15 ideas
| 17266 | Using modal logic, philosophers tried to handle all metaphysics in modal terms [Correia/Schnieder] |
| Full Idea: In the heyday of modal logic, philosophers typically tried to account for any metaphysical notions in modal terms. | |
| From: Correia,F/Schnieder,B (Grounding: an opinionated introduction [2012], 2.4) | |
| A reaction: Lewisian realism about possible worlds actually gets rid of purely 'modal' terms, but I suppose they include possible worlds in their remark. Annoying for modal logicians to be told they had a 'heyday' - a nice example of the rhetoric of philosophy. |
| 17263 | Why do rationalists accept Sufficient Reason, when it denies the existence of fundamental facts? [Correia/Schnieder] |
| Full Idea: What is most puzzling about the rationalist tradition is the steadfast certainty with which the Principle of Sufficient Reason was often accepted, since it in effect denies that there are fundamental facts. | |
| From: Correia,F/Schnieder,B (Grounding: an opinionated introduction [2012], 2.2) | |
| A reaction: A very simple and interesting observation. The principle implies either a circle of reasons, or an infinite regress of reasons. Nothing can be labelled as 'primitive' or 'foundational' or 'given'. The principle is irrational! |
| 9470 | Modal logic is not an extensional language [Parsons,C] |
| Full Idea: Modal logic is not an extensional language. | |
| From: Charles Parsons (A Plea for Substitutional Quantification [1971], p.159 n8) | |
| A reaction: [I record this for investigation. Possible worlds seem to contain objects] |
| 13418 | The old problems with the axiom of choice are probably better ascribed to the law of excluded middle [Parsons,C] |
| Full Idea: The difficulties historically attributed to the axiom of choice are probably better ascribed to the law of excluded middle. | |
| From: Charles Parsons (Review of Tait 'Provenance of Pure Reason' [2009], §2) | |
| A reaction: The law of excluded middle was a target for the intuitionists, so presumably the debate went off in that direction. |
| 9469 | Substitutional existential quantifier may explain the existence of linguistic entities [Parsons,C] |
| Full Idea: I argue (against Quine) that the existential quantifier substitutionally interpreted has a genuine claim to express a concept of existence, which may give the best account of linguistic abstract entities such as propositions, attributes, and classes. | |
| From: Charles Parsons (A Plea for Substitutional Quantification [1971], p.156) | |
| A reaction: Intuitively I have my doubts about this, since the whole thing sounds like a verbal and conventional game, rather than anything with a proper ontology. Ruth Marcus and Quine disagree over this one. |
| 9468 | On the substitutional interpretation, '(∃x) Fx' is true iff a closed term 't' makes Ft true [Parsons,C] |
| Full Idea: For the substitutional interpretation of quantifiers, a sentence of the form '(∃x) Fx' is true iff there is some closed term 't' of the language such that 'Ft' is true. For the objectual interpretation some object x must exist such that Fx is true. | |
| From: Charles Parsons (A Plea for Substitutional Quantification [1971], p.156) | |
| A reaction: How could you decide if it was true for 't' if you didn't know what object 't' referred to? |
| 17447 | Parsons says counting is tagging as first, second, third..., and converting the last to a cardinal [Parsons,C, by Heck] |
| Full Idea: In Parsons's demonstrative model of counting, '1' means the first, and counting says 'the first, the second, the third', where one is supposed to 'tag' each object exactly once, and report how many by converting the last ordinal into a cardinal. | |
| From: report of Charles Parsons (Frege's Theory of Numbers [1965]) by Richard G. Heck - Cardinality, Counting and Equinumerosity 3 | |
| A reaction: This sounds good. Counting seems to rely on that fact that numbers can be both ordinals and cardinals. You don't 'convert' at the end, though, because all the way you mean 'this cardinality in this order'. |
| 18201 | General principles can be obvious in mathematics, but bold speculations in empirical science [Parsons,C] |
| Full Idea: The existence of very general principles in mathematics are universally regarded as obvious, where on an empiricist view one would expect them to be bold hypotheses, about which a prudent scientist would maintain reserve. | |
