73 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. |
| 13252 | Some truths have true negations [Beall/Restall] |
| Full Idea: Dialetheism is the view that some truths have true negations. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 7.4) | |
| A reaction: The important thing to remember is that they are truths. Thus 'Are you feeling happy?' might be answered 'Yes and no'. |
| 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. |
| 13247 | A truthmaker is an object which entails a sentence [Beall/Restall] |
| Full Idea: The truthmaker thesis is that an object is a truthmaker for a sentence if and only if its existence entails the sentence. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 5.5.3) | |
| A reaction: The use of the word 'object' here is even odder than usual, and invites many questions. And the 'only if' seems peculiar, since all sorts of things can make a sentence true. 'There is someone in the house' for example. |
| 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. |
| 13249 | (∀x)(A v B) |- (∀x)A v (∃x)B) is valid in classical logic but invalid intuitionistically [Beall/Restall] |
| Full Idea: The inference of 'distribution' (∀x)(A v B) |- (∀x)A v (∃x)B) is valid in classical logic but invalid intuitionistically. It is straightforward to construct a 'stage' at which the LHS is true but the RHS is not. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 6.1.2) | |
| A reaction: This seems to parallel the iterative notion in set theory, that you must construct your hierarchy. All part of the general 'constructivist' approach to things. Is some kind of mad platonism the only alternative? |
| 13243 | Excluded middle must be true for some situation, not for all situations [Beall/Restall] |
| Full Idea: Relevant logic endorses excluded middle, ..but says instances of the law may fail. Bv¬B is true in every situation that settles the matter of B. It is necessary that there is some such situation. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 5.2) | |
| A reaction: See next idea for the unusual view of necessity on which this rests. It seems easier to assert something about all situations than just about 'some' situation. |
| 13242 | It's 'relevantly' valid if all those situations make it true [Beall/Restall] |
| Full Idea: The argument from P to A is 'relevantly' valid if and only if, for every situation in which each premise in P is true, so is A. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 5.2) | |
| A reaction: I like the idea that proper inference should have an element of relevance to it. A falsehood may allow all sorts of things, without actually implying them. 'Situations' sound promising here. |
| 13246 | Relevant logic does not abandon classical logic [Beall/Restall] |
| Full Idea: We have not abandoned classical logic in our acceptance of relevant logic. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 5.4) | |
| A reaction: It appears that classical logic is straightforwardly accepted, but there is a difference of opinion over when it is applicable. |
| 13245 | Relevant consequence says invalidity is the conclusion not being 'in' the premises [Beall/Restall] |
| Full Idea: Relevant consequence says the conclusion of a relevantly invalid argument is not 'carried in' the premises - it does not follow from the premises. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 5.3.3) | |
| A reaction: I find this appealing. It need not invalidate classical logic. It is just a tougher criterion which is introduced when you want to do 'proper' reasoning, instead of just playing games with formal systems. |
| 13254 | A doesn't imply A - that would be circular [Beall/Restall] |
| Full Idea: We could reject the inference from A to itself (on grounds of circularity). | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 8) | |
| A reaction: [Martin-Meyer System] 'It's raining today'. 'Are you implying that it is raining today?' 'No, I'm SAYING it's raining today'. Logicians don't seem to understand the word 'implication'. Logic should capture how we reason. Nice proposal. |
| 13255 | Relevant logic may reject transitivity [Beall/Restall] |
| Full Idea: Some relevant logics reject transitivity, but we defend the classical view. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 8) | |
| A reaction: [they cite Neil Tennant for this view] To reject transitivity (A?B ? B?C ? A?C) certainly seems a long way from classical logic. But in everyday inference Tennant's idea seems good. The first premise may be irrelevant to the final conclusion. |
| 13250 | Free logic terms aren't existential; classical is non-empty, with referring names [Beall/Restall] |
