26 ideas
| 19335 | Reasonings have a natural ordering in God's understanding, but only a temporal order in ours [Leibniz] |
| Full Idea: All reasonings are eminent in God, and they preserve an order among themselves in his understanding as well as in ours; but for him this is just an order and a priority of nature, whereas for us there is a priority of time. | |
| From: Gottfried Leibniz (The Theodicy [1710], p.192), quoted by Franklin Perkins - Leibniz: Guide for the Perplexed 2.III | |
| A reaction: This view is found in Frege, and seems to be the hallmark of rationalist philosophy. There is an apriori assumption that reality has a rational order, so that pure reason is a tool for grasping it. Lewis's 'mosaic' of experiences has no order. |
| 9944 | We understand some statements about all sets [Putnam] |
| Full Idea: We seem to understand some statements about all sets (e.g. 'for every set x and every set y, there is a set z which is the union of x and y'). | |
| From: Hilary Putnam (Mathematics without Foundations [1967], p.308) | |
| A reaction: His example is the Axiom of Choice. Presumably this is why the collection of all sets must be referred to as a 'class', since we can talk about it, but cannot define it. |
| 9937 | I do not believe mathematics either has or needs 'foundations' [Putnam] |
| Full Idea: I do not believe mathematics either has or needs 'foundations'. | |
| From: Hilary Putnam (Mathematics without Foundations [1967]) | |
| A reaction: Agreed that mathematics can function well without foundations (given that the enterprise got started with no thought for such things), the ontology of the subject still strikes me as a major question, though maybe not for mathematicians. |
| 9939 | It is conceivable that the axioms of arithmetic or propositional logic might be changed [Putnam] |
| Full Idea: I believe that under certain circumstances revisions in the axioms of arithmetic, or even of the propositional calculus (e.g. the adoption of a modular logic as a way out of the difficulties in quantum mechanics), is fully conceivable. | |
| From: Hilary Putnam (Mathematics without Foundations [1967], p.303) | |
| A reaction: One can change the axioms of a system without necessarily changing the system (by swapping an axiom and a theorem). Especially if platonism is true, since the eternal objects reside calmly above our attempts to axiomatise them! |
| 9940 | Maybe mathematics is empirical in that we could try to change it [Putnam] |
| Full Idea: Mathematics might be 'empirical' in the sense that one is allowed to try to put alternatives into the field. | |
| From: Hilary Putnam (Mathematics without Foundations [1967], p.303) | |
| A reaction: He admits that change is highly unlikely. It take hardcore Millian arithmetic to be only changeable if pebbles start behaving very differently with regard to their quantities, which appears to be almost inconceivable. |
| 9941 | Science requires more than consistency of mathematics [Putnam] |
| Full Idea: Science demands much more of a mathematical theory than that it should merely be consistent, as the example of the various alternative systems of geometry dramatizes. | |
| From: Hilary Putnam (Mathematics without Foundations [1967]) | |
| A reaction: Well said. I don't agree with Putnam's Indispensability claims, but if an apparent system of numbers or lines has no application to the world then I don't consider it to be mathematics. It is a new game, like chess. |
| 9943 | You can't deny a hypothesis a truth-value simply because we may never know it! [Putnam] |
| Full Idea: Surely the mere fact that we may never know whether the continuum hypothesis is true or false is by itself just no reason to think that it doesn't have a truth value! | |
| From: Hilary Putnam (Mathematics without Foundations [1967]) | |
| A reaction: This is Putnam in 1967. Things changed later. Personally I am with the younger man all they way, but I reserve the right to totally change my mind. |
| 19553 | Commitment to 'I have a hand' only makes sense in a context where it has been doubted [Hawthorne] |
| Full Idea: If I utter 'I know I have a hand' then I can only be reckoned a cooperative conversant by my interlocutors on the assumption that there was a real question as to whether I have a hand. | |
| From: John Hawthorne (The Case for Closure [2005], 2) | |
| A reaction: This seems to point to the contextualist approach to global scepticism, which concerns whether we are setting the bar high or low for 'knowledge'. |
| 19551 | How can we know the heavyweight implications of normal knowledge? Must we distort 'knowledge'? [Hawthorne] |
| Full Idea: Those who deny skepticism but accept closure will have to explain how we know the various 'heavyweight' skeptical hypotheses to be false. Do we then twist the concept of knowledge to fit the twin desiderata of closue and anti-skepticism? | |
| From: John Hawthorne (The Case for Closure [2005], Intro) | |
| A reaction: [He is giving Dretske's view; Dretske says we do twist knowledge] Thus if I remember yesterday, that has the heavyweight implication that the past is real. Hawthorne nicely summarises why closure produces a philosophical problem. |
| 19552 | We wouldn't know the logical implications of our knowledge if small risks added up to big risks [Hawthorne] |
| Full Idea: Maybe one cannot know the logical consequences of the proposition that one knows, on account of the fact that small risks add up to big risks. | |
