35 ideas
| 14018 | Is Sufficient Reason self-refuting (no reason to accept it!), or is it a legitimate explanatory tool? [Bourne] |
| Full Idea: Mackie (1983) dismisses the Principle of Sufficient Reason quickly, arguing that it is self-refuting: there is no sufficient reason to accept it. However, a principle is not invalidated by not applying to itself; it can be a powerful heuristic tool. | |
| From: Craig Bourne (A Future for Presentism [2006], 6.VI) | |
| A reaction: If God was entirely rational, and created everything, that would be a sufficient reason to accept the principle. You would never, though, get to the reason why God was entirely rational. Something will always elude the principle. |
| 16877 | A 'constructive' (as opposed to 'analytic') definition creates a new sign [Frege] |
| Full Idea: We construct a sense out of its constituents and introduce an entirely new sign to express this sense. This may be called a 'constructive definition', but we prefer to call it a 'definition' tout court. It contrasts with an 'analytic' definition. | |
| From: Gottlob Frege (Logic in Mathematics [1914], p.210) | |
| A reaction: An analytic definition is evidently a deconstruction of a past constructive definition. Fregean definition is a creative activity. |
| 11219 | Frege suggested that mathematics should only accept stipulative definitions [Frege, by Gupta] |
| Full Idea: Frege has defended the austere view that, in mathematics at least, only stipulative definitions should be countenanced. | |
| From: report of Gottlob Frege (Logic in Mathematics [1914]) by Anil Gupta - Definitions 1.3 | |
| A reaction: This sounds intriguingly at odds with Frege's well-known platonism about numbers (as sets of equinumerous sets). It makes sense for other mathematical concepts. |
| 16878 | We must be clear about every premise and every law used in a proof [Frege] |
| Full Idea: It is so important, if we are to have a clear insight into what is going on, for us to be able to recognise the premises of every inference which occurs in a proof and the law of inference in accordance with which it takes place. | |
| From: Gottlob Frege (Logic in Mathematics [1914], p.212) | |
| A reaction: Teachers of logic like natural deduction, because it reduces everything to a few clear laws, which can be stated at each step. |
| 14008 | The redundancy theory conflates metalinguistic bivalence with object-language excluded middle [Bourne] |
| Full Idea: The problem with the redundancy theory of truth is that it conflates the metalinguistic notion of bivalence with a theorem of the object language, namely the law of excluded middle. | |
| From: Craig Bourne (A Future for Presentism [2006], 3.III Pr3) |
| 16867 | Logic not only proves things, but also reveals logical relations between them [Frege] |
| Full Idea: A proof does not only serve to convince us of the truth of what is proved: it also serves to reveal logical relations between truths. Hence we find in Euclid proofs of truths that appear to stand in no need of proof because they are obvious without one. | |
| From: Gottlob Frege (Logic in Mathematics [1914], p.204) | |
| A reaction: This is a key idea in Frege's philosophy, and a reason why he is the founder of modern analytic philosophy, with logic placed at the centre of the subject. I take the value of proofs to be raising questions, more than giving answers. |
| 16863 | Does some mathematical reasoning (such as mathematical induction) not belong to logic? [Frege] |
| Full Idea: Are there perhaps modes of inference peculiar to mathematics which …do not belong to logic? Here one may point to inference by mathematical induction from n to n+1. | |
| From: Gottlob Frege (Logic in Mathematics [1914], p.203) | |
| A reaction: He replies that it looks as if induction can be reduced to general laws, and those can be reduced to logic. |
| 16862 | The closest subject to logic is mathematics, which does little apart from drawing inferences [Frege] |
| Full Idea: Mathematics has closer ties with logic than does almost any other discipline; for almost the entire activity of the mathematician consists in drawing inferences. | |
| From: Gottlob Frege (Logic in Mathematics [1914], p.203) | |
| A reaction: The interesting question is who is in charge - the mathematician or the logician? |
| 16865 | 'Theorems' are both proved, and used in proofs [Frege] |
| Full Idea: Usually a truth is only called a 'theorem' when it has not merely been obtained by inference, but is used in turn as a premise for a number of inferences in the science. ….Proofs use non-theorems, which only occur in that proof. | |
| From: Gottlob Frege (Logic in Mathematics [1914], p.204) |
| 16866 | Tracing inference backwards closes in on a small set of axioms and postulates [Frege] |