| Full Idea: A logic is 'free' to the degree it refrains from existential import of its singular and general terms. Classical logic must have non-empty domain, and each name must denote in the domain. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 7.1) | |
| A reaction: My intuition is that logic should have no ontology at all, so I like the sound of 'free' logic. We can't say 'Pegasus does not exist', and then reason about Pegasus just like any other horse. |
| 13235 | Logic studies consequence; logical truths are consequences of everything, or nothing [Beall/Restall] |
| Full Idea: Nowadays we think of the consequence relation itself as the primary subject of logic, and view logical truths as degenerate instances of this relation. Logical truths follow from any set of assumptions, or from no assumptions at all. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 2.2) | |
| A reaction: This seems exactly right; the alternative is the study of necessities, but that may not involve logic. |
| 13238 | Syllogisms are only logic when they use variables, and not concrete terms [Beall/Restall] |
| Full Idea: According to the Peripatetics (Aristotelians), only syllogistic laws stated in variables belong to logic, and not their applications to concrete terms. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 2.5) | |
| A reaction: [from Lukasiewicz] Seems wrong. I take it there are logical relations between concrete things, and the variables are merely used to describe these relations. Variables lack the internal powers to drive logical necessities. Variables lack essence! |
| 13234 | The view of logic as knowing a body of truths looks out-of-date [Beall/Restall] |
| Full Idea: Through much of the 20th century the conception of logic was inherited from Frege and Russell, as knowledge of a body of logical truths, as arithmetic or geometry was a knowledge of truths. This is odd, and a historical anomaly. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 2.2) | |
| A reaction: Interesting. I have always taken this idea to be false. I presume logic has minimal subject matter and truths, and preferably none at all. |
| 13232 | Logic studies arguments, not formal languages; this involves interpretations [Beall/Restall] |
| Full Idea: Logic does not study formal languages for their own sake, which is formal grammar. Logic evaluates arguments, and primarily considers formal languages as interpreted. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 2.1) | |
| A reaction: Hodges seems to think logic just studies formal languages. The current idea strikes me as a much more sensible view. |
| 13241 | The model theory of classical predicate logic is mathematics [Beall/Restall] |
| Full Idea: The model theory of classical predicate logic is mathematics if anything is. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 4.2.1) | |
| A reaction: This is an interesting contrast to the claim of logicism, that mathematics reduces to logic. This idea explains why students of logic are surprised to find themselves involved in mathematics. |
| 13253 | There are several different consequence relations [Beall/Restall] |
| Full Idea: We are pluralists about logical consequence because we take there to be a number of different consequence relations, each reflecting different precisifications of the pre-theoretic notion of deductive logical consequence. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 8) | |
| A reaction: I don't see how you avoid the slippery slope that leads to daft logical rules like Prior's 'tonk' (from which you can infer anything you like). I say that nature imposes logical conquence on us - but don't ask me to prove it. |
| 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. |
| 13240 | A sentence follows from others if they always model it [Beall/Restall] |
| Full Idea: The sentence X follows logically from the sentences of the class K if and only if every model of the class K is also a model of the sentence X. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 3.2) | |
| A reaction: This why the symbol |= is often referred to as 'models'. |
| 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. |
| 10001 | An adjective contributes semantically to a noun phrase [Hofweber] |
| Full Idea: The semantic value of a determiner (an adjective) is a function from semantic values to nouns to semantic values of full noun phrases. | |
| From: Thomas Hofweber (Number Determiners, Numbers, Arithmetic [2005], §3.1) | |
| A reaction: This kind of states the obvious (assuming one has a compositional view of sentences), but his point is that you can't just eliminate adjectival uses of numbers by analysing them away, as if they didn't do anything. |
