24 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. |
| 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) |
| 13931 | By using aporiai as his start, Aristotle can defer to the wise, as well as to the many [Haslanger] |
| Full Idea: The Aristotelian method of working form aporia allows one to use as starting points not only what is said by 'the many', but also what is said by 'the wise', including philosophers. | |
| From: Sally Haslanger (Persistence, Change and Explanation [1989], 1 n2) | |
| A reaction: [She mentions Nussbaum 1986:ch 7 for the opposing view] I like this thought a lot. Aristotle's democratic respect for widespread views can be a bit puzzling sometimes. |
| 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. |
| 13925 | Ontology disputes rest on more basic explanation disputes [Haslanger] |
| Full Idea: Disputes over ontology derive from more fundamental disputes over forms of explanation. | |
| From: Sally Haslanger (Persistence, Change and Explanation [1989], 1) | |
| A reaction: It immediately strikes me that Haslanger has stolen my master idea, but unfortunately the dating suggests that she has priority. The tricky part is to combine this view with realism. |
| 13924 | The persistence of objects seems to be needed if the past is to explain the present [Haslanger] |
| Full Idea: The notion that things persist through change is deeply embedded in ideas we have about explanation, and in particular, in the idea that the present is constrained by the past. | |
| From: Sally Haslanger (Persistence, Change and Explanation [1989], 1) | |
| A reaction: I take this to be both an important and an attractive idea. Deniers of persistence (4D-ists) will presumably have some ability to explain the present, but it is the idea of the present being 'constrained' by the past which is a challenge. |
| 13930 | Persistence makes change and its products intelligible [Haslanger] |
| Full Idea: Persistence offers intelligibility: the possibility of understanding a change, and of understanding the products of it. | |
| From: Sally Haslanger (Persistence, Change and Explanation [1989], 8) | |
| A reaction: I think this is exactly right, and it is a powerful idea with wide implications for metaphysics. Haslanger claims that an understanding of 'substance' is needed, which leads towards my defence of essentialism. |
| 13927 | We must explain change amongst 'momentary entities', or else the world is inexplicable [Haslanger] |
| Full Idea: If the world of time-slices is to be explicable, then it must be possible to provide explanations of change understood as a continual generation and destruction of these 'momentary entities'. | |
| From: Sally Haslanger (Persistence, Change and Explanation [1989], 7) | |
| A reaction: While fans of time-slices can offer some sort of explanation, in the process of explaining a 'worm', there don't seem to be the sort of causal chains that we traditionally rely on. Maybe there are no explanations of anything? |
| 13928 | If the things which exist prior to now are totally distinct, they need not have existed [Haslanger] |
| Full Idea: How is the case in which A exists prior to B, but is distinct from B, different (especially from B's point of view) from the case in which nothing exists prior to B? | |
| From: Sally Haslanger (Persistence, Change and Explanation [1989], 7) | |
| A reaction: I sympathise with her view, but this isn't persuasive. For A substitute 'Sally's mother' and for B substitute 'Sally'. A 4D-ist could bite the bullet and say that, indeed, previous parts of my 'worm' need not have existed. |
| 13929 | Natural explanations give the causal interconnections [Haslanger] |
| Full Idea: Natural explanations work by showing the systematic causal interconnections between things. | |
| From: Sally Haslanger (Persistence, Change and Explanation [1989], 7) | |
| A reaction: On the whole I love this sort of idea, but I am wondering if this one prevents mathematical or logical explanations from being natural. |
| 13926 | Best explanations, especially natural ones, need grounding, notably by persistent objects [Haslanger] |
| Full Idea: I am not resting my ontology on a simple 'argument to the best explanation'. ..What I want to say is that there are general demands on a kind of explanation, in particular, natural explanation, which require that there are persisting things. | |
| From: Sally Haslanger (Persistence, Change and Explanation [1989], 5) | |
| A reaction: This is a really nice idea - that best explanation is not just about specific cases, but also about best foundations for explanations in general, which brings in our metaphysics. I defend the role of essences in these best explanations. |
| 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. |
| 1748 | Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius] |
| Full Idea: Archelaus was the first person to say that the universe is boundless. | |
| From: report of Archelaus (fragments/reports [c.450 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 02.Ar.3 |
| 5989 | Archelaus said life began in a primeval slime [Archelaus, by Schofield] |
| Full Idea: Archelaus wrote that life on Earth began in a primeval slime. | |
| From: report of Archelaus (fragments/reports [c.450 BCE]) by Malcolm Schofield - Archelaus | |
| A reaction: This sounds like a fairly clearcut assertion of the production of life by evolution. Darwin's contribution was to propose the mechanism for achieving it. We should honour the name of Archelaus for this idea. |