| Full Idea: We can trace the chains of inference backwards, …and the circle of theorems closes in more and more. ..We must eventually come to an end by arriving at truths can cannot be inferred, …which are the axioms and postulates. | |
| From: Gottlob Frege (Logic in Mathematics [1914], p.204) | |
| A reaction: The rival (more modern) view is that that all theorems are equal in status, and axioms are selected for convenience. |
| 16868 | The essence of mathematics is the kernel of primitive truths on which it rests [Frege] |
| Full Idea: Science must endeavour to make the circle of unprovable primitive truths as small as possible, for the whole of mathematics is contained in this kernel. The essence of mathematics has to be defined by this kernel of truths. | |
| From: Gottlob Frege (Logic in Mathematics [1914], p.204-5) | |
| A reaction: [compressed] I will make use of this thought, by arguing that mathematics may be 'explained' by this kernel. |
| 16871 | A truth can be an axiom in one system and not in another [Frege] |
| Full Idea: It is possible for a truth to be an axiom in one system and not in another. | |
| From: Gottlob Frege (Logic in Mathematics [1914], p.205) | |
| A reaction: Frege aspired to one huge single system, so this is a begrudging concession, one which modern thinkers would probably take for granted. |
| 16870 | Axioms are truths which cannot be doubted, and for which no proof is needed [Frege] |
| Full Idea: The axioms are theorems, but truths for which no proof can be given in our system, and no proof is needed. It follows from this that there are no false axioms, and we cannot accept a thought as an axiom if we are in doubt about its truth. | |
| From: Gottlob Frege (Logic in Mathematics [1914], p.205) | |
| A reaction: He struggles to be as objective as possible, but has to concede that whether we can 'doubt' the axiom is one of the criteria. |
| 16869 | To create order in mathematics we need a full system, guided by patterns of inference [Frege] |
| Full Idea: We cannot long remain content with the present fragmentation [of mathematics]. Order can be created only by a system. But to construct a system it is necessary that in any step forward we take we should be aware of the logical inferences involved. | |
| From: Gottlob Frege (Logic in Mathematics [1914], p.205) |
| 16864 | If principles are provable, they are theorems; if not, they are axioms [Frege] |
| Full Idea: If the law [of induction] can be proved, it will be included amongst the theorems of mathematics; if it cannot, it will be included amongst the axioms. | |
| From: Gottlob Frege (Logic in Mathematics [1914], p.203) | |
| A reaction: This links Frege with the traditional Euclidean view of axioms. The question, then, is how do we know them, given that we can't prove them. |
| 14010 | All relations between spatio-temporal objects are either spatio-temporal, or causal [Bourne] |
| Full Idea: If there are any genuine relations at all between spatio-temporal objects, then they are all either spatio-temporal or causal. | |
| From: Craig Bourne (A Future for Presentism [2006], 3.III Pr4) | |
| A reaction: This sounds too easy, but I have wracked my brains for counterexamples and failed to find any. How about qualitative relations? |
| 14009 | It is a necessary condition for the existence of relations that both of the relata exist [Bourne] |
| Full Idea: It is widely held, and I think correctly so, that a necessary condition for the existence of relations is that both of the relata exist. | |
| From: Craig Bourne (A Future for Presentism [2006], 3.III Pr4) | |
| A reaction: This is either trivial or false. Relations in the actual world self-evidently relate components of it. But I seem able to revere Sherlock Holmes, and speculate about relations between possible entities. |
| 9388 | Every concept must have a sharp boundary; we cannot allow an indeterminate third case [Frege] |
| Full Idea: Of any concept, we must require that it have a sharp boundary. Of any object it must hold either that it falls under the concept or it does not. We may not allow a third case in which it is somehow indeterminate whether an object falls under a concept. | |
| From: Gottlob Frege (Logic in Mathematics [1914], p.229), quoted by Ian Rumfitt - The Logic of Boundaryless Concepts p.1 n1 | |
| A reaction: This is the voice of the classical logician, which has echoed by Russell. I'm with them, I think, in the sense that logic can only work with precise concepts. The jury is still out. Maybe we can 'precisify', without achieving total precision. |
| 16876 | We need definitions to cram retrievable sense into a signed receptacle [Frege] |
