17263
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Why do rationalists accept Sufficient Reason, when it denies the existence of fundamental facts? [Correia/Schnieder]
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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.
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From:
Correia,F/Schnieder,B (Grounding: an opinionated introduction [2012], 2.2)
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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!
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9469
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Substitutional existential quantifier may explain the existence of linguistic entities [Parsons,C]
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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.
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From:
Charles Parsons (A Plea for Substitutional Quantification [1971], p.156)
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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.
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17447
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Parsons says counting is tagging as first, second, third..., and converting the last to a cardinal [Parsons,C, by Heck]
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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.
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From:
report of Charles Parsons (Frege's Theory of Numbers [1965]) by Richard G. Heck - Cardinality, Counting and Equinumerosity 3
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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'.
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17270
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Is existential dependence by grounding, or do grounding claims arise from existential dependence? [Correia/Schnieder]
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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.
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From:
Correia,F/Schnieder,B (Grounding: an opinionated introduction [2012], 4.3)
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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).
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17267
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The identity of two facts may depend on how 'fine-grained' we think facts are [Correia/Schnieder]
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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.
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From:
Correia,F/Schnieder,B (Grounding: an opinionated introduction [2012], 3.3)
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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.
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13417
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If a mathematical structure is rejected from a physical theory, it retains its mathematical status [Parsons,C]
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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.
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From:
Charles Parsons (Review of Tait 'Provenance of Pure Reason' [2009], §2)
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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.
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