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Reading about the paradox of analysis here:

https://en.wikipedia.org/wiki/Paradox_of_analysis

Instead of the brother=male sibling example given in the article, suppose we use "triangle" instead. So 3 ways I can refer to a triangle are:

  1. triangle
  2. A polygon that has 3 sides
  3. A polygon that has 3 angles

So the paradox the way I understand it is... if these 3 denote the same concept... then it is vacuous to say that a triangle is a polygon with 3 sides or a polygon with 3 angles.

Why can't we simply say... our minds can apprehend the same object (in this case triangle) in multiple ways. So there isn't a one-correct way to "apprehend" a triangle. There are multiple ways... yet they point to the same entity a triangle. Even different people may apprehend the same word differently... ie: what exactly comes to mind when someone uses the word 'polygon'. It may different student to student.

So our minds don't necessarily grasp entities like triangles "directly". There are different configurations of concepts that happen to point to the same object... but it isn't immediately obvious to our minds that they point to the same object.

So "3-sided polygon" and "3-angled polygon" are different in the sense that they are different ways for a mind to apprehend an object... which only upon further reflection we see to be the same.

Ameet Sharma
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  • This is exactly Frege's distinction between [Sinn und Bedeutung](https://en.wikipedia.org/wiki/Sense_and_reference) – Mauro ALLEGRANZA May 10 '20 at 14:18
  • Yes. But I assume Frege's distinction isn't commonly taken as a solution to the paradox? – Ameet Sharma May 10 '20 at 14:45
  • Frege's classical example was the evening star and the morning star as two different ways to "apprehend" Venus. Yet they are not interchangeable without shift of meaning in "The evening star is the morning star". Same with "polygon with 3 sides is polygon with 3 angles". This generally happens with substitution into [intensional contexts](https://en.wikipedia.org/wiki/Extensional_context). So this is not a solution because the intersubstitutivity fails, hence they are different concepts. Indeed, it is the first non-solution discussed under your Wikipedia link. – Conifold May 10 '20 at 14:48
  • What about the example given in the article... "brother" and "male sibling"... are those different concepts? – Ameet Sharma May 10 '20 at 14:56
  • Either that or "brother = male sibling" is a mere linguistic stipulation with no conceptual import. That is the dilemma of analysis, and both horns are unattractive. – Conifold May 10 '20 at 15:06
  • But what I'm getting at is... when I think of the word "brother"... I do have some kind of single concept in mind... when I think of the words "male sibling"... I apprehend this as two concepts... concept of male and concept of sibling. I'm not even sure concept is the right word here. There are 2 different psychological processes... yet they apprehend the same object, but it is not immediately obvious that they point to the same object. Similarly, one may apprehend "triangle" as a single unified idea... someone else may apprehend it as "a polygon, that happens to have 3 sides". – Ameet Sharma May 10 '20 at 15:20
  • So we can have 2 different psychological processes leading to apprehending the same object. – Ameet Sharma May 10 '20 at 15:22
  • In other words, you are picking the first horn. They *are* different concepts (with the same extension = object = referent), and we only get an extensional analysis, not a conceptual one. Alternatively, if you believe in the analytic/synthetic distinction, you can relax the intersubstitutivity condition and call Y a conceptual analysis of X if X=Y is analytic. This is just the Quine's problem of defining analyticity in a different guise. – Conifold May 10 '20 at 16:06
  • Let us [continue this discussion in chat](https://chat.stackexchange.com/rooms/107838/discussion-between-ameet-sharma-and-conifold). – Ameet Sharma May 10 '20 at 16:33

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