| Full Idea: If we need such signs, we also need definitions so that we can cram this sense into the receptacle and also take it out again. | |
| From: Gottlob Frege (Logic in Mathematics [1914], p.209) | |
| A reaction: Has anyone noticed that Frege is the originator of the idea of the mental file? Has anyone noticed the role that definition plays in his account? |
| 16875 | We use signs to mark receptacles for complex senses [Frege] |
| Full Idea: We often need to use a sign with which we associate a very complex sense. Such a sign seems a receptacle for the sense, so that we can carry it with us, while being always aware that we can open this receptacle should we need what it contains. | |
| From: Gottlob Frege (Logic in Mathematics [1914], p.209) | |
| A reaction: This exactly the concept of a mental file, which I enthusiastically endorse. Frege even talks of 'opening the receptacle'. For Frege a definition (which he has been discussing) is the assigment of a label (the 'definiendum') to the file (the 'definiens'). |
| 16879 | A sign won't gain sense just from being used in sentences with familiar components [Frege] |
| Full Idea: No sense accrues to a sign by the mere fact that it is used in one or more sentences, the other constituents of which are known. | |
| From: Gottlob Frege (Logic in Mathematics [1914], p.213) | |
| A reaction: Music to my ears. I've never grasped how meaning could be grasped entirely through use. |
| 16873 | Thoughts are not subjective or psychological, because some thoughts are the same for us all [Frege] |
| Full Idea: A thought is not something subjective, is not the product of any form of mental activity; for the thought that we have in Pythagoras's theorem is the same for everybody. | |
| From: Gottlob Frege (Logic in Mathematics [1914], p.206) | |
| A reaction: When such thoughts are treated as if the have objective (platonic) existence, I become bewildered. I take a thought (or proposition) to be entirely psychological, but that doesn't stop two people from having the same thought. |
| 16872 | A thought is the sense expressed by a sentence, and is what we prove [Frege] |
| Full Idea: The sentence is of value to us because of the sense that we grasp in it, which is recognisably the same in a translation. I call this sense the thought. What we prove is not a sentence, but a thought. | |
| From: Gottlob Frege (Logic in Mathematics [1914], p.206) | |
| A reaction: The 'sense' is presumably the German 'sinn', and a 'thought' in Frege is what we normally call a 'proposition'. So the sense of a sentence is a proposition, and logic proves propositions. I'm happy with that. |
| 16874 | The parts of a thought map onto the parts of a sentence [Frege] |
| Full Idea: A sentence is generally a complex sign, so the thought expressed by it is complex too: in fact it is put together in such a way that parts of a thought correspond to parts of the sentence. | |
| From: Gottlob Frege (Logic in Mathematics [1914], p.207) | |
| A reaction: This is the compositional view of propositions, as opposed to the holistic view. |
| 468 | Musical performance can reveal a range of virtues [Damon of Ath.] |
| Full Idea: In singing and playing the lyre, a boy will be likely to reveal not only courage and moderation, but also justice. | |
| From: Damon (fragments/reports [c.460 BCE], B4), quoted by (who?) - where? |
| 14016 | The idea of simultaneity in Special Relativity is full of verificationist assumptions [Bourne] |
| Full Idea: Special Relativity, with its definition of simultaneity, is shot through with verificationist assumptions. | |
| From: Craig Bourne (A Future for Presentism [2006], 6.IIc) | |
| A reaction: [He credits Sklar with this] I love hearing such points made, because all my instincts have rebelled against Einstein's story, even after I have been repeatedly told how stupid I am, and how I should study more maths etc. |
| 14019 | Relativity denies simultaneity, so it needs past, present and future (unlike Presentism) [Bourne] |
| Full Idea: Special Relativity denies absolute simultaneity, and therefore requires a past and a future, as well as a present. The Presentist, however, only requires the present. | |
| From: Craig Bourne (A Future for Presentism [2006], 6.VII) | |
| A reaction: It is nice to accuse Relativity of ontological extravagence. When it 'requires' past and future, that may not be a massive commitment, since the whole theory is fairly operationalist, according to Putnam. |
| 14013 | Special Relativity allows an absolute past, future, elsewhere and simultaneity [Bourne] |
| Full Idea: There is in special relativity a notion of 'absolute past', and of 'absolute future', and of 'absolute elsewhere', and of 'absolute simultaneity' (of events occurring at their space-time conjunction). | |