| From: John Hawthorne (The Case for Closure [2005], 1) | |
| A reaction: The idea of closure is that the new knowledge has the certainty of logic, and each step is accepted. An array of receding propositions can lose reliability, but that shouldn't apply to logic implications. Assuming monotonic logic, of course. |
| 19554 | Denying closure is denying we know P when we know P and Q, which is absurd in simple cases [Hawthorne] |
| Full Idea: How could we know that P and Q but not be in a position to know that P (as deniers of closure must say)? If my glass is full of wine, we know 'g is full of wine, and not full of non-wine'. How can we deny that we know it is not full of non-wine? | |
| From: John Hawthorne (The Case for Closure [2005], 2) | |
| A reaction: Hawthorne merely raises this doubt. Dretske is concerned with heavyweight implications, but how do you accept lightweight implications like this one, and then suddenly reject them when they become too heavy? [see p.49] |
| 19367 | Saying we must will whatever we decide to will leads to an infinite regress [Leibniz] |
| Full Idea: As for volition itself, to say that it is the object of free will is incorrect. We will to act, strictly speaking, and we do not will to will, else we should still say we will to have the will to will, and that would go on to infinity. | |
| From: Gottfried Leibniz (The Theodicy [1710], p.151), quoted by Franklin Perkins - Leibniz: Guide for the Perplexed 4.IV | |
| A reaction: This strikes me as an elementary difficulty which most fans of free will appear to evade. Thoughts just arise in us, and some of them are volitions. We can say there is then a 'gap' (Searle) where we choose, but what happens in the gap? |
| 19351 | Perfections of soul subordinate the body, but imperfections of soul submit to the body [Leibniz] |
| Full Idea: Insofar as the soul has perfection ...God has accommodated the body to the soul, and has arranged beforehand that the body is impelled to execute its orders. Insofar as it is imperfect and confused, God accommodates soul to body, swayed by passions. | |
| From: Gottfried Leibniz (The Theodicy [1710], p.159), quoted by Franklin Perkins - Leibniz: Guide for the Perplexed 3.IV | |
| A reaction: Perkins says this is the nearest Leibniz gets to the idea of interaction between body and soul. Perfection and confusion are on a continuum for Leibniz. With such speculations I always wonder how these things can be known. How perfect is my mind? |
| 19331 | Will is an inclination to pursue something good [Leibniz] |
| Full Idea: One may say that 'will' consists in the inclination to do something in proportion to the good it contains. | |
| From: Gottfried Leibniz (The Theodicy [1710], p.136), quoted by Franklin Perkins - Leibniz: Guide for the Perplexed 2.III | |
| A reaction: This emphasises that the will is faced with options, rather than generating the options. The context is a discussion of the nature of God's will. I think 'will' is a really useful concept, and dislike the Hobbesian rejection of will. |
| 19346 | Most people facing death would happily re-live a similar life, with just a bit of variety [Leibniz] |
| Full Idea: I believe there would be few persons who, being at the point of death, were not content to take up life again, on condition of passing through the same amount of good and evil, provided that it were not the same kind. | |
| From: Gottfried Leibniz (The Theodicy [1710], p.130), quoted by Franklin Perkins - Leibniz: Guide for the Perplexed 2.IV | |
| A reaction: Nice challenge. People who refuse the offer are not necessarily suicidal. He's probably right, but Leibniz doesn't recognise the factor of boredom. Look up the suicide note of the actor George Sanders! One life may be enough. |
| 19340 | Metaphysical evil is imperfection; physical evil is suffering; moral evil is sin [Leibniz] |
| Full Idea: Evil may be taken metaphysically, physically, and morally. Metaphysical evil consists in mere imperfection, physical evil is suffering, and moral evil is sin. | |
| From: Gottfried Leibniz (The Theodicy [1710], p.136), quoted by Franklin Perkins - Leibniz: Guide for the Perplexed 2.IV | |
| A reaction: There seem to be plenty of imperfections in the world which don't look like evil. Or do you only declare it to be an imperfection because it seems to be evil (by some other standard)? Human evil comes from ignorance, so metaphysical explains moral. |
| 19366 | You can't assess moral actions without referring to the qualities of character that produce them [Leibniz] |
| Full Idea: One is more worthy of praise when one owes the action to one's good qualities, and more culpable in proportion as one has been impelled by one's evil qualities; assessing actions without weighing the qualities whence they spring is to talk at random. | |
| From: Gottfried Leibniz (The Theodicy [1710], p.426), quoted by Franklin Perkins - Leibniz: Guide for the Perplexed 4.IV | |
| A reaction: Mill tries to separate judgement of the agent from judgement of the consequences of the action, but I think Leibniz has spotted that just judging outcomes ceases to be a 'moral' judgement. |
| 19326 | God must be intelligible, to select the actual world from the possibilities [Leibniz] |
| Full Idea: The cause of the world must be intelligent: for this existing world being contingent and an infinity of worlds being equally possible, with equal claim to existence, the cause of the world must have regarded all of these worlds to fix on one of them. | |
