15 ideas
| 14263 | Strong Kleene disjunction just needs one true disjunct; Weak needs the other to have some value [Fine,K] |
| Full Idea: Under strong Kleene tables, a disjunction will be true if one of the disjuncts is true, regardless of whether or not the other disjunct has a truth-value; under the weak table it is required that the other disjunct also have a value. So for other cases. | |
| From: Kit Fine (Some Puzzles of Ground [2010], n7) | |
| A reaction: [see also p.111 of Fine's article] The Kleene tables seem to be the established form of modern three-valued logic, with the third value being indeterminate. |
| 18739 | Three stages of philosophical logic: syntactic (1905-55), possible worlds (1963-85), widening (1990-) [Horsten/Pettigrew] |
| Full Idea: Three periods can be distinguished in philosophical logic: the syntactic stage, from Russell's definite descriptions to the 1950s, the dominance of possible world semantics from the 50s to 80s, and a current widening of the subject. | |
| From: Horsten,L/Pettigrew,R (Mathematical Methods in Philosophy [2014], 1) | |
| A reaction: [compressed] I've read elsewhere that the arrival of Tarski's account of truth in 1933, taking things beyond the syntactic, was also a landmark. |
| 18741 | Logical formalization makes concepts precise, and also shows their interrelation [Horsten/Pettigrew] |
| Full Idea: Logical formalization forces the investigator to make the central philosophical concepts precise. It can also show how some philosophical concepts and objects can be defined in terms of others. | |
| From: Horsten,L/Pettigrew,R (Mathematical Methods in Philosophy [2014], 2) | |
| A reaction: This is the main rationale of the highly formal and mathematical approach to such things. The downside is when you impose 'precision' on language that was never intended to be precise. |
| 18744 | Models are sets with functions and relations, and truth built up from the components [Horsten/Pettigrew] |
| Full Idea: A (logical) model is a set with functions and relations defined on it that specify the denotation of the non-logical vocabulary. A series of recursive clauses explicate how truth values of complex sentences are compositionally determined from the parts. | |
| From: Horsten,L/Pettigrew,R (Mathematical Methods in Philosophy [2014], 3) | |
| A reaction: See the ideas on 'Functions in logic' and 'Relations in logic' (in the alphabetical list) to expand this important idea. |
| 18740 | If 'exist' doesn't express a property, we can hardly ask for its essence [Horsten/Pettigrew] |
| Full Idea: If there is indeed no property of existence that is expressed by the word 'exist', then it makes no sense to ask for its essence. | |
| From: Horsten,L/Pettigrew,R (Mathematical Methods in Philosophy [2014], 2) | |
| A reaction: As far as I can tell, this was exactly Aristotle's conclusion, so he skirted round the question of 'being qua being', and focused on the nature of objects instead. Grand continental talk of 'Being' doesn't sound very interesting. |
| 14262 | Formal grounding needs transitivity of grounding, no self-grounding, and the existence of both parties [Fine,K] |
| Full Idea: The general formal principles of grounding are Transitivity (A«B, B«C/A«C: if A helps ground B and B helps C, then A helps C), Irreflexivity (A«A/absurd: A can't ground itself) and Factivity (A«B/A; A«/B: for grounding both A and B must be the case). | |
| From: Kit Fine (Some Puzzles of Ground [2010], 4) |
| 18745 | A Tarskian model can be seen as a possible state of affairs [Horsten/Pettigrew] |
| Full Idea: A Tarskian model can in a sense be seen as a model of a possible state of affairs. | |
| From: Horsten,L/Pettigrew,R (Mathematical Methods in Philosophy [2014], 3) | |
| A reaction: I include this remark to show how possible worlds semantics built on the arrival of model theory. |
| 18747 | The 'spheres model' was added to possible worlds, to cope with counterfactuals [Horsten/Pettigrew] |
| Full Idea: The notion of a possible worlds model was extended (resulting in the concept of a 'spheres model') in order to obtain a satisfactory logical treatment of counterfactual conditional sentences. | |
| From: Horsten,L/Pettigrew,R (Mathematical Methods in Philosophy [2014], 4) | |
