30 ideas
17641 | Discoveries in mathematics can challenge philosophy, and offer it a new foundation [Russell] |
Full Idea: Any new discovery as to mathematical method and principles is likely to upset a great deal of otherwise plausible philosophising, as well as to suggest a new philosophy which will be solid in proportion as its foundations in mathematics are securely laid. | |
From: Bertrand Russell (Regressive Method for Premises in Mathematics [1907], p.283) | |
A reaction: This is a manifesto for modern analytic philosophy. I'm not convinced, especially if a fictionalist view of maths is plausible. What Russell wants is rigour, but there are other ways of getting that. Currently I favour artificial intelligence. |
17729 | Examining concepts can recover information obtained through the senses [Jenkins] |
Full Idea: My idea is that conceptual examination might be a way of recovering information previously obtained through the senses. | |
From: Carrie Jenkins (Grounding Concepts [2008], 4.8) | |
A reaction: Now you're talking! This is really interesting conceptual analysis, rather than the sort of stamp-collecting approach to analsis practised by the duller sort of philosopher. But why bother with conceptual examination, when you have senses? |
17638 | If one proposition is deduced from another, they are more certain together than alone [Russell] |
Full Idea: Two obvious propositions of which one can be deduced from the other both become more certain than either in isolation; thus in a complicated deductive system, many parts of which are obvious, the total probability may become all but absolute certainty. | |
From: Bertrand Russell (Regressive Method for Premises in Mathematics [1907], p.279) | |
A reaction: Thagard picked this remark out, in support of his work on coherence. |
17632 | Non-contradiction was learned from instances, and then found to be indubitable [Russell] |
Full Idea: The law of contradiction must have been originally discovered by generalising from instances, though, once discovered, it was found to be quite as indubitable as the instances. | |
From: Bertrand Russell (Regressive Method for Premises in Mathematics [1907], p.274) |
17740 | Instead of correspondence of proposition to fact, look at correspondence of its parts [Jenkins] |
Full Idea: Instead of considering only a proposition's 'correspondence to the facts', we should also consider the correspondence between parts of the proposition and parts of the world (a 'correspondence-as-congruence' view). | |
From: Carrie Jenkins (Grounding Concepts [2008], Final - Branching) | |
A reaction: This is something like Russell's Othello example (1912), except that the parts there, with relations seemed to add up to the whole proposition. For Jenkins, presumably parts might correspond, but the whole proposition fail to. |
17629 | Which premises are ultimate varies with context [Russell] |
Full Idea: Premises which are ultimate in one investigation may cease to be so in another. | |
From: Bertrand Russell (Regressive Method for Premises in Mathematics [1907], p.273) |
17630 | The sources of a proof are the reasons why we believe its conclusion [Russell] |
Full Idea: In mathematics, except in the earliest parts, the propositions from which a given proposition is deduced generally give the reason why we believe the given proposition. | |
From: Bertrand Russell (Regressive Method for Premises in Mathematics [1907], p.273) |
17640 | Finding the axioms may be the only route to some new results [Russell] |
Full Idea: The premises [of a science] ...are pretty certain to lead to a number of new results which could not otherwise have been known. | |
From: Bertrand Russell (Regressive Method for Premises in Mathematics [1907], p.282) | |
A reaction: I identify this as the 'fruitfulness' that results when the essence of something is discovered. |
10245 | One geometry cannot be more true than another [Poincaré] |
Full Idea: One geometry cannot be more true than another; it can only be more convenient. | |
From: Henri Poincaré (Science and Method [1908], p.65), quoted by Stewart Shapiro - Philosophy of Mathematics | |
A reaction: This is the culminating view after new geometries were developed by tinkering with Euclid's parallels postulate. |
17730 | Combining the concepts of negation and finiteness gives the concept of infinity [Jenkins] |
Full Idea: We might arrive to the concept of infinity by composing concepts of negation and finiteness. | |
From: Carrie Jenkins (Grounding Concepts [2008], 5.3) | |
A reaction: Presumably lots of concepts can be arrived at by negating prior concepts (such as not-wet, not-tall, not-loud, not-straight). So not-infinite is perfectly plausible, and is a far better account than some a priori intuition of pure infinity. Love it. |
17627 | It seems absurd to prove 2+2=4, where the conclusion is more certain than premises [Russell] |
