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Single Idea 8884

[filed under theme 6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism ]

Full Idea

You could detect the absence of an eleven-dot pattern without having counted the dots, so your phenomenal concept of that array is not an arithmetical concept, and its content will not yield that its dots do indeed number eleven.

Gist of Idea

The phenomenal concept of an eleven-dot pattern does not include the concept of eleven

Source

Ernest Sosa (Beyond internal Foundations to external Virtues [2003], 7.3)

Book Ref

Bonjour,L/Sosa,E: 'Epistemic Justification' [Blackwells 2003], p.128

A Reaction

Sosa is discussing foundational epistemology, but this draws attention to the gulf that has to be leaped by structuralists. If eleven is not derived from the pattern, where does it come from? Presumably two eleven-dotters are needed, to map them.

The 20 ideas from Ernest Sosa

8876 Much propositional knowledge cannot be formulated, as in recognising a face [Sosa]
8877 We can't attain a coherent system by lopping off any beliefs that won't fit [Sosa]
8878 It is acceptable to say a supermarket door 'knows' someone is approaching [Sosa]
8879 Fully comprehensive beliefs may not be knowledge [Sosa]
8880 In reducing arithmetic to self-evident logic, logicism is in sympathy with rationalism [Sosa]
8881 Most of our knowledge has insufficient sensory support [Sosa]
8882 Perception may involve thin indexical concepts, or thicker perceptual concepts [Sosa]
8883 Do beliefs only become foundationally justified if we fully attend to features of our experience? [Sosa]
8884 The phenomenal concept of an eleven-dot pattern does not include the concept of eleven [Sosa]
8885 Some features of a thought are known directly, but others must be inferred [Sosa]
8798 Vision causes and justifies beliefs; but to some extent the cause is the justification [Sosa]
8799 If mental states are not propositional, they are logically dumb, and cannot be foundations [Sosa]
8794 There are very few really obvious truths, and not much can be proved from them [Sosa]
8795 Mental states cannot be foundational if they are not immune to error [Sosa]
8796 A single belief can trail two regresses, one terminating and one not [Sosa]
8797 The negation of all my beliefs about my current headache would be fully coherent [Sosa]
8442 What law would explain causation in the case of causing a table to come into existence? [Sosa]
8443 Mereological essentialism says an entity must have exactly those parts [Sosa]
8444 Where is the necessary causation in the three people being tall making everybody tall? [Sosa]
8445 The necessitated is not always a result or consequence of the necessitator [Sosa]