19 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) |
| 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. |
| 10580 | Mathematics is both necessary and a priori because it really consists of logical truths [Yablo] |
| Full Idea: Mathematics seems necessary because the real contents of mathematical statements are logical truths, which are necessary, and it seems a priori because logical truths really are a priori. | |
| From: Stephen Yablo (Abstract Objects: a Case Study [2002], 10) | |
| A reaction: Yablo says his logicism has a Kantian strain, because numbers and sets 'inscribed on our spectacles', but he takes a different view (in the present Idea) from Kant about where the necessity resides. Personally I am tempted by an a posteriori necessity. |
| 10579 | Putting numbers in quantifiable position (rather than many quantifiers) makes expression easier [Yablo] |
| Full Idea: Saying 'the number of Fs is 5', instead of using five quantifiers, puts the numeral in quantifiable position, which brings expressive advantages. 'There are more sheep in the field than cows' is an infinite disjunction, expressible in finite compass. | |
| From: Stephen Yablo (Abstract Objects: a Case Study [2002], 08) | |
| A reaction: See Hofweber with similar thoughts. This idea I take to be a key one in explaining many metaphysical confusions. The human mind just has a strong tendency to objectify properties, relations, qualities, categories etc. - for expression and for reasoning. |
| 10577 | Concrete objects have few essential properties, but properties of abstractions are mostly essential [Yablo] |
| Full Idea: Objects like me have a few essential properties, and numerous accidental ones. Abstract objects are a different story. The intrinsic properties of the empty set are mostly essential. The relations of numbers are also mostly essential. | |
| From: Stephen Yablo (Abstract Objects: a Case Study [2002], 01) |
| 10578 | We are thought to know concreta a posteriori, and many abstracta a priori [Yablo] |
| Full Idea: Our knowledge of concreta is a posteriori, but our knowledge of numbers, at least, has often been considered a priori. | |
| From: Stephen Yablo (Abstract Objects: a Case Study [2002], 02) |
| 14286 | In nearby worlds where A is true, 'if A,B' is true or false if B is true or false [Stalnaker] |
| Full Idea: Consider a possible world in which A is true and otherwise differs minimally from the actual world. 'If A, then B' is true (false) just in case B is true (false) in that possible world. | |
| From: Robert C. Stalnaker (A Theory of Conditionals [1968], p.34), quoted by Dorothy Edgington - Conditionals (Stanf) 4.1 | |
| A reaction: This is the first proposal to give a possible worlds semantics for conditional statements. Edgington observes that worlds which are nearby for me may not be nearby for you. |
| 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. |
| 14285 | A possible world is the ontological analogue of hypothetical beliefs [Stalnaker] |
| Full Idea: A possible world is the ontological analogue of a stock of hypothetical beliefs. | |
| From: Robert C. Stalnaker (A Theory of Conditionals [1968], p.34), quoted by Dorothy Edgington - Conditionals (Stanf) 4.1 | |
| A reaction: Sounds neat and persuasive. What is the ontological analogue of a stock of hopes? Heaven! |
| 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. |
| 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. |