| From: Charles Parsons (Mathematical Intuition [1980], p.152), quoted by Penelope Maddy - Naturalism in Mathematics | |
| A reaction: This is mainly aimed at Quine's and Putnam's indispensability (to science) argument about mathematics. |
| 13419 | If functions are transfinite objects, finitists can have no conception of them [Parsons,C] |
| Full Idea: The finitist may have no conception of function, because functions are transfinite objects. | |
| From: Charles Parsons (Review of Tait 'Provenance of Pure Reason' [2009], §4) | |
| A reaction: He is offering a view of Tait's. Above my pay scale, but it sounds like a powerful objection to the finitist view. Maybe there is a finitist account of functions that could be given? |
| 17270 | Is existential dependence by grounding, or do grounding claims arise from existential dependence? [Correia/Schnieder] |
| Full Idea: We may take existential dependence to be a relation induced by certain cases of grounding, but one may also think that facts about existential dependence are prior to corresponding ground claims, and in fact ground those claims. | |
| From: Correia,F/Schnieder,B (Grounding: an opinionated introduction [2012], 4.3) | |
| A reaction: I would vote for grounding, since dependence seems more abstract, and seems to demand explanation, whereas grounding seems more like a feature of reality, and to resist further intrinsic explanation (on the whole). |
| 17268 | Grounding is metaphysical and explanation epistemic, so keep them apart [Correia/Schnieder] |
| Full Idea: To us it seems advisable to separate the objective notion of grounding, which belongs to the field of metaphysics, from the epistemically loaded notion of explanation. | |
| From: Correia,F/Schnieder,B (Grounding: an opinionated introduction [2012], 4.2) | |
| A reaction: Paul Audi is the defender of the opposite view. I'm with Audi. The 'epistemically loaded' pragmatic aspect is just contextual - that we have different interests in different aspects of the grounding on different occasions. |
| 17267 | The identity of two facts may depend on how 'fine-grained' we think facts are [Correia/Schnieder] |
| Full Idea: There is a disagreement on the issue of factual identity, concerning the 'granularity' of facts, the question of how fine-grained they are. | |
| From: Correia,F/Schnieder,B (Grounding: an opinionated introduction [2012], 3.3) | |
| A reaction: If they are very fine-grained, then no two descriptions of a supposed fact will capture the same details. If we go broadbrush, facts become fuzzy and less helpful. 'Fact' was never going to be a clear term. |
| 13417 | If a mathematical structure is rejected from a physical theory, it retains its mathematical status [Parsons,C] |
| Full Idea: If experience shows that some aspect of the physical world fails to instantiate a certain mathematical structure, one will modify the theory by sustituting a different structure, while the original structure doesn't lose its status as part of mathematics. | |
| From: Charles Parsons (Review of Tait 'Provenance of Pure Reason' [2009], §2) | |
| A reaction: This seems to be a beautifully simple and powerful objection to the Quinean idea that mathematics somehow only gets its authority from physics. It looked like a daft view to begin with, of course. |
| 20921 | How can we state relativism of sweet and sour, if they have no determinate nature? [Theophrastus] |
| Full Idea: How could what is bitter for us be sweet and sour for others, if there is not some determinate nature for them? | |
| From: Theophrastus (On the Senses [c.321 BCE], 70) | |
| A reaction: The remark is aimed at Democritus. This is part of the general question of how you can even talk about relativism, without attaching stable meanings to the concepts employed. |
| 5990 | Theophrastus doubted whether nature could be explained teleologically [Theophrastus, by Gottschalk] |
| Full Idea: Theophrastus questioned Aristotle's teaching on the extent to which teleological explanations could be applied to the natural world. | |
| From: report of Theophrastus (On Metaphysics (frags) [c.320 BCE]) by H.B. Gottschalk - Aristotelianism | |
| A reaction: It is interesting to see that Aristotle's own immediate successor had doubts about teleology. We usually assume that the ancients were teleological, and this was rejected in the seventeenth century (e.g. Idea 4826). |