Mathematician Reuben hersh makes the following interesting claim:
>>Study of the lawful, predictable parts of the physical world has a name: “physics.” Study of the lawful, predictable, parts of the social-conceptual world also has a name: “mathematics.” A world of ideas exists, created by human beings, existing in their shared consciousness. These ideas have objective properties, in the same sense that material objects have objective properties.<<<
Do mathematical objects really have objective properties?
Certainly, if you are a supporter of Platonism - which Hersh explicitly rejects. For him mathematics is situated in the "social-cultural-historical" sphere. Humans did not discover the properties of, say, circles and the numeber Pi, but they created it.
Hersh likenes mathematical objects to institutions like the Supreme Court, but in this case I'd call its properties not 'objective' but 'intersubjective'' or 'social'.
What do you think?
3
Enjoy being online again!
Welcome to the community of good people who base their values on evidence and appreciate civil discourse - the social network you will enjoy.Create your free account
5 comments
Feel free to reply to any comment by clicking the "Reply" button.It's the same old runaround with Plato's forms, Hume's empiricism, Leibnitz's rationalism and Kant's combination of the two. Kant puts maths in the (synthetic) a priori department. I'm not so sure. I think nature's forms might easily have suggested more deliberate shapes to a person. As for culture and its institutions, I think they developed from mythos as a growing rationalisation took precedence over individuality.
brentan
Level 8
Oct 29, 2019
2
The social conceptual world is studied by sociology and psychology not mathematics.. And the the properties of the circle and pi weren't created, they were discovered...
Cutiebeauty
Level 9
Oct 29, 2019
2
Totally with you on that. There is also the existence of Platonic solids in crystalline structures, although I’m not to sure if the dodecahedron fits that model
“Although Dirac apparently showed his usual Trappist calm, he was jubilant. In a few squiggles of his pen, he had described the behaviour of every single electron that had ever existed in the universe.
"The equation was ‘achingly beautiful’, as theoretical physicist Frank Wilczek later described it: like Einstein’s equations of general relativity, the Dirac equation was universal yet fundamentally simple; nothing in it could be changed without destroying its power.” — Graham Farmelo, “The Strangest Man - The Hidden Life of Paul Dirac, Mystic of the Atom,” 2009
Daco2007
Level 7
Oct 29, 2019
0
“Paul Dirac told physics students they should not worry about the meaning of equations, only about their beauty. This advice was good only for physicists whose sense of purely mathematical beauty is so keen that they can rely on it to see the way ahead. There have not been many such physicists - perhaps only Dirac himself.”
-- STEVEN WEINBERG, Dirac Centenary Meeting, University of Bristol, 8 August 2002
Daco2007
Level 7
Oct 29, 2019
0
Recent Visitors 26
Photos
Posted by JettyPerspective
Posted by PontifexMarximusWhy Evolution Is True … I never realised that there was still so much opposition to science. [livescience.com]
Posted by NR92What is the reason to live? What are we living for?
Posted by NR92Is it correct that Nietzsche was Hitler's inspiration?
Posted by mzeeWhat is fear?
Posted by DonaldHRobertsThe Most Complicated question ever asked. WHY?
Posted by TheMiddleWayRussel, the greatest salesman the world has ever known!