| A reaction: Thus we add 'centred' worlds, and an 'actual' world, to the loose original model. It is important to remember when we discuss 'close' worlds that we are then committed to these presuppositions. |
| 18748 | Epistemic logic introduced impossible worlds [Horsten/Pettigrew] |
| Full Idea: The idea of 'impossible worlds' was introduced into epistemic logic. | |
| From: Horsten,L/Pettigrew,R (Mathematical Methods in Philosophy [2014], 4) | |
| A reaction: Nathan Salmon seems interested in their role in metaphysics (presumably in relation to Meinongian impossible objects, like circular squares, which must necessarily be circular). |
| 18746 | Possible worlds models contain sets of possible worlds; this is a large metaphysical commitment [Horsten/Pettigrew] |
| Full Idea: Each possible worlds model contains a set of possible worlds. For this reason, possible worlds semantics is often charged with smuggling in heavy metaphysical commitments. | |
| From: Horsten,L/Pettigrew,R (Mathematical Methods in Philosophy [2014], 3) | |
| A reaction: To a beginner it looks very odd that you should try to explain possibility by constructing a model of it in terms of 'possible' worlds. |
| 18750 | Using possible worlds for knowledge and morality may be a step too far [Horsten/Pettigrew] |
| Full Idea: When the possible worlds semantics were further extended to model notions of knowledge and of moral obligation, the application was beginning to look distinctly forced and artificial. | |
| From: Horsten,L/Pettigrew,R (Mathematical Methods in Philosophy [2014], 5) | |
| A reaction: They accept lots of successes in modelling necessity and time. |
| 9086 | The idea of abstract objects is not ontological; it comes from the epistemological idea of abstraction [Plantinga] |
| Full Idea: The notion of an abstract object comes from the notion of abstraction; it is in origin an epistemological rather than an ontological category. | |
| From: Alvin Plantinga (Why Propositions cannot be concrete [1993], p.232) | |
| A reaction: Etymology doesn't prove anything. However, if you define abstract objects as not existing in space or time, you must recognise that this may only be because that is how humans imaginatively created them in the first place. |
| 9087 | Theists may see abstract objects as really divine thoughts [Plantinga] |
| Full Idea: Theists may find attractive a view popular among medieval philosophers from Augustine on: that abstract objects are really divine thoughts. More exactly, propositions are divine thoughts, properties divine concepts, and sets divine collections. | |
| From: Alvin Plantinga (Why Propositions cannot be concrete [1993], p.233) | |
| A reaction: Hm. I pass this on because we should be aware that there is a theological history to discussions of abstract objects, and some people have vested interests in keeping them outside of the natural world. Aren't properties natural? Does God gerrymander sets? |
| 9085 | If propositions are concrete they don't have to exist, and so they can't be necessary truths [Plantinga] |
| Full Idea: Someone who believes propositions are concrete cannot agree that some propositions are necessary. For propositions are contingent beings, and could have failed to exist. But if they fail to exist, then they fail to be true. | |
| From: Alvin Plantinga (Why Propositions cannot be concrete [1993], p.230) | |
| A reaction: [compressed] He implies the actual existence of an infinity of trivial, boring or ridiculous necessary truths. I suspect that he is just confusing a thought with its content. Or we might just treat necessary propositions as hypothetical. |
| 9084 | Propositions can't just be in brains, because 'there are no human beings' might be true [Plantinga] |
| Full Idea: If propositions are brain inscriptions, then if there had been no human beings there would have been no propositions. But then 'there are no human beings' would have been true, so there would have been at least one truth (and thus one proposition). | |
| From: Alvin Plantinga (Why Propositions cannot be concrete [1993], p.229) | |
| A reaction: This would make 'there are no x's' true for any value of x apart from actual objects, which implies an infinity of propositions. Does Plantinga really believe that these all exist? He may be confusing propositions with facts. |