30 ideas
| 18781 | Inconsistency doesn't prevent us reasoning about some system [Mares] |
| Full Idea: We are able to reason about inconsistent beliefs, stories, and theories in useful and important ways | |
| From: Edwin D. Mares (Negation [2014], 1) |
| 18789 | Intuitionist logic looks best as natural deduction [Mares] |
| Full Idea: Intuitionist logic appears most attractive in the form of a natural deduction system. | |
| From: Edwin D. Mares (Negation [2014], 5.5) |
| 18790 | Intuitionism as natural deduction has no rule for negation [Mares] |
| Full Idea: In intuitionist logic each connective has one introduction and one elimination rule attached to it, but in the classical system we have to add an extra rule for negation. | |
| From: Edwin D. Mares (Negation [2014], 5.5) | |
| A reaction: How very intriguing. Mares says there are other ways to achieve classical logic, but they all seem rather cumbersome. |
| 18787 | Three-valued logic is useful for a theory of presupposition [Mares] |
| Full Idea: One reason for wanting a three-valued logic is to act as a basis of a theory of presupposition. | |
| From: Edwin D. Mares (Negation [2014], 3.1) | |
| A reaction: [He cites Strawson 1950] The point is that you can get a result when the presupposition does not apply, as in talk of the 'present King of France'. |
| 18793 | Material implication (and classical logic) considers nothing but truth values for implications [Mares] |
| Full Idea: The problem with material implication, and classical logic more generally, is that it considers only the truth value of formulas in deciding whether to make an implication stand between them. It ignores everything else. | |
| From: Edwin D. Mares (Negation [2014], 7.1) | |
| A reaction: The obvious problem case is conditionals, and relevance is an obvious extra principle that comes to mind. |
| 18784 | In classical logic the connectives can be related elegantly, as in De Morgan's laws [Mares] |
| Full Idea: Among the virtues of classical logic is the fact that the connectives are related to one another in elegant ways that often involved negation. For example, De Morgan's Laws, which involve negation, disjunction and conjunction. | |
| From: Edwin D. Mares (Negation [2014], 2.2) | |
| A reaction: Mares says these enable us to take disjunction or conjunction as primitive, and then define one in terms of the other, using negation as the tool. |
| 18786 | Excluded middle standardly implies bivalence; attacks use non-contradiction, De M 3, or double negation [Mares] |
| Full Idea: On its standard reading, excluded middle tells us that bivalence holds. To reject excluded middle, we must reject either non-contradiction, or ¬(A∧B) ↔ (¬A∨¬B) [De Morgan 3], or the principle of double negation. All have been tried. | |
| From: Edwin D. Mares (Negation [2014], 2.2) |
| 18780 | Standard disjunction and negation force us to accept the principle of bivalence [Mares] |
| Full Idea: If we treat disjunction in the standard way and take the negation of a statement A to mean that A is false, accepting excluded middle forces us also to accept the principle of bivalence, which is the dictum that every statement is either true or false. | |
| From: Edwin D. Mares (Negation [2014], 1) | |
| A reaction: Mates's point is to show that passively taking the normal account of negation for granted has important implications. |
| 18782 | The connectives are studied either through model theory or through proof theory [Mares] |
| Full Idea: In studying the logical connectives, philosophers of logic typically adopt the perspective of either model theory (givng truth conditions of various parts of the language), or of proof theory (where use in a proof system gives the connective's meaning). | |
| From: Edwin D. Mares (Negation [2014], 1) | |
| A reaction: [compressed] The commonest proof theory is natural deduction, giving rules for introduction and elimination. Mates suggests moving between the two views is illuminating. |
| 11115 | 'All horses' either picks out the horses, or the things which are horses [Jubien] |
| Full Idea: Two ways to see 'all horses are animals' are as picking out all the horses (so that it is a 'horse-quantifier'), ..or as ranging over lots of things in addition to horses, with 'horses' then restricting the things to those that satisfy 'is a horse'. | |
| From: Michael Jubien (Analyzing Modality [2007], 2) | |
| A reaction: Jubien says this gives you two different metaphysical views, of a world of horses etc., or a world of things which 'are horses'. I vote for the first one, as the second seems to invoke an implausible categorical property ('being a horse'). Cf Idea 11116. |
