Skolem property. | |
| From: John Mayberry (What Required for Foundation for Maths? [1994], p.412-1) |
| 17779 | 'Classificatory' axioms aim at revealing similarity in morphology of structures [Mayberry] |
| Full Idea: The purpose of a 'classificatory' axiomatic theory is to single out an otherwise disparate species of structures by fixing certain features of morphology. ...The aim is to single out common features. | |
| From: John Mayberry (What Required for Foundation for Maths? [1994], p.406-2) |
| 17778 | Axiomatiation relies on isomorphic structures being essentially the same [Mayberry] |
| Full Idea: The central dogma of the axiomatic method is this: isomorphic structures are mathematically indistinguishable in their essential properties. | |
| From: John Mayberry (What Required for Foundation for Maths? [1994], p.406-2) | |
| A reaction: Hence it is not that we have to settle for the success of a system 'up to isomorphism', since that was the original aim. The structures must differ in their non-essential properties, or they would be the same system. |
| 17780 | 'Eliminatory' axioms get rid of traditional ideal and abstract objects [Mayberry] |
| Full Idea: The purpose of what I am calling 'eliminatory' axiomatic theories is precisely to eliminate from mathematics those peculiar ideal and abstract objects that, on the traditional view, constitute its subject matter. | |
| From: John Mayberry (What Required for Foundation for Maths? [1994], p.407-1) | |
| A reaction: A very interesting idea. I have a natural antipathy to 'abstract objects', because they really mess up what could otherwise be a very tidy ontology. What he describes might be better called 'ignoring' axioms. The objects may 'exist', but who cares? |
| 17789 | No logic which can axiomatise arithmetic can be compact or complete [Mayberry] |
| Full Idea: No logic which can axiomatise arithmetic can be compact or complete. | |
| From: John Mayberry (What Required for Foundation for Maths? [1994], p.412-1) | |
| A reaction: I take this to be because there are new truths in the transfinite level (as well as the problem of incompleteness). |
| 17784 | Real numbers can be eliminated, by axiom systems for complete ordered fields [Mayberry] |
| Full Idea: We eliminate the real numbers by giving an axiomatic definition of the species of complete ordered fields. These axioms are categorical (mutually isomorphic), and thus are mathematically indistinguishable. | |
| From: John Mayberry (What Required for Foundation for Maths? [1994], p.408-2) | |
| A reaction: Hence my clever mathematical friend says that it is a terrible misunderstanding to think that mathematics is about numbers. Mayberry says the reals are one ordered field, but mathematics now studies all ordered fields together. |
| 17782 | Greek quantities were concrete, and ratio and proportion were their science [Mayberry] |
| Full Idea: Quantities for Greeks were concrete things - lines, surfaces, solids, times, weights. At the centre of their science of quantity was the beautiful theory of ratio and proportion (...in which the notion of number does not appear!). | |
| From: John Mayberry (What Required for Foundation for Maths? [1994], p.407-2) | |
| A reaction: [He credits Eudoxus, and cites Book V of Euclid] |
| 17781 | Real numbers were invented, as objects, to simplify and generalise 'quantity' [Mayberry] |
| Full Idea: The abstract objects of modern mathematics, the real numbers, were invented by the mathematicians of the seventeenth century in order to simplify and to generalize the Greek science of quantity. | |
| From: John Mayberry (What Required for Foundation for Maths? [1994], p.407-2) |
| 17799 | Cantor's infinite is an absolute, of all the sets or all the ordinal numbers [Mayberry] |
| Full Idea: In Cantor's new vision, the infinite, the genuine infinite, does not disappear, but presents itself in the guise of the absolute, as manifested in the species of all sets or the species of all ordinal numbers. | |
| From: John Mayberry (What Required for Foundation for Maths? [1994], p.414-2) |
| 17797 | Cantor extended the finite (rather than 'taming the infinite') [Mayberry] |
| Full Idea: We may describe Cantor's achievement by saying, not that he tamed the infinite, but that he extended the finite. | |
| From: John Mayberry (What Required for Foundation for Maths? [1994], p.414-2) |
| 17775 | If proof and definition are central, then mathematics needs and possesses foundations [Mayberry] |
| Full Idea: If we grant, as surely we must, the central importance of proof and definition, then we must also grant that mathematics not only needs, but in fact has, foundations. | |
| From: John Mayberry (What Required for Foundation for Maths? [1994], p.405-1) |
| 17776 | The ultimate principles and concepts of mathematics are presumed, or grasped directly [Mayberry] |