Full Idea: It is an apparent absurdity in proceeding ...through many rather recondite propositions of symbolic logic, to the 'proof' of such truisms as 2+2=4: for it is plain that the conclusion is more certain than the premises, and the supposed proof seems futile. | |
From: Bertrand Russell (Regressive Method for Premises in Mathematics [1907], p.272) | |
A reaction: Famously, 'Principia Mathematica' proved this fact at enormous length. I wonder if this thought led Moore to his common sense view of his own hand - the conclusion being better than the sceptical arguments? |
17628 | Arithmetic was probably inferred from relationships between physical objects [Russell] |
Full Idea: When 2 + 2 =4 was first discovered, it was probably inferred from the case of sheep and other concrete cases. | |
From: Bertrand Russell (Regressive Method for Premises in Mathematics [1907], p.272) |
17719 | Arithmetic concepts are indispensable because they accurately map the world [Jenkins] |
Full Idea: The indispensability of arithmetical concepts is evidence that they do in fact accurately represent features of the independent world. | |
From: Carrie Jenkins (Grounding Concepts [2008], Intro) | |
A reaction: This seems to me to be by far the best account of the matter. So why is the world so arithmetical? Dunno, mate; ask someone else. |
17717 | Senses produce concepts that map the world, and arithmetic is known through these concepts [Jenkins] |
Full Idea: I propose that arithmetical truths are known through an examination of our own arithmetical concepts; that basic arithmetical concepts map the arithmetical structure of the world; that the map obtains in virtue of our normal sensory apparatus. | |
From: Carrie Jenkins (Grounding Concepts [2008], Pref) | |
A reaction: She defends the nice but unusual position that arithmetical knowledge is both a priori and empirical (so that those two notions are not, as usually thought, opposed). I am a big Carrie Jenkins fan. |
17724 | It is not easy to show that Hume's Principle is analytic or definitive in the required sense [Jenkins] |
Full Idea: A problem for the neo-Fregeans is that it has not proved easy to establish that Hume's Principle is analytic or definitive in the required sense. | |
From: Carrie Jenkins (Grounding Concepts [2008], 4.3) | |
A reaction: It is also asked how we would know the principle, if it is indeed analytic or definitional (Jenkins p.119). |
17727 | We can learn about the world by studying the grounding of our concepts [Jenkins] |
Full Idea: What concept grounding does for us is ensure that our concepts, like the results of our empirical tests, can be treated as a source of information about the independent world. | |
From: Carrie Jenkins (Grounding Concepts [2008], 4.4) | |
A reaction: Presumably we learn our concepts hand-in-hand with experience, so learning our concepts is itself learning about the world. Later checking of concepts and their relations largely confirms what we already knew? |
17720 | There's essential, modal, explanatory, conceptual, metaphysical and constitutive dependence [Jenkins, by PG] |
Full Idea: Dependence comes in essential, modal, explanatory, conceptual, metaphysical and constitutive forms. | |
From: report of Carrie Jenkins (Grounding Concepts [2008], 1.2) by PG - Db (ideas) | |
A reaction: You'll have to look up Jenkins for the details. |
17728 | The concepts we have to use for categorising are ones which map the real world well [Jenkins] |
Full Idea: Concepts which are indispensably useful for categorising, understanding, explaining, and predicting our sensory input are likely to be ones which map the structure of that input well. | |
From: Carrie Jenkins (Grounding Concepts [2008], 4.6) | |
A reaction: Anti-realists about classification seem to think that we just invent an array of concepts, and then start classifying with them. The truth seems to be that the actual classes of worldly thing have generated our concepts. |
17637 | The most obvious beliefs are not infallible, as other obvious beliefs may conflict [Russell] |
Full Idea: Even where there is the highest degree of obviousness, we cannot assume that we are infallible - a sufficient conflict with other obvious propositions may lead us to abandon our belief, as in the case of a hallucination afterwards recognised as such. | |
From: Bertrand Russell (Regressive Method for Premises in Mathematics [1907], p.279) | |
A reaction: This approach to fallibilism seems to arise from the paradox that undermined Frege's rather obvious looking axioms. After Peirce and Russell, fallibilism has become a secure norm of modern thought. |
17726 | Examining accurate, justified or grounded concepts brings understanding of the world [Jenkins] |
Full Idea: Examining accurate concepts can help us acquire true beliefs about the world, examining justified concepts can help us acquire justified beliefs about the world, and examining grounded concepts can help us acquire knowledge of it. | |
From: Carrie Jenkins (Grounding Concepts [2008], 4.4) | |