| 10007 | Quantifiers for domains and for inference come apart if there are no entities [Hofweber] |
| Full Idea: Quantifiers have two functions in communication - to range over a domain of entities, and to have an inferential role (e.g. F(t)→'something is F'). In ordinary language these two come apart for singular terms not standing for any entities. | |
| From: Thomas Hofweber (Number Determiners, Numbers, Arithmetic [2005], §6.3) | |
| A reaction: This simple observations seems to me to be wonderfully illuminating of a whole raft of problems, the sort which logicians get steamed up about, and ordinary speakers don't. Context is the key to 90% of philosophical difficulties (?). See Idea 10008. |
| 13236 | Logical truth is much more important if mathematics rests on it, as logicism claims [Beall/Restall] |
| Full Idea: If mathematical truth reduces to logical truth then it is important what counts as logically true, …but if logicism is not a going concern, then the body of purely logical truths will be less interesting. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 2.2) | |
| A reaction: Logicism would only be one motivation for pursuing logical truths. Maybe my new 'Necessitism' will derive the Peano Axioms from broad necessary truths, rather than from logic. |
| 13237 | Preface Paradox affirms and denies the conjunction of propositions in the book [Beall/Restall] |
| Full Idea: The Paradox of the Preface is an apology, that you are committed to each proposition in the book, but admit that collectively they probably contain a mistake. There is a contradiction, of affirming and denying the conjunction of propositions. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 2.4) | |
| A reaction: This seems similar to the Lottery Paradox - its inverse perhaps. Affirm all and then deny one, or deny all and then affirm one? |
| 10002 | '2 + 2 = 4' can be read as either singular or plural [Hofweber] |
| Full Idea: There are two ways to read to read '2 + 2 = 4', as singular ('two and two is four'), and as plural ('two and two are four'). | |
| From: Thomas Hofweber (Number Determiners, Numbers, Arithmetic [2005], §4.1) | |
| A reaction: Hofweber doesn't notice that this phenomenon occurs elsewhere in English. 'The team is playing well', or 'the team are splitting up'; it simply depends whether you are holding the group in though as an entity, or as individuals. Important for numbers. |
| 9998 | What is the relation of number words as singular-terms, adjectives/determiners, and symbols? [Hofweber] |
| Full Idea: There are three different uses of the number words: the singular-term use (as in 'the number of moons of Jupiter is four'), the adjectival (or determiner) use (as in 'Jupiter has four moons'), and the symbolic use (as in '4'). How are they related? | |
| From: Thomas Hofweber (Number Determiners, Numbers, Arithmetic [2005], §1) | |
| A reaction: A classic philosophy of language approach to the problem - try to give the truth-conditions for all three types. The main problem is that the first one implies that numbers are objects, whereas the others do not. Why did Frege give priority to the first? |
| 10003 | Why is arithmetic hard to learn, but then becomes easy? [Hofweber] |
| Full Idea: Why is arithmetic so hard to learn, and why does it seem so easy to us now? For example, subtracting 789 from 26,789. | |
| From: Thomas Hofweber (Number Determiners, Numbers, Arithmetic [2005], §4.2) | |
| A reaction: His answer that we find thinking about objects very easy, but as children we have to learn with difficulty the conversion of the determiner/adjectival number words, so that we come to think of them as objects. |
| 10008 | Arithmetic is not about a domain of entities, as the quantifiers are purely inferential [Hofweber] |
| Full Idea: I argue for an internalist conception of arithmetic. Arithmetic is not about a domain of entities, not even quantified entities. Quantifiers over natural numbers occur in their inferential-role reading in which they merely generalize over the instances. | |
| From: Thomas Hofweber (Number Determiners, Numbers, Arithmetic [2005], §6.3) | |
| A reaction: Hofweber offers the hope that modern semantics can disentangle the confusions in platonist arithmetic. Very interesting. The fear is that after digging into the semantics for twenty years, you find the same old problems re-emerging at a lower level. |
| 10005 | Arithmetic doesn’t simply depend on objects, since it is true of fictional objects [Hofweber] |
| Full Idea: That 'two dogs are more than one' is clearly true, but its truth doesn't depend on the existence of dogs, as is seen if we consider 'two unicorns are more than one', which is true even though there are no unicorns. | |