| From: Gottfried Leibniz (The Theodicy [1710], p.127), quoted by Franklin Perkins - Leibniz: Guide for the Perplexed 2.II | |
| A reaction: A wonderfully Leibnizian way of putting what looks like the design argument. |
| 19327 | The intelligent cause must be unique and all-perfect, to handle all the interconnected possibilities [Leibniz] |
| Full Idea: The intelligent cause ought to be infinite in all ways, and absolutely perfect in power, in wisdom, and in goodness, since it relates to all that which is possible. Also, since all is connected together, there is no ground for admitting more than one. | |
| From: Gottfried Leibniz (The Theodicy [1710], p.128), quoted by Franklin Perkins - Leibniz: Guide for the Perplexed 2.II | |
| A reaction: Notice that Leibniz's possible worlds seem to be all connected together, unlike David Lewis's worlds, which are discrete. Personally I suspect that all perfections will lead to contradiction, though Leibniz strongly argues against it. |
| 19344 | God prefers men to lions, but might not exterminate lions to save one man [Leibniz] |
| Full Idea: It is certain that God sets greater store by a man than a lion; nevertheless it can hardly be said with certainty that God prefers a single man in all respects to the whole of lion-kind. | |
| From: Gottfried Leibniz (The Theodicy [1710], p.189), quoted by Franklin Perkins - Leibniz: Guide for the Perplexed 2.IV | |
| A reaction: Lovely problems arise when you guess at God's values! We have the same problem. Would you kill a poacher who was wiping out the last remaining lions? How many lions would you kill to save a human? |
| 19330 | If justice is arbitrary, or fixed but not observed, or not human justice, this undermines God [Leibniz] |
| Full Idea: The three dogmas (1) that the nature of justice is arbitrary, (2) it is fixed, but not certain God will observe it, or (3) the justice we know is not that which God observes, destroy our confidence in the love of God. | |
| From: Gottfried Leibniz (The Theodicy [1710], p.237), quoted by Franklin Perkins - Leibniz: Guide for the Perplexed 2.III | |
| A reaction: Leibniz proceeds to carefully refute these three responses to the dilemma about how justice relates to God. |
| 19325 | God is the first reason of things; our experiences are contingent, and contain no necessity [Leibniz] |
| Full Idea: God is the first reason of things: all that we see and experience is contingent and nothing in them renders their existence necessary. | |
| From: Gottfried Leibniz (The Theodicy [1710], p.127), quoted by Franklin Perkins - Leibniz: Guide for the Perplexed 2.II | |
| A reaction: Perkins presents this as the first step in one of Leibniz's arguments for God. They all seem to be variants of the ontological argument. [His 'Theodicy' is the Huggard translation, 1985] This resembles Aquinas's Third Way. |
| 19329 | The laws of physics are wonderful evidence of an intelligent and free being [Leibniz] |
| Full Idea: These admirable laws [of physics] are wonderful evidence of an intelligent and free being, as opposed to the system of absolute and brute necessity, advocated by Strato and Spinoza. | |
| From: Gottfried Leibniz (The Theodicy [1710], p.332), quoted by Franklin Perkins - Leibniz: Guide for the Perplexed 2.II | |
| A reaction: Note the swipe at Spinoza. Leibniz defends the absolute necessities residing in God, but is too polite to call those 'brute', though personally I can't see the difference. But he says the laws arise from 'perfection and order', not from God's necessity. |
| 19437 | Prayers are useful, because God foresaw them in his great plan [Leibniz] |
| Full Idea: Not only cares and labours but also prayers are useful; God having had these prayers in view before he regulated things. | |
| From: Gottfried Leibniz (The Theodicy [1710], Abridge III) | |
| A reaction: Hm. I'm struggling with this one. So I can't skip prayers today, because God has foreseen them and included them in his great plan? Hard to motivate yourself, like starting a game of chess after you've already been declared the winner. |
| 19337 | How can an all-good, wise and powerful being allow evil, sin and apparent injustice? [Leibniz] |
| Full Idea: There is this question of natural theology, how a sole Principle, all-good, all-wise and all-powerful, has been able to admit evil, and especially to permit sin, and how it could resolve to make the wicked often happy and the good unhappy? | |
| From: Gottfried Leibniz (The Theodicy [1710], p.098), quoted by Franklin Perkins - Leibniz: Guide for the Perplexed 2.IV | |
| A reaction: His answer is, roughly, that there is an unavoidable trade-off, which humans cannot fully understand. Personally I would say that if there is a God, the evidence for his benevolence towards humanity is not encouraging. |
| 19345 | Being confident of God's goodness, we disregard the apparent local evils in the visible world [Leibniz] |
| Full Idea: Being made confident by demonstrations of the goodness and the justice of God, we disregard the appearances of harshness and justice which we see in this small portion of his Kingdom that is exposed to our gaze. | |
| From: Gottfried Leibniz (The Theodicy [1710], p.120), quoted by Franklin Perkins - Leibniz: Guide for the Perplexed 2.IV | |
| A reaction: Hm. If this locality is full of evils, and the rest of it is much better, how come we are stuck in this miserable corner of things? God is obliged to compromise, but did he select us to get the worst of it? |