| Full Idea: The ultimate principles upon which mathematics rests are those to which mathematicians appeal without proof; and the primitive concepts of mathematics ...themselves are grasped directly, if grasped at all, without the mediation of definition. | |
| From: John Mayberry (What Required for Foundation for Maths? [1994], p.405-1) | |
| A reaction: This begs the question of whether the 'grasping' is purely a priori, or whether it derives from experience. I defend the latter, and Jenkins puts the case well. |
| 17777 | Foundations need concepts, definition rules, premises, and proof rules [Mayberry] |
| Full Idea: An account of the foundations of mathematics must specify four things: the primitive concepts for use in definitions, the rules governing definitions, the ultimate premises of proofs, and rules allowing advance from premises to conclusions. | |
| From: John Mayberry (What Required for Foundation for Maths? [1994], p.405-2) |
| 17804 | Axiom theories can't give foundations for mathematics - that's using axioms to explain axioms [Mayberry] |
| Full Idea: No axiomatic theory, formal or informal, of first or of higher order can logically play a foundational role in mathematics. ...It is obvious that you cannot use the axiomatic method to explain what the axiomatic method is. | |
| From: John Mayberry (What Required for Foundation for Maths? [1994], p.415-2) |
| 17792 | 1st-order PA is only interesting because of results which use 2nd-order PA [Mayberry] |
| Full Idea: The sole theoretical interest of first-order Peano arithmetic derives from the fact that it is a first-order reduct of a categorical second-order theory. Its axioms can be proved incomplete only because the second-order theory is categorical. | |
| From: John Mayberry (What Required for Foundation for Maths? [1994], p.412-1) |
| 17793 | It is only 2nd-order isomorphism which suggested first-order PA completeness [Mayberry] |
| Full Idea: If we did not know that the second-order axioms characterise the natural numbers up to isomorphism, we should have no reason to suppose, a priori, that first-order Peano Arithmetic should be complete. | |
| From: John Mayberry (What Required for Foundation for Maths? [1994], p.412-1) |
| 17794 | Set theory is not just first-order ZF, because that is inadequate for mathematics [Mayberry] |
| Full Idea: The idea that set theory must simply be identified with first-order Zermelo-Fraenkel is surprisingly widespread. ...The first-order axiomatic theory of sets is clearly inadequate as a foundation of mathematics. | |
| From: John Mayberry (What Required for Foundation for Maths? [1994], p.412-2) | |
| A reaction: [He is agreeing with a quotation from Skolem]. |
| 17802 | We don't translate mathematics into set theory, because it comes embodied in that way [Mayberry] |
| Full Idea: One does not have to translate 'ordinary' mathematics into the Zermelo-Fraenkel system: ordinary mathematics comes embodied in that system. | |
| From: John Mayberry (What Required for Foundation for Maths? [1994], p.415-1) | |
| A reaction: Mayberry seems to be a particular fan of set theory as spelling out the underlying facts of mathematics, though it has to be second-order. |
| 17805 | Set theory is not just another axiomatised part of mathematics [Mayberry] |
| Full Idea: The fons et origo of all confusion is the view that set theory is just another axiomatic theory and the universe of sets just another mathematical structure. ...The universe of sets ...is the world that all mathematical structures inhabit. | |
| From: John Mayberry (What Required for Foundation for Maths? [1994], p.416-1) |
| 19226 | We now know that mathematics only studies hypotheses, not facts [Peirce] |
| Full Idea: It did not become clear to mathematicians before modern times that they study nothing but hypotheses without as pure mathematicians caring at all how the actual facts may be. | |
| From: Charles Sanders Peirce (Reasoning and the Logic of Things [1898], I) | |
| A reaction: 'Modern' here is 1898. As a logical principle this would seem to qualify as 'if-thenism' (see alphabetical themes). It's modern descendant might be modal structuralism (see Geoffrey Hellman). It take maths to be hypotheses abstracted from experience. |
| 19240 | Realism is the belief that there is something in the being of things corresponding to our reasoning [Peirce] |
| Full Idea: If there is any reality, then it consists of this: that there is in the being of things something which corresponds to the process of reasoning. | |
| From: Charles Sanders Peirce (Reasoning and the Logic of Things [1898], III) | |
| A reaction: A nice definition of realism, a little different from usual. I belief that the normal logic of daily thought corresponds (in its rules and connectives) to the way the world is. We evaluate success in logic by truth-preservation. |
| 19239 | There may be no reality; it's just our one desperate hope of knowing anything [Peirce] |