| From: Thomas Hofweber (Number Determiners, Numbers, Arithmetic [2005], §6.2) | |
| A reaction: This is an objection to crude empirical accounts of arithmetic, but the idea would be that there is a generalisation drawn from objects (dogs will do nicely), which then apply to any entities. If unicorns are entities, it will be true of them. |
| 10000 | We might eliminate adjectival numbers by analysing them into blocks of quantifiers [Hofweber] |
| Full Idea: Determiner uses of number words may disappear on analysis. This is inspired by Russell's elimination of the word 'the'. The number becomes blocks of first-order quantifiers at the level of semantic representation. | |
| From: Thomas Hofweber (Number Determiners, Numbers, Arithmetic [2005], §2) | |
| A reaction: [compressed] The proposal comes from platonists, who argue that numbers cannot be analysed away if they are objects. Hofweber says the analogy with Russell is wrong, as 'the' can't occur in different syntactic positions, the way number words can. |
| 10006 | First-order logic captures the inferential relations of numbers, but not the semantics [Hofweber] |
| Full Idea: Representing arithmetic formally we do not primarily care about semantic features of number words. We are interested in capturing the inferential relations of arithmetical statements to one another, which can be done elegantly in first-order logic. | |
| From: Thomas Hofweber (Number Determiners, Numbers, Arithmetic [2005], §6.3) | |
| A reaction: This begins to pinpoint the difference between the approach of logicists like Frege, and those who are interested in the psychology of numbers, and the empirical roots of numbers in the process of counting. |
| 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. |
| 13244 | Relevant necessity is always true for some situation (not all situations) [Beall/Restall] |
| Full Idea: In relevant logic, the necessary truths are not those which are true in every situation; rather, they are those for which it is necessary that there is a situation making them true. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 5.2) | |
| A reaction: This seems to rest on the truthmaker view of such things, which I find quite attractive (despite Merricks's assault). Always ask what is making some truth necessary. This leads you to essences. |
| 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. |
| 10004 | Our minds are at their best when reasoning about objects [Hofweber] |
| Full Idea: Our minds mainly reason about objects. Most cognitive problems we are faced with deal with particular objects, whether they are people or material things. Reasoning about them is what our minds are good at. | |
| From: Thomas Hofweber (Number Determiners, Numbers, Arithmetic [2005], §4.3) | |
| A reaction: Hofweber is suggesting this as an explanation of why we continually reify various concepts, especially numbers. Very plausible. It works for qualities of character, and explains our tendency to talk about universals as objects ('redness'). |
| 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. |
| 13239 | Judgement is always predicating a property of a subject [Beall/Restall] |
| Full Idea: All judgement, for Kant, is essentially the predication of some property to some subject. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 2.5) | |
| A reaction: Presumably the denial of a predicate could be a judgement, or the affirmation of ambiguous predicates? |
| 13248 | We can rest truth-conditions on situations, rather than on possible worlds [Beall/Restall] |
| Full Idea: Situation semantics is a variation of the truth-conditional approach, taking the salient unit of analysis not to be the possible world, or some complete consistent index, but rather the more modest 'situation'. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 5.5.4) | |
| A reaction: When I read Davidson (and implicitly Frege) this is what I always assumed was meant. The idea that worlds are meant has crept in to give truth conditions for modal statements. Hence situation semantics must cover modality. |
| 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. |
| 13233 | Propositions commit to content, and not to any way of spelling it out [Beall/Restall] |
| Full Idea: Our talk of propositions expresses commitment to the general notion of content, without a commitment to any particular way of spelling this out. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 2.1) | |
| A reaction: As a fan of propositions I like this. It leaves open the question of whether the content belongs to the mind or the language. Animals entertain propositions, say I. |
| 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. |