28 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. |
| 13838 | A decent modern definition should always imply a semantics [Hacking] |
| Full Idea: Today we expect that anything worth calling a definition should imply a semantics. | |
| From: Ian Hacking (What is Logic? [1979], §10) | |
| A reaction: He compares this with Gentzen 1935, who was attempting purely syntactic definitions of the logical connectives. |
| 13833 | 'Thinning' ('dilution') is the key difference between deduction (which allows it) and induction [Hacking] |
| Full Idea: 'Dilution' (or 'Thinning') provides an essential contrast between deductive and inductive reasoning; for the introduction of new premises may spoil an inductive inference. | |
| From: Ian Hacking (What is Logic? [1979], §06.2) | |
| A reaction: That is, inductive logic (if there is such a thing) is clearly non-monotonic, whereas classical inductive logic is monotonic. |
| 13834 | Gentzen's Cut Rule (or transitivity of deduction) is 'If A |- B and B |- C, then A |- C' [Hacking] |
| Full Idea: If A |- B and B |- C, then A |- C. This generalises to: If Γ|-A,Θ and Γ,A |- Θ, then Γ |- Θ. Gentzen called this 'cut'. It is the transitivity of a deduction. | |
| From: Ian Hacking (What is Logic? [1979], §06.3) | |
| A reaction: I read the generalisation as 'If A can be either a premise or a conclusion, you can bypass it'. The first version is just transitivity (which by-passes the middle step). |
| 13835 | Only Cut reduces complexity, so logic is constructive without it, and it can be dispensed with [Hacking] |
| Full Idea: Only the cut rule can have a conclusion that is less complex than its premises. Hence when cut is not used, a derivation is quite literally constructive, building up from components. Any theorem obtained by cut can be obtained without it. | |
| From: Ian Hacking (What is Logic? [1979], §08) |
| 13845 | The various logics are abstractions made from terms like 'if...then' in English [Hacking] |
| Full Idea: I don't believe English is by nature classical or intuitionistic etc. These are abstractions made by logicians. Logicians attend to numerous different objects that might be served by 'If...then', like material conditional, strict or relevant implication. | |
| From: Ian Hacking (What is Logic? [1979], §15) | |
| A reaction: The idea that they are 'abstractions' is close to my heart. Abstractions from what? Surely 'if...then' has a standard character when employed in normal conversation? |
| 13840 | First-order logic is the strongest complete compact theory with Löwenheim-Skolem [Hacking] |
| Full Idea: First-order logic is the strongest complete compact theory with a Löwenheim-Skolem theorem. | |
| From: Ian Hacking (What is Logic? [1979], §13) |
| 13844 | A limitation of first-order logic is that it cannot handle branching quantifiers [Hacking] |
| Full Idea: Henkin proved that there is no first-order treatment of branching quantifiers, which do not seem to involve any idea that is fundamentally different from ordinary quantification. | |
| From: Ian Hacking (What is Logic? [1979], §13) | |
| A reaction: See Hacking for an example of branching quantifiers. Hacking is impressed by this as a real limitation of the first-order logic which he generally favours. |
| 13842 | Second-order completeness seems to need intensional entities and possible worlds [Hacking] |
| Full Idea: Second-order logic has no chance of a completeness theorem unless one ventures into intensional entities and possible worlds. | |
| From: Ian Hacking (What is Logic? [1979], §13) |
| 13837 | With a pure notion of truth and consequence, the meanings of connectives are fixed syntactically [Hacking] |
| Full Idea: My doctrine is that the peculiarity of the logical constants resides precisely in that given a certain pure notion of truth and consequence, all the desirable semantic properties of the constants are determined by their syntactic properties. | |
| From: Ian Hacking (What is Logic? [1979], §09) | |
| A reaction: He opposes this to Peacocke 1976, who claims that the logical connectives are essentially semantic in character, concerned with the preservation of truth. |
| 13839 | Perhaps variables could be dispensed with, by arrows joining places in the scope of quantifiers [Hacking] |
| Full Idea: For some purposes the variables of first-order logic can be regarded as prepositions and place-holders that could in principle be dispensed with, say by a system of arrows indicating what places fall in the scope of which quantifier. | |
| From: Ian Hacking (What is Logic? [1979], §11) | |
| A reaction: I tend to think of variables as either pronouns, or as definite descriptions, or as temporary names, but not as prepositions. Must address this new idea... |
| 13843 | If it is a logic, the Löwenheim-Skolem theorem holds for it [Hacking] |
| Full Idea: A Löwenheim-Skolem theorem holds for anything which, on my delineation, is a logic. | |
| From: Ian Hacking (What is Logic? [1979], §13) | |
| A reaction: I take this to be an unusually conservative view. Shapiro is the chap who can give you an alternative view of these things, or Boolos. |
| 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. |
| 14409 | I am a presentist, and all language and common sense supports my view [Bigelow] |
| Full Idea: I am a presentist: nothing exists which is not present. Everyone believed this until the nineteenth century; it is writing into the grammar of natural languages; it is still assumed in everyday life, even by philosophers who deny it. | |
| From: John Bigelow (Presentism and Properties [1996], p.36), quoted by Trenton Merricks - Truth and Ontology | |
| A reaction: The most likely deniers of presentism seem to be physicists and cosmologists who have overdosed on Einstein. On the whole I vote for presentism, but what justifies truths about the past and future. Traces existing in the present? |
| 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? |