| From: Craig Bourne (A Future for Presentism [2006], 5.III) | |
| A reaction: [My summary of his paragraph] I am inclined to agree with Bourne that there is enough here to build some sort of notion of 'present' that will support the doctrine of Presentism. |
| 14015 | No-Futurists believe in past and present, but not future, and say the world grows as facts increase [Bourne] |
| Full Idea: 'No-Futurists' believe in the real existence of the past and present but not the future, and hold that the world grows as more and more facts come into existence. | |
| From: Craig Bourne (A Future for Presentism [2006], 6.IIb) | |
| A reaction: [He cites Broad 1923 and Tooley 1997] My sympathies are with Presentism, but there seems not denying that past events fix truths in a way that future events don't. The unchangeability of past events seems to make them factual. |
| 14007 | How can presentists talk of 'earlier than', and distinguish past from future? [Bourne] |
| Full Idea: Presentists have a difficulty with how they can help themselves to the notion of 'earlier than' without having to invoke real relata, and how presentism can distinguish the past from the future. | |
| From: Craig Bourne (A Future for Presentism [2006], 2.IV) | |
| A reaction: The obvious response is to infer the past from the present (fossils), and infer the future from the present (ticking bomb). But what is it that is being inferred, if the past and future are denied a priori? Tricky! |
| 14011 | Presentism seems to deny causation, because the cause and the effect can never coexist [Bourne] |
| Full Idea: It seems that presentism cannot accommodate causation at all. In a true instance of 'c causes e', it seems to follow that both c and e exist, and it is widely accepted that c is earlier than e. But for presentists that means c and e can't coexist. | |
| From: Craig Bourne (A Future for Presentism [2006], 4) | |
| A reaction: A nice problem. Obviously if the flying ball smashed the window, we are left with only the effect existing - otherwise we could intercept the ball and prevent the disaster. To say this cause and this effect coexist would be even dafter than the problem. |
| 14017 | Since presentists treat the presentness of events as basic, simultaneity should be define by that means [Bourne] |
| Full Idea: Since for presentism there is an ontologically significant and basic sense in which events are present, we should expect a definition of simultaneity in terms of presentness, rather than the other way round. | |
| From: Craig Bourne (A Future for Presentism [2006], 6.IV) | |
| A reaction: Love it. I don't see how you can even articulate questions about simultaneity if you don't already have a notion of presentness. What are the relata you are enquiring about? |
| 14003 | Time is tensed or tenseless; the latter says all times and objects are real, and there is no passage of time [Bourne] |
| Full Idea: Theories of time are in two broad categories, the tenseless and the tensed theories. In tenseless theories, all times are equally real, as are all objects located at them, and there is no passage of time from future to present to past. It's the B-series. | |
| From: Craig Bourne (A Future for Presentism [2006], Intro IIa) | |
| A reaction: It might solve a few of the problems, but is highly counterintuitive. Presumably it makes the passage of time an illusion, and gives no account of how events 'happen', or of their direction, and it leaves causation out on a limb. I'm afraid not. |
| 14005 | B-series objects relate to each other; A-series objects relate to the present [Bourne] |
| Full Idea: Objects in the B-series are earlier than, later than, or simultaneous with each other, whereas objects in the A-series are earlier than, later than or simultaneous with the present. | |
| From: Craig Bourne (A Future for Presentism [2006], Intro IIb) | |
| A reaction: Must we choose? Two past events relate to each other, but there is a further relation when 'now' falls between the events. If I must choose, I suppose I go for the A-series view. The B-series is a subsequent feat of imagination. McTaggart agreed. |
| 14006 | Time flows, past is fixed, future is open, future is feared but not past, we remember past, we plan future [Bourne] |
| Full Idea: We say that time 'flows', that the past is 'fixed' but the future is 'open'; we only dread the future, but not the past; we remember the past but not the future; we plan for the future but not the past. | |
| From: Craig Bourne (A Future for Presentism [2006], Intro III) | |
| A reaction: These seem pretty overwhelming reasons for accepting an asymmetry between the past and the future. If you reject that, you seem to be mired in a multitude of contradictions. Your error theory is going to be massive. |