17713 | After 1903, Husserl avoids metaphysical commitments |
Full Idea: In Husserl's philosophy after 1903, he is unwilling to commit himself to any specific metaphysical views. | |
From: Edwin D. Mares (A Priori [2011], 08.2) |
18781 | Inconsistency doesn't prevent us reasoning about some system |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
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) |
17715 | The truth of the axioms doesn't matter for pure mathematics, but it does for applied |
Full Idea: The epistemological burden of showing that the axioms are true is removed if we are only studying pure mathematics. If, however, we want to look at applied mathematics, then this burden returns. | |
From: Edwin D. Mares (A Priori [2011], 11.4) | |
A reaction: One of those really simple ideas that hits the spot. Nice. The most advanced applied mathematics must rest on counting and measuring. |
17716 | Mathematics is relations between properties we abstract from experience |
Full Idea: Aristotelians treat mathematical facts as relations between properties. These properties, moreover, are abstracted from our experience of things. ...This view finds a natural companion in structuralism. | |
From: Edwin D. Mares (A Priori [2011], 11.7) | |
A reaction: This is the view of mathematics that I personally favour. The view that we abstract 'five' from a group of five pebbles is too simplistic, but this is the right general approach. |
18788 | For intuitionists there are not numbers and sets, but processes of counting and collecting |
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. |
17703 | Light in straight lines is contingent a priori; stipulated as straight, because they happen to be so |
Full Idea: It seems natural to claim that light rays moving in straight lines is contingent but a priori. Scientists stipulate that they are the standard by which we measure straightness, but their appropriateness for this task is a contingent feature of the world. | |
From: Edwin D. Mares (A Priori [2011], 02.9) | |
A reaction: This resembles the metre rule in Paris. It is contingent that something is a certain way, so we make being that way a conventional truth, which can therefore be known via the convention, rather than via the contingent fact. |
17714 | Aristotelians dislike the idea of a priori judgements from pure reason |
Full Idea: Aristotelians tend to eschew talk about a special faculty of pure reason that is responsible for all of our a priori judgements. | |
From: Edwin D. Mares (A Priori [2011], 08.9) | |
A reaction: He is invoking Carrie Jenkins's idea that the a priori is knowledge of relations between concepts which have been derived from experience. Nice idea. We thus have an empirical a priori, integrated into the natural world. Abstraction must be involved. |
17705 | Empiricists say rationalists mistake imaginative powers for modal insights |
Full Idea: Empiricist critiques of rationalism often accuse rationalists of confusing the limits of their imaginations with real insight into what is necessarily true. | |
From: Edwin D. Mares (A Priori [2011], 03.01) | |
A reaction: See ideas on 'Conceivable as possible' for more on this. You shouldn't just claim to 'see' that something is true, but be willing to offer some sort of reason, truthmaker or grounding. Without that, you may be right, but you are on weak ground. |
17700 | The most popular view is that coherent beliefs explain one another |
Full Idea: In what is perhaps the most popular version of coherentism, a system of beliefs is a set of beliefs that explain one another. | |
From: Edwin D. Mares (A Priori [2011], 01.5) | |
A reaction: These seems too simple. My first response would be that explanations are what result from coherence sets of beliefs. I may have beliefs that explain nothing, but at least have the virtue of being coherent. |
17704 | Operationalism defines concepts by our ways of measuring them |
Full Idea: The central claim of Percy Bridgman's theory of operational definitions (1920s), is that definitions of certain scientific concepts are given by the ways that we have to measure them. For example, a straight line is 'the path of a light ray'. | |
From: Edwin D. Mares (A Priori [2011], 02.9) | |
A reaction: It is often observed that this captures the spirit of Special Relativity. |
17710 | Aristotelian justification uses concepts abstracted from experience |
Full Idea: Aristotelian justification is the process of reasoning using concepts that are abstracted from experience (rather than, say, concepts that are innate or those that we associate with the meanings of words). | |
From: Edwin D. Mares (A Priori [2011], 08.1) | |
A reaction: See Carrie Jenkins for a full theory along these lines (though she doesn't mention Aristotle). This is definitely my preferred view of concepts. |
17706 | The essence of a concept is either its definition or its conceptual relations? |
Full Idea: In the 'classical theory' a concept includes in it those concepts that define it. ...In the 'theory theory' view the content of a concept is determined by its relationship to other concepts. | |
From: Edwin D. Mares (A Priori [2011], 03.10) | |
A reaction: Neither of these seem to give an intrinsic account of a concept, or any account of how the whole business gets off the ground. |
18791 | In 'situation semantics' our main concepts are abstracted from situations |
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. |
17701 | Possible worlds semantics has a nice compositional account of modal statements |
Full Idea: Possible worlds semantics is appealing because it gives a compositional analysis of the truth conditions of statements about necessity and possibility. | |
From: Edwin D. Mares (A Priori [2011], 02.2) | |
A reaction: Not sure I get this. Is the meaning composed by the gradual addition of worlds? If not, how is meaning composed in the normal way, from component words and phrases? |
17702 | Unstructured propositions are sets of possible worlds; structured ones have components |
Full Idea: An unstructured proposition is a set of possible worlds. ....Structured propositions contain entities that correspond to various parts of the sentences or thoughts that express them. | |
From: Edwin D. Mares (A Priori [2011], 02.3) | |
A reaction: I am definitely in favour of structured propositions. It strikes me as so obvious as to be not worth discussion - so I am obviously missing something here. Mares says structured propositions are 'more convenient'. |
17708 | Maybe space has points, but processes always need regions with a size |
Full Idea: One theory is that space is made up of dimensionless points, but physical processes cannot take place in regions of less than a certain size. | |
From: Edwin D. Mares (A Priori [2011], 06.7) | |
A reaction: Thinkers in sympathy with verificationism presumably won't like this, and may prefer Feynman's view. |