## Labels

### Some polygon is triangular

In  yesterday's post Bill Vallicella reiterates his insistence that though they are logically equivalent there is nevertheless a semantic distinction between 'Some cat is fat' and 'A fat cat exists'.   Clearly expecting the answer No he asks the rhetorical question Does 'Some unicorn is angry' require by its very sense that an angry unicorn exists?  Since for me the answer is an immediate and obvious Yes I have been racking my brains trying to understand how we can possibly differ on this.  Here is what I have come up with.

Let me change our example.  Suppose the possible worlds are sheets of paper on which are drawn polygons (or should that be polylaterals?)  So the only objects are triangles, quadrilaterals, pentagons, etc, of various sizes and orientations.  Consider a particular sheet.  If it's true to say (of this sheet) 'A triangular polygon exists' then it's true to say (again of this sheet) 'Some polygon is triangular'.  Conversely, if it's true (of this sheet) that some polygon is triangular then it's true (of the sheet) that a triangular polygon exists.  This shows the logical equivalence of  'A triangular polygon exists' and 'Some polygon is triangular'.  Logical equivalence is an extensional notion.  Our sentences have to agree in truth value on every possible sheet.  Indeed, the only way to assign a truth value to 'A triangular polygon exists' is by reference to a particular sheet.  In contrast, there does seem to be a reading of 'Some polygon is triangular' that makes it a conceptual truth, independent of any possible world.  We have to see it as saying that the concept Polygon is compatible with the concept Triangle.  By this I mean that there is nothing in the two concepts that rules out an object falling under both.  Or, modally, it is possible that an object be both a polygon and a triangle.  Or, in medieval spirit, 'Some Polygon is Triangle'.  So, although we might see 'Some polygon is triangular' as conceptually true it doesn't follow that in any given world that there exists a triangular polygon.  And this, I suggest, is the source of the asymmetry between our some-sentence and our exists-sentence that Bill notes here.

We can also give a non-extensional, non-quantificational reading to 'all'.  'All Triangle is Polygon' says that the concept Triangle is subordinate to the concept Polygon.