| Full Idea: What is reality? Perhaps there isn't any such thing at all. It is but a working hypothesis which we try, our one desperate forlorn hope of knowing anything. | |
| From: Charles Sanders Peirce (Reasoning and the Logic of Things [1898], III) | |
| A reaction: I'm not quite sure why the hope is 'forlorn'. We have no current reason to doubt that the hypothesis is working out extremely well. Lovely idea, though. |
| 14296 | Dispositions are physical states of mechanism; when known, these replace the old disposition term [Quine] |
| Full Idea: Each disposition, in my view, is a physical state or mechanism. ...In some cases nowadays we understand the physical details and set them forth explicitly in terms of the arrangement and interaction of small bodies. This replaces the old disposition. | |
| From: Willard Quine (The Roots of Reference [1990], p.11), quoted by Stephen Mumford - Dispositions 01.3 | |
| A reaction: A challenge to the dispositions and powers view of nature, one which rests on the 'categorical' structural properties, rather than the 'hypothetical' dispositions. But can we define a mechanism without mentioning its powers? |
| 17785 | Real numbers as abstracted objects are now treated as complete ordered fields [Mayberry] |
| Full Idea: The abstractness of the old fashioned real numbers has been replaced by generality in the modern theory of complete ordered fields. | |
| From: John Mayberry (What Required for Foundation for Maths? [1994], p.408-2) | |
| A reaction: In philosophy, I'm increasingly thinking that we should talk much more of 'generality', and a great deal less about 'universals'. (By which I don't mean that redness is just the set of red things). |
| 19252 | Objective chance is the property of a distribution [Peirce] |
| Full Idea: Chance, as an objective phenomenon, is a property of a distribution. ...In order to have any meaning, it must refer to some definite arrangement of all the things. | |
| From: Charles Sanders Peirce (Reasoning and the Logic of Things [1898], VI) |
| 19232 | In ordinary language a conditional statement assumes that the antecedent is true [Peirce] |
| Full Idea: In our ordinary use of language we always understand the range of possibility in such a sense that in some possible case the antecedent shall be true. | |
| From: Charles Sanders Peirce (Reasoning and the Logic of Things [1898], II) | |
| A reaction: Peirce is discussing Diodorus, and proposes the view nowadays defended by Edgington, though in the end Peirce defends the standard material conditional as simpler. I suspect that this discussion by Peirce is not well known. |
| 19223 | We act on 'full belief' in a crisis, but 'opinion' only operates for trivial actions [Peirce] |
| Full Idea: 'Full belief' is willingness to upon a proposition in vital crises, 'opinion' is willingness to act on it in relatively insignificant affairs. But pure science has nothing at all to do with action. | |
| From: Charles Sanders Peirce (Reasoning and the Logic of Things [1898], I) | |
| A reaction: A nice clear statement of the pragmatic view of beliefs. It is not much help in distinguishing full belief about the solar system from mere opinion about remote galaxies. Ditto for historical events. |
| 19253 | We talk of 'association by resemblance' but that is wrong: the association constitutes the resemblance [Peirce] |
| Full Idea: Allying certain ideas like 'crimson' and 'scarlet' is called 'association by resemblance'. The name is not a good one, since it implies that resemblance causes association, while in point of fact it is the association which constitutes the resemblance. | |
| From: Charles Sanders Peirce (Reasoning and the Logic of Things [1898], VII) | |
| A reaction: I take it that Hume would have agreed with this. It is an answer to Russell's claim that 'resemblance' must itself be a universal. |
| 19224 | Scientists will give up any conclusion, if experience opposes it [Peirce] |
| Full Idea: The scientific man is not in the least wedded to his conclusions. He risks nothing upon them. He stands ready to abandon one or all as experience opposes them. | |
| From: Charles Sanders Peirce (Reasoning and the Logic of Things [1898], I) | |
| A reaction: In the age of massive speculative research grants, the idea that 'he risks nothing upon them' is no longer true. Ditto for building aircraft and bridges, which are full of theoretical science. Notoriously, many scientists don't live up to Peirce's idea. |
| 19243 | If each inference slightly reduced our certainty, science would soon be in trouble [Peirce] |
| Full Idea: Were every probable inference less certain than its premises, science, which piles inference upon inference, often quite deeply, would soon be in a bad way. | |
| From: Charles Sanders Peirce (Reasoning and the Logic of Things [1898], IV) | |
| A reaction: This seems to endorse Aristotle's picture of demonstration about scientific and practical things as being a form of precise logic, rather than progressive probabilities. Our generalisations may be more certain than the particulars they rely on. |
