38 ideas
| 12780 | We can grasp the wisdom of God a priori [Leibniz] |
| Full Idea: We can grasp the wisdom of God a priori, and not from the order of the phenomena alone. ... For the senses put nothing forward concerning metaphysical matters. | |
| From: Gottfried Leibniz (Letters to Des Bosses [1715], 1716.05.29) | |
| A reaction: Nice instance of the aspirations of big metaphysics, before Kant cut it down to size. The claim is not far off Plato's, that by dialectic we can work out the necessities of the Forms, to which even the gods must bow. Are necessities really kept from us? |
| 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'. |
| 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. |
| 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. |
| 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'. |
| 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? |
| 12774 | Without a substantial chain to link monads, they would just be coordinated dreams [Leibniz] |
| Full Idea: If that substantial chain [vinculum substantiale] for monads did not exist, all bodies, together with all of their qualities, would be nothing but well-founded phenomena, like a rainbow or an image in a mirror, continual dreams perfectly in agreement. | |
| From: Gottfried Leibniz (Letters to Des Bosses [1715], 1712.02.05) | |
| A reaction: [The first appearance, apparently, of the 'susbtantial chain' in his writings] I take this to be a hugely significant move, either a defeat for monads, or the arrival of common sense. Spiritual monads must unify things, so they can't just be 'parallel'. |
| 12777 | Monads do not make a unity unless a substantial chain is added to them [Leibniz] |
| Full Idea: Monads do not constitute a complete composite substance, since they make up, not something one per se, but only a mere aggregate, unless some substantial chain is added. | |
| From: Gottfried Leibniz (Letters to Des Bosses [1715], 1712.05.26) | |
| A reaction: This is the clearest statement in the Des Bosses letters of the need for something extra to unite monads. Since the main role of monads was to replace substances, which are only postulated to provide unity, this is rather a climb-down. |
| 12782 | Monads control nothing outside of themselves [Leibniz] |
| Full Idea: Monads aren't a principle of operation for things outside of themselves. | |
| From: Gottfried Leibniz (Letters to Des Bosses [1715], 1716.05.29) | |
| A reaction: This is why Leibniz has got into a tangle, and is proposing his 'substantial chain' to join the monads together. I suspect that he would have dumped monads if he had lived a bit longer. |
| 12778 | There is active and passive power in the substantial chain and in the essence of a composite [Leibniz] |
| Full Idea: I do not say there is a chain midway between matter and form, but that the substantial form and primary matter of the composite, in the Scholastic sense (the primitive power, active and passive) are in the chain, and in the essence of the composite. | |
| From: Gottfried Leibniz (Letters to Des Bosses [1715], 1716.05.29) | |
| A reaction: Note that this implies an essence of primitive power, and not just a collection of all properties. This is the clearest account in these letters of the nature of the 'substantial chain' he has added to his monads. |
| 12783 | Primitive force is what gives a composite its reality [Leibniz] |
| Full Idea: The first entelechy of a composite is a constitutive part of the composite substance, namely its primitive force. | |
| From: Gottfried Leibniz (Letters to Des Bosses [1715], 1716.05.29) | |
| A reaction: For me, Leibniz's most interesting proposal is to characterise Aristotelian 'form' as an active thing, which offers an intrinsic account of movement, and a bottom level for explanations. There always remains the inexplicable. Why anything? Why this? |
| 12775 | Things seem to be unified if we see duration, position, interaction and connection [Leibniz] |
| Full Idea: Important relations are duration (order of successive things) and position (order of coexisting things) and interaction. Position without a thing mediating is presence. Beyond these is connection when things move one another. Thus things seem to be one. | |
| From: Gottfried Leibniz (Letters to Des Bosses [1715], 1712.02.05) | |
| A reaction: [compressed] This is the best account I can find of his epistemological angle on the unity of things. They are symptoms of the inner power of unification, and he says that God sees these relations most clearly. |
| 12776 | Every substance is alive [Leibniz] |
