Structuralism

Structuralism-

 

The idea behind the structuralist view of mathematical objects is that such

objects have no more of a 'nature' than is given by the basic relations of a

structure to which they belong. A natural implication of this might be that

they have no properties beyond what would be definable from the basic

relations of the structure by some appropriate logical means. Although that

inference has been drawn, it is pretty obviously incorrect; for example,

mathematical objects have what I call 'external relations' arising from their

application, such as those arising from a one-to-one correspondence between the numbers from I to 9 and the planets.

 

Charles Parsons, Structuralism and Metaphysics

 

Parsons is concluding that the application of structuralism in mathematics is futile since the basic relations of numbers and formulas cannot be compared really to other basic relations of themselves. However, at times it does seem possible to promote the use of structuralism within the confines of mathematics because everything is relative when it comes to numbers. In proven ways, multiplication is relative to division, addition is relative to subtractions, squares is relative to rectangles, and so on. But if you break down mathematics you will only get to the prime and nothing else, according to Parsons.

 

This picture depicts two sumo wrestlers. This is a product of structuralism by the contrast of each sumo wrestler. We have a kid sumo versus the prime adult sumo. We know, from the slight smile on his face that he will not hurt the kid, knowing that he is not a competition to him. With structualist, they will say the joke of the picture will not be so funny if we couldn't deconstruct each sumo for who they are.

Done