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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.
| 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] |
| 8879 | Fully comprehensive beliefs may not be knowledge [Sosa] |
| 8878 | It is acceptable to say a supermarket door 'knows' someone is approaching [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] |