| 18783 | Many-valued logics lack a natural deduction system [Mares] |
| Full Idea: Many-valued logics do not have reasonable natural deduction systems. | |
| From: Edwin D. Mares (Negation [2014], 1) |
| 18792 | Situation semantics for logics: not possible worlds, but information in situations [Mares] |
| Full Idea: Situation semantics for logics consider not what is true in worlds, but what information is contained in situations. | |
| From: Edwin D. Mares (Negation [2014], 6.2) | |
| A reaction: Since many theoretical physicists seem to think that 'information' might be the most basic concept of a natural ontology, this proposal is obviously rather appealing. Barwise and Perry are the authors of the theory. |
| 18785 | Consistency is semantic, but non-contradiction is syntactic [Mares] |
| Full Idea: The difference between the principle of consistency and the principle of non-contradiction is that the former must be stated in a semantic metalanguage, whereas the latter is a thesis of logical systems. | |
| From: Edwin D. Mares (Negation [2014], 2.2) |
| 18788 | For intuitionists there are not numbers and sets, but processes of counting and collecting [Mares] |
| Full Idea: For the intuitionist, talk of mathematical objects is rather misleading. For them, there really isn't anything that we should call the natural numbers, but instead there is counting. What intuitionists study are processes, such as counting and collecting. | |
| From: Edwin D. Mares (Negation [2014], 5.1) | |
| A reaction: That is the first time I have seen mathematical intuitionism described in a way that made it seem attractive. One might compare it to a metaphysics based on processes. Apparently intuitionists struggle with infinite sets and real numbers. |
| 11116 | Being a physical object is our most fundamental category [Jubien] |
| Full Idea: Being a physical object (as opposed to being a horse or a statue) really is our most fundamental category for dealing with the external world. | |
| From: Michael Jubien (Analyzing Modality [2007], 2) | |
| A reaction: This raises the interesting question of why any categories should be considered to be more 'fundamental' than others. I can only think that we perceive something to be an object fractionally before we (usually) manage to identify it. |
| 11117 | Haecceities implausibly have no qualities [Jubien] |
| Full Idea: Properties of 'being such and such specific entity' are often called 'haecceities', but this term carries the connotation of non-qualitativeness which I don't favour. | |
| From: Michael Jubien (Analyzing Modality [2007], 2) | |
| A reaction: The way he defines it makes it sound as if it was a category, but I take it to be more like a bare individual essence. If it has not qualities then it has no causal powers, so there could be no evidence for its existence. |
| 11119 | De re necessity is just de dicto necessity about object-essences [Jubien] |
| Full Idea: I suggest that the de re is to be analyzed in terms of the de dicto. ...We have a case of modality de re when (and only when) the appropriate property in the de dicto formulation is an object-essence. | |
| From: Michael Jubien (Analyzing Modality [2007], 5) |
| 11118 | Modal propositions transcend the concrete, but not the actual [Jubien] |
| Full Idea: Where modal propositions may once have seemed to transcend the actual, they now seem only to transcend the concrete. | |
| From: Michael Jubien (Analyzing Modality [2007], 4) | |
| A reaction: This is because Jubien has defended a form of platonism. Personally I take modal propositions to be perceptible in the concrete world, by recognising the processes involved, not the mere static stuff. |
| 11108 | Your properties, not some other world, decide your possibilities [Jubien] |
| Full Idea: The possibility of your having been a playwright has nothing to do with how people are on other planets, whether in our own or in some other realm. It is only to do with you and the relevant property. | |
| From: Michael Jubien (Analyzing Modality [2007], 1) | |
| A reaction: I'm inclined to think that this simple point is conclusive disproof of possible worlds as an explanation of modality (apart from Jubien's other nice points). What we need to understand are modal properties, not other worlds. |
| 11111 | Modal truths are facts about parts of this world, not about remote maximal entities [Jubien] |
| Full Idea: Typical modal truths are just facts about our world, and generally facts about very small parts of it, not facts about some infinitude of complex, maximal entities. | |
