Ideas from 'A Priori' by Edwin D. Mares [2011], by Theme Structure

[found in 'A Priori' by Mares,Edwin [Acumen 2011,978-1-84465-285-3]].

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1. Philosophy / E. Nature of Metaphysics / 7. Against Metaphysics
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)
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / a. Axioms for numbers
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.
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / a. Mathematical empiricism
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.
10. Modality / D. Knowledge of Modality / 2. A Priori Contingent
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.
12. Knowledge Sources / A. A Priori Knowledge / 6. A Priori from Reason
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.
12. Knowledge Sources / C. Rationalism / 1. Rationalism
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.
13. Knowledge Criteria / B. Internal Justification / 5. Coherentism / a. Coherence as justification
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.
14. Science / B. Scientific Theories / 3. Instrumentalism
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.
18. Thought / D. Concepts / 2. Origin of Concepts / b. Empirical concepts
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.
18. Thought / D. Concepts / 4. Structure of Concepts / c. Classical concepts
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.
19. Language / C. Assigning Meanings / 8. Possible Worlds Semantics
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?
19. Language / D. Propositions / 3. Concrete Propositions
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'.
27. Natural Reality / C. Space / 3. Points in Space
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.