| 19225 | I classify science by level of abstraction; principles derive from above, and data from below [Peirce] |
| Full Idea: I classify the sciences on Comte's general principles, in order of the abstractness of their objects, so that each science may largely rest for its principles upon those above it in the scale, while drawing its data in part from those below it. | |
| From: Charles Sanders Peirce (Reasoning and the Logic of Things [1898], I) | |
| A reaction: He places mathematics at the peak of abstraction. I assume physics is more abstract than biology. So chemistry draws principles from physics and data from biology. Not sure about this. Probably need to read Comte on it. |
| 19234 | 'Induction' doesn't capture Greek 'epagoge', which is singulars in a mass producing the general [Peirce] |
| Full Idea: The word 'inductio' is Cicero's imitation of Aristotle's term 'epagoge'. It fails to convey the full significance of the Greek word, which implies the examples are arrayed and brought forward in a mass. 'The assault upon the generals by the singulars'. | |
| From: Charles Sanders Peirce (Reasoning and the Logic of Things [1898], II) | |
| A reaction: Interesting, thought I don't think there is enough evidence in Aristotle to get the Greek idea fully clear. |
| 19235 | How does induction get started? [Peirce] |
| Full Idea: Induction can never make a first suggestion. | |
| From: Charles Sanders Peirce (Reasoning and the Logic of Things [1898], II) | |
| A reaction: This seems to lead to the general modern problem of the 'theory-laden' nature of observation. You don't see anything at all without some idea of what you are looking for. How do you spot the 'next instance'. Instance of what? Nice. |
| 19236 | Induction can never prove that laws have no exceptions [Peirce] |
| Full Idea: Induction can never afford the slightest reason to think that a law is without an exception. | |
| From: Charles Sanders Peirce (Reasoning and the Logic of Things [1898], II) | |
| A reaction: Part of the general Humean doubts about induction, but very precisely stated, and undeniable. You can then give up on universal laws, or look for deeper reasons to justify your conviction that there are no exceptions. E.g. observe mass, or Higgs Boson. |
| 19251 | The worst fallacy in induction is generalising one recondite property from a sample [Peirce] |
| Full Idea: The most dangerous fallacy of inductive reasoning consists in examining a sample, finding some recondite property in it, and concluding at once that it belongs to the whole collection. | |
| From: Charles Sanders Peirce (Reasoning and the Logic of Things [1898], V) | |
| A reaction: The point, I take it, is not that you infer that the whole collection has all the properties of the sample, but that some 'recondite' or unusual property is sufficiently unusual to be treated as general. |
| 19222 | Men often answer inner 'whys' by treating unconscious instincts as if they were reasons [Peirce] |
| Full Idea: Men many times fancy that they act from reason, when the reasons they attribute to themselves are nothing but excuses which unconscious instinct invents to satisfy the teasing 'whys' of the ego. | |
| From: Charles Sanders Peirce (Reasoning and the Logic of Things [1898], I) | |
| A reaction: A strikely modern thought, supported by a lot of modern neuro-science and psychology. It is crucial to realise that we don't have to accept the best explanation we can think of. |
| 19220 | We may think animals reason very little, but they hardly ever make mistakes! [Peirce] |
| Full Idea: Those whom we are so fond of referring to as the 'lower animals' reason very little. Now I beg you to observe that those beings very rarely commit a mistake, while we ---- ! | |
| From: Charles Sanders Peirce (Reasoning and the Logic of Things [1898], I) | |
| A reaction: We might take this as pessimism about reason, but I would take it as inviting a much broader view of rationality. I think nearly all animal behaviour is highly rational. Are animals 'sensible' in what they do? Their rationality is unadventurous. |
| 19255 | Generalisation is the great law of mind [Peirce] |
| Full Idea: The generalising tendency is the great law of mind. | |
| From: Charles Sanders Peirce (Reasoning and the Logic of Things [1898], VII) | |
| A reaction: How else could a small and compact mind get a grip on a vast and diverse reality? This must even apply to inarticulate higher animals. |
| 19242 | Generalization is the true end of life [Peirce] |
| Full Idea: Generalization, the spelling out of continuous systems, in thought, in sentiment, in deed, is the true end of life. | |
| From: Charles Sanders Peirce (Reasoning and the Logic of Things [1898], III) | |
| A reaction: I take understanding to be the true aim of life, and full grasp of particulars (e.g. of particular people) is as necessary as generalisation. This is still a very nice bold idea. |
