23 ideas
| 17713 | After 1903, Husserl avoids metaphysical commitments [Mares] |
| 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) |
| 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. |
| 17715 | The truth of the axioms doesn't matter for pure mathematics, but it does for applied [Mares] |
| 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 [Mares] |
| 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. |
| 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. |
| 17703 | Light in straight lines is contingent a priori; stipulated as straight, because they happen to be so [Mares] |
| 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. |
| 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. |
| 17714 | Aristotelians dislike the idea of a priori judgements from pure reason [Mares] |
| 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 [Mares] |
| 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 [Mares] |
| 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. |
| 2975 | That honey is sweet I do not affirm, but I agree that it appears so [Timon] |
| Full Idea: That honey is sweet I do not affirm, but I agree that it appears so. | |
| From: Timon (On Sensations (frags) [c.285 BCE]), quoted by Diogenes Laertius - Lives of Eminent Philosophers 09.104-5 |
| 17704 | Operationalism defines concepts by our ways of measuring them [Mares] |
| 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 [Mares] |
| 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? [Mares] |
| 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. |
| 17701 | Possible worlds semantics has a nice compositional account of modal statements [Mares] |
| 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 [Mares] |
| 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 [Mares] |
| 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. |