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How to analyse the fact that , at the same time, my 7 y. old nephew

(1) knows that : 1+1 =2

(2) does not know that : sqrt (1) + 1² = the absolute value of the cube root of -8. ?

Certainly, "intensionality" plays a role here. Extensionnally, the two propositions ( the one that my nephew knows and the one the he doesn't know) are identical ( they have the same denotation or reference) ; however they differ as to "intension" ( they do not have the same concepts as constituents, they do not expresss the same thought).

My question is: is the phenomenon specific to cases similar to the example I've just given , or does intensionality always play a role in knowledge? does the usual analysis of knowledge as a binary relation between a subject and a proposition take into account the ( possible) role of intensionality? are there authors who have made significant attempts to include intensionality in their analysis of knowldge, defining it, mayby, as a ternary relation ( knower, extension , intension).

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    Despite common etymology, intensionality and intentionality are two different things. Intensionality is a semantic property modeled in logic by modal operators, such as those that express propositional attitudes: "knows that", "believes that", etc., see SEP Intensional logic and epistemic logic. It is part of the standard analysis of knowledge. Intentionality is something else from philosophy of mind.
    – Conifold
    Mar 30 '19 at 21:26
  • @Conifold - Thanks for the links to these SEP papers. Is there any epistemology handbookbook that could offer an elementary introduction to the use of " intensionality" in the analysis of the "knowledge" concept. ( I have a copy of Dancy's Contemp Intro To Epist.) and I can't even find " intensionality" in the index).
    – user37859
    Mar 30 '19 at 21:57
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    Here is a paper on Husserl and these subjects IEP. iep.utm.edu/huss-int I have not read it but it may help you.
    – Gordon
    Mar 30 '19 at 22:14
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    The term is not favored, perhaps in part, due to Quine's contempt for "intensionality" and "meaning" as loose blobs. Look at SEP's epistemic logic article, it is full of the modal B- and K-operators, but does not mention "intensionality" even once. Same with propositional attitudes, which at least references Forbes's article titled Intensionality. What you want is called formal epistemology, but look for different keywords.
    – Conifold
    Mar 30 '19 at 22:19

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