A reaction: This summarises Jenkins's empirical account of concepts, and I love it all to bits. I feel that contemporary philosophy is beginning to produce a coherent naturalistic worldview which can replace religion. Bar the rituals. We can have priests... |
17734 | It is not enough that intuition be reliable - we need to know why it is reliable [Jenkins] |
Full Idea: The mere reliability of intuition is not a satisfactory ground for saying it is a source of knowledge - we need to know why it is reliable to understand whether it can be a source of knowledge. | |
From: Carrie Jenkins (Grounding Concepts [2008], 6.5) | |
A reaction: My theory is that intuition is simply believing things for reasons which we have either forgotten, or (more likely) reasons which are too complex or subtle to be articulated. Intuition feels rational, because it is rational. Updated view of mind needed. |
17639 | Believing a whole science is more than believing each of its propositions [Russell] |
Full Idea: Although intrinsic obviousness is the basis of every science, it is never, in a fairly advanced science, the whole of our reason for believing any one proposition of the science. | |
From: Bertrand Russell (Regressive Method for Premises in Mathematics [1907], p.279) |
17723 | Knowledge is true belief which can be explained just by citing the proposition believed [Jenkins] |
Full Idea: I propose that knowledge is true belief which can be well explained .....just by citing the proposition believed. | |
From: Carrie Jenkins (Grounding Concepts [2008], 3.1) | |
A reaction: I don't find this appealing, and my reservation about Jenkins's book is her reliabilist, externalist epistemology. I would add an internalist coherentist epistemology to her very nice theory. 'I believe there are fairies at the bottom of my garden'? |
17631 | Induction is inferring premises from consequences [Russell] |
Full Idea: The inferring of premises from consequences is the essence of induction. | |
From: Bertrand Russell (Regressive Method for Premises in Mathematics [1907], p.274) | |
A reaction: So induction is just deduction in reverse? Induction is transcendental deduction? Do I deduce the premises from observing a lot of white swans? Hm. |
17739 | The physical effect of world on brain explains the concepts we possess [Jenkins] |
Full Idea: I think the physical effects of the world on the brain explain our possessing the concepts we do. | |
From: Carrie Jenkins (Grounding Concepts [2008], 8.2) | |
A reaction: A nice slogan for a thought which strikes me as exactly right. |
17718 | Grounded concepts are trustworthy maps of the world [Jenkins] |
Full Idea: Grounded concepts are like trustworthy on-board maps of the independent world. | |
From: Carrie Jenkins (Grounding Concepts [2008], Intro) | |
A reaction: You'll probably need more than one concept for it to qualify as a 'map', but I like this idea a lot. The world, rather than we ourselves, creates our concepts. The opposite of the view of Geach in 'Mental Acts'. |
17731 | Verificationism is better if it says meaningfulness needs concepts grounded in the senses [Jenkins] |
Full Idea: I find an updated verificationism plausible, in which we say something meaningful just in case we employ only concepts whose possession could be justified or disjustified by sensory input. | |
From: Carrie Jenkins (Grounding Concepts [2008], 5.6) | |
A reaction: Wow! This is the first time I have ever had the slightest sympathy for verificationism. It saves my favourite problem case - of wild but meaningful speculation, for example about the contents of another universe. A very nice idea. |
17732 | Success semantics explains representation in terms of success in action [Jenkins] |
Full Idea: Success semantics is the attempt to understand mental representation by thinking about the ways in which representing the world can lead to success in action. | |
From: Carrie Jenkins (Grounding Concepts [2008], 6.3) | |
A reaction: I take this to be what is also known as 'teleological semantics'. It sounds to me as if this might help to explain success in action, but isn't going to explain the representations that result in the success. |
17725 | 'Analytic' can be conceptual, or by meaning, or predicate inclusion, or definition... [Jenkins] |
Full Idea: 'Analytic' might mean conceptually true, or true in virtue of meaning, or where the predicate is contained in the subject, or for sentences which define something, or where meaning is sufficient for the truth. | |
From: Carrie Jenkins (Grounding Concepts [2008], 4.3) | |
A reaction: The second one says meaning grounds the truth, where the last one says meaning entails the truth. |
17633 | The law of gravity has many consequences beyond its grounding observations [Russell] |
Full Idea: The law of gravitation leads to many consequences which could not be discovered merely from the apparent motions of the heavenly bodies. | |
From: Bertrand Russell (Regressive Method for Premises in Mathematics [1907], p.275) |