| 19249 | 'Know yourself' is not introspection; it is grasping how others see you [Peirce] |
| Full Idea: 'Know thyself' does not mean instrospect your soul. It means see yourself as others would see you if they were intimate enough with you. | |
| From: Charles Sanders Peirce (Reasoning and the Logic of Things [1898], V) | |
| A reaction: When it comes to anger management, I would have thought that introspection had some use. You can see a tantrum coming before even your intimates can. Nice disagreement with Sartre! (Idea 7123) |
| 19257 | Whatever is First must be sentient [Peirce] |
| Full Idea: I think that what is First is ipso facto sentient. | |
| From: Charles Sanders Peirce (Reasoning and the Logic of Things [1898], VIII) | |
| A reaction: He doesn't mention Leibniz's monads, but that looks like the ancestor of Peirce's idea. He doesn't make clear (here) how far he would take the idea. I would just say that whatever is 'First' must be active rather than passive. |
| 19248 | Reasoning involves observation, experiment, and habituation [Peirce] |
| Full Idea: The mental operations concerning in reasoning are three. The first is Observation; the second is Experimentation; and the third is Habituation. | |
| From: Charles Sanders Peirce (Reasoning and the Logic of Things [1898], V) | |
| A reaction: I like the breadth of this. Even those who think scientific reasoning has priority over logic (as I do, thinking of it as the evaluation of evidence, with Sherlock Holmes as its role model) will be surprised to finding observation and habituation there. |
| 19221 | Everybody overrates their own reasoning, so it is clearly superficial [Peirce] |
| Full Idea: The very fact that everybody so ridiculously overrates his own reasoning, is sufficient to show how superficial the faculty is. | |
| From: Charles Sanders Peirce (Reasoning and the Logic of Things [1898], I) | |
| A reaction: A nice remark. The obvious counter-thought is that the collective reasoning of mankind really has been rather impressive, even though people haven't yet figured out how to live at peace with one another. |
| 19233 | Indexicals are unusual words, because they stimulate the hearer to look around [Peirce] |
| Full Idea: Words like 'this', 'that', 'I', 'you', enable us to convey meanings which words alone are incompetent to express; they stimulate the hearer to look about him. | |
| From: Charles Sanders Peirce (Reasoning and the Logic of Things [1898], II) | |
| A reaction: Peirce was once of the first to notice the interest of indexicals, and this is a very nice comment on them. A word like 'Look!' isn't like the normal flow of verbiage, and may be the key to indexicals. |
| 19230 | People should follow what lies before them, and is within their power [Peirce] |
| Full Idea: Each person ought to select some definite duty that clearly lies before him and is well within his power as the special task of his life. | |
| From: Charles Sanders Peirce (Reasoning and the Logic of Things [1898], I) | |
| A reaction: I like that. Note especially that it should be 'well' within his power. Note also that this is a 'duty', and not just a friendly suggestion. Not sure what the basis of the duty is. |
| 19245 | We are not inspired by other people's knowledge; a sense of our ignorance motivates study [Peirce] |
| Full Idea: It is not the man who thinks he knows it all, that can bring other men to feel their need for learning, and it is only a deep sense that one is miserably ignorant that can spur one on in the toilsome path of learning. | |
| From: Charles Sanders Peirce (Reasoning and the Logic of Things [1898], IV) |
| 19244 | Chemists rely on a single experiment to establish a fact; repetition is pointless [Peirce] |
| Full Idea: The chemist contents himself with a single experiment to establish any qualitative fact, because he knows there is such a uniformity in the behavior of chemical bodies that another experiment would be a mere repetition of the first in every respect. | |
| From: Charles Sanders Peirce (Reasoning and the Logic of Things [1898], IV) | |
| A reaction: I take it this endorses my 'Upanishads' view of natural kinds - that for each strict natural kind, if you've seen one you've them all. This seems to fit atoms and molecules, but only roughly fits tigers. |
| 19254 | Our laws of nature may be the result of evolution [Peirce] |
| Full Idea: We may suppose that the laws of nature are results of an evolutionary process. ...But this evolution must proceed according to some principle: and this principle will itself be of the nature of a law. | |
| From: Charles Sanders Peirce (Reasoning and the Logic of Things [1898], VII) | |
| A reaction: Maybe I've missed something, but this seems a rather startling idea that doesn't figure much in modern discussions of laws of nature. Lee Smolin's account of evolving universes comes to mind. |