| From: Michael Jubien (Analyzing Modality [2007], 1) | |
| A reaction: I think we should embrace this simple fact immediately, and drop all this nonsense about possible worlds, even if they are useful for the semantics of modal logic. |
| 11105 | We have no idea how many 'possible worlds' there might be [Jubien] |
| Full Idea: As soon as we start talking about 'possible world', we beg the question of their relevance to our prior notion of possibility. For all we know, there are just two such realms, or twenty-seven, or uncountably many, or even set-many. | |
| From: Michael Jubien (Analyzing Modality [2007], 1) |
| 11107 | If there are no other possible worlds, do we then exist necessarily? [Jubien] |
| Full Idea: Suppose there happen to be no other concrete realms. Would we happily accept the consequence that we exist necessarily? | |
| From: Michael Jubien (Analyzing Modality [2007], 1) |
| 11106 | If all possible worlds just happened to include stars, their existence would be necessary [Jubien] |
| Full Idea: If all of the possible worlds happened to include stars, how plausible is it to think that if this is how things really are, then we've just been wrong to regard the existence of stars as contingent? | |
| From: Michael Jubien (Analyzing Modality [2007], 1) |
| 11112 | Possible worlds just give parallel contingencies, with no explanation at all of necessity [Jubien] |
| Full Idea: In the world theory, what passes for 'necessity' is just a bunch of parallel 'contingencies'. The theory provides no basis for understanding why these contingencies repeat unremittingly across the board (while others do not). | |
| From: Michael Jubien (Analyzing Modality [2007], 1) |
| 11109 | If other worlds exist, then they are scattered parts of the actual world [Jubien] |
| Full Idea: Any other realms that happened to exist would just be scattered parts of the actual world, not entire worlds at all. It would just happen that physical reality was fragmented in this remarkable but modally inconsequential way. | |
| From: Michael Jubien (Analyzing Modality [2007], 1) | |
| A reaction: This is aimed explicitly at Lewis's modal realism, and strikes me as correct. Jubien's key point here is that they are irrelevant to modality, just as foreign countries are irrelevant to the modality of this one. |
| 11113 | Worlds don't explain necessity; we use necessity to decide on possible worlds [Jubien] |
| Full Idea: The suspicion is that the necessity doesn't arise from how worlds are, but rather that the worlds are taken to be as they are in order to capture the intuitive necessity. | |
| From: Michael Jubien (Analyzing Modality [2007], 1) | |
| A reaction: It has always seemed to me rather glaring that you need a prior notion of 'possible' before you can start to talk about 'possible worlds', but I have always been too timid to disagree with the combination of Saul Kripke and David Lewis. Thank you, Jubien! |
| 11110 | We mustn't confuse a similar person with the same person [Jubien] |
| Full Idea: If someone similar to Humphrey won the election, that nicely establishes the possibility of someone's winning who is similar to Humphrey. But we mustn't confuse this possibility with the intuitively different possibility of Humphrey himself winning. | |
| From: Michael Jubien (Analyzing Modality [2007], 1) |
| 18791 | In 'situation semantics' our main concepts are abstracted from situations [Mares] |
| Full Idea: In 'situation semantics' individuals, properties, facts, and events are treated as abstractions from situations. | |
| From: Edwin D. Mares (Negation [2014], 6.1) | |
| A reaction: [Barwise and Perry 1983 are cited] Since I take the process of abstraction to be basic to thought, I am delighted to learn that someone has developed a formal theory based on it. I am immediately sympathetic to situation semantics. |
| 21997 | In Marxism the state will be superseded [Singer] |
| Full Idea: It is a famous Marxist doctrine that the state will be superseded. | |
| From: Peter Singer (Marx [1980], 9) | |
| A reaction: Why is that final state communism rather than anarchism? |
| 21993 | Materialist history says we are subject to incomprehensible forces [Singer] |
| Full Idea: The materialist conception of history tells us that human beings are totally subject to forces they do not understand and control. | |
| From: Peter Singer (Marx [1980], 6) | |
| A reaction: How does Marx know the forces? An exceptionally influential idea, because it is a modern commonplace that we have very little control over our own lives (apart from right wingers asserting that 'you can have anything if you really really want it'). |