Can you just assume a situation with no figures or data to back it ? Is it reasonable?
#Logic #mathematics #data
Dear Kwadwo Boakye
If I remember well, people who are born blind create some kind of geometrical concept of reality although they can only hear and touch everything direct or/and indirect. I suppose they will not do it if it is really simple to imagine reality without any geometrical “metric”.
In physics we have hypotheses that propose multi-dimensional space (> 3D, like String theory) and even a whole universe that is created out of a singularity (Standard cosmological model). These hypotheses exist for decades but there is no reason to conclude that physicists can handle data without some geometry in an easy way. It seems to be the opposite: without “tangible” relations we can hardly create useful and permanent concepts.
With kind regards, Sydney
Then what is available (no figures, no data) for credible consideration. Well, higher level of abstraction.
Kwadwo Boakye RE: "Can you just assume a situation with no figures or data to back it ? Is it reasonable?"
Yes to both questions. If you are giving a reductio ad absurdum argument, your assumption is formulated solely for the purpose of showing that it is untenable because it entails a logical contradiction or absurdity.
A reductio ad absurdum argument that the square root of two is not rational has been attributed to Aristotle.
Dear Kwadwo Boakye
An interesting answer can be found in Kant's philosophy.
See the article:
https://www.jstor.org/stable/27902038
Regards
One of my PhD students took an exams in philosophy of mathematics. The problem concerned chaotic behavior. The question is, what if he were asked the question as above?
To prove that, for example, a function in R is convex, you can use convexity arguments, based on its graph; if the function is twice differentiable, you have a test based on second derivatives; in R^n it is more work, but the principle is the same, based on the Hessian.
The main concepts of topology and algebra are defined without the need for figures.
Of course. Math is not (natural) science. https://blogs.ams.org/phdplus/2017/04/17/math-is-like-science-only-proof-y/
Figures and graphs are for two or three dimensions. There are more than three dimensions in mathematics. It might hep to visualize things in three dimensions, but when you have more than three dimensions, you just rely on equations.
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