| Full Idea: Every substance is alive. | |
| From: Gottfried Leibniz (Letters to Des Bosses [1715], 1712.02.05) | |
| A reaction: The most charitable interpretation of this is that substances are what have unity, and the best model of unity that we can grasp is the unity of an organism. The less charitable view is that he literally thinks a pebble is 'alive'. Hm. |
| 12753 | A substantial bond of powers is needed to unite composites, in addition to monads [Leibniz] |
| Full Idea: Some realising thing must bring it about that composite substance contains something substantial besides monads, otherwise composites will be mere phenomena. The scholastics' active and passive powers are the substantial bond I am urging. | |
| From: Gottfried Leibniz (Letters to Des Bosses [1715], 1716.01.13), quoted by Daniel Garber - Leibniz:Body,Substance,Monad 9 | |
| A reaction: [compressed] This appears to be a major retreat, in the last year of Leibniz's life, from the full monadology he had espoused. How do monads connect to matter, and thus unify it? He is returning to Aristotelian hylomorphism. |
| 12781 | A composite substance is a mere aggregate if its essence is just its parts [Leibniz] |
| Full Idea: An aggregate, but not a composite substance, is resolved into parts. A composite substance only needs the coming together of parts, but is not essentially constituted by them, otherwise it would be an aggregate. | |
| From: Gottfried Leibniz (Letters to Des Bosses [1715], 1716.05.29) | |
| A reaction: The point is that there is more to some things than there mere parts. Only some unifying principle, in addition to the mere parts, bestows a unity. Mereology is a limited activity if it has nothing to say about this issue. |
| 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. |
| 12779 | There is a reason why not every possible thing exists [Leibniz] |
| Full Idea: There is a reason why not every possible thing exists. | |
| From: Gottfried Leibniz (Letters to Des Bosses [1715], 1716.05.29) | |
| A reaction: This is the kind of wonderful speculative metaphysical remark that we are not allowed to make any more. Needless to say, he doesn't tell us what the reason is. Overcrowding, perhaps. |
| 12785 | Truth is mutually agreed perception [Leibniz] |
| Full Idea: In the mutual agreement of perceivers consists the truth of the phenomena. | |
| From: Gottfried Leibniz (Letters to Des Bosses [1715], 1716.05.29) | |
| A reaction: This remark is startling close to the 'perspectivism' that crops up in the late notebooks of Nietzsche. Leibniz was keen on relativism in many areas, starting with the nature of space. I personally think Leibniz meant 'knowledge' rather than 'truth'. |
| 18699 | Carnap tried to define all scientific predicates in terms of primitive relations, using type theory [Carnap, by Button] |
| Full Idea: Carnap's ultimate ambition in the Aufbau is to provide a constitution-system within which any predicate of any scientific vocabulary can be explicitly defined in terms of primitive relations holding among basic elements, using type theory. | |
| From: report of Rudolph Carnap (The Logical Structure of the World (Aufbau) [1928]) by Tim Button - The Limits of Reason 05.2 | |
| A reaction: David Chalmers has a modern shot at the same project in 'Constructing the World'. Ramsey sentences seem to be part of the same game. |
| 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? |
| 12131 | All concepts can be derived from a few basics, making possible one science of everything [Carnap, by Brody] |
| Full Idea: In the 'Aufbau', Carnap tried to show how all of our concepts can be derived from a few basic concepts. ..Consequently there can be one science which studied all that existed, the science of the objects corresponding to the basic concepts. | |
| From: report of Rudolph Carnap (The Logical Structure of the World (Aufbau) [1928]) by Baruch Brody - Identity and Essence 2.2 | |
| A reaction: This is Carnap's Constructionist programme. |
| 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. |
| 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. |
| 12784 | Allow no more miracles than are necessary [Leibniz] |
| Full Idea: Miracles should not be increased beyond necessity. | |
| From: Gottfried Leibniz (Letters to Des Bosses [1715], 1716.05.29) | |
| A reaction: Leibniz defends miracles (where Spinoza dismisses them). This remark is, of course, an echo of Ockham's Razor, that 'entities' should not be multiplied beyond necessity. It is hard to disagree with his proposal. Zero might be result, though. |