Brief Bullets reply to what Arne sent me: Math has a fatal flaw/certainty

 

This posting was updated for an academic article on academia.edu for October 22, 2023

Fatal flaw/certainty

Preface

In 2022, a friend sent me the link below:

https://www.youtube.com/watch?v=HeQX2HjkcNo

Cited from You Tube

‘Not everything that is true can be proven. This discovery transformed infinity, changed the course of a world war and led to the modern computer.’

Cited references from You Tube

References:

Dunham, W. (2013, July). A Note on the Origin of the Twin Prime Conjecture. In Notices of the International Congress of Chinese Mathematicians (Vol. 1, No. 1, pp. 63-65). International Press of Boston. — https://ve42.co/Dunham2013

Conway, J. (1970). The game of life. Scientific American, 223(4), 4. — https://ve42.co/Conway1970 Churchill, A., Biderman, S., Herrick, A. (2019). Magic: The Gathering is Turing Complete. ArXiv. — https://ve42.co/Churchill2019

Gaifman, H. (2006). Naming and Diagonalization, from Cantor to Godel to Kleene. Logic Journal of the IGPL, 14(5), 709-728. — https://ve42.co/Gaifman2006

Lénárt, I. (2010). Gauss, Bolyai, Lobachevsky–in General Education?(Hyperbolic Geometry as Part of the Mathematics Curriculum). In Proceedings of Bridges 2010: Mathematics, Music, Art, Architecture, Culture (pp. 223-230). Tessellations Publishing. — https://ve42.co/Lnrt2010

Attribution of Poincare’s quote, The Mathematical Intelligencer, vol. 13, no. 1, Winter 1991. — https://ve42.co/Poincare

Irvine, A. D., & Deutsch, H. (1995). Russell’s paradox. — https://ve42.co/Irvine1995

Gödel, K. (1992). On formally undecidable propositions of Principia Mathematica and related systems. Courier Corporation. — https://ve42.co/Godel1931

Russell, B., & Whitehead, A. (1973). Principia Mathematica [PM], vol I, 1910, vol. II, 1912, vol III, 1913, vol. I, 1925, vol II & III, 1927, Paperback Edition to* 56. Cambridge UP. — https://ve42.co/Russel1910

Gödel, K. (1986). Kurt Gödel: Collected Works: Volume I: Publications 1929-1936 (Vol. 1). Oxford University Press, USA. — https://ve42.co/Godel1986

Cubitt, T. S., Perez-Garcia, D., & Wolf, M. M. (2015). Undecidability of the spectral gap. Nature, 528(7581), 207-211. — https://ve42.co/Cubitt2015

(End) 

Fatal flaw/certainty

As a non-mathematician, I am not qualified to opine on the view that math has a fatal flaw. But, I can comment where academic disciplines, somewhat overlap. In the video, at approximately the eight second mark forward, the presenter mentions (paraphrased) that we never know everything with certainty. As mathematics is not my academic discipline, I accept what is stated, as a view within that academic discipline. Although I can reason that there is debate within that academic discipline and in all academic disciplines. My educational background in philosophy (philosophy of religion, in particular) and philosophical theology, has dealt with absolute certainty and reasonable certainty. 

Within my academic work, I have noted: I can have reasonable certainty that I exist, but not absolute 100% certainty. I will admit I had an adviser and professor at Trinity Western University that disagreed with my view on certainty. He stated that the gospel was 100% absolutely certain. But I held to and hold to, that only God has the ontological ability of absolute certainty. I have reasonable certainty in regard to the gospel as being true. During my MPhil/PhD theses work, when I had to study Kant and Wittgenstein, I further developed partly through the Cambridge Philosophy Dictionary, an understanding that there is humanly, no absolute, 100% certainty. Reasonable certainty is that internally and externally premises and conclusion (s) are consistent and not disproved by counter propositions and conclusions.

In regards to approximately the 35 second mark, forward in the video, I will reply that infinity in mathematics is not the same as infinity in theistic, philosophy of religion or philosophical theology. Within my PhD work, there were some identical terms I would define one way within philosophy and another way within social research methods/statistics. In other words terms can have different definitions in different academic disciplines. 

I hold to, within theistic, philosophy of religion, philosophical theology and theology, that God alone is the only infinite entity. God alone as an actual entity, is limitless, but not logically contradictory with attributes. I do understand that in mathematics and physics, infinity is defined differently, within a different context.  

https://study.com/academy/lesson/what-is-infinity-in-math.html 

Cited 

‘Infinity is not a number, it is not a place, and it is not something that is just really big. In this lesson, we will talk about what infinity really is!’  

Cited

‘What is Infinity? ''To infinity... and beyond!'' If you've ever seen Toy Story, you've probably heard this famous phrase said by Buzz Lightyear. Have you ever wondered what 'infinity' means? Is it a place? Is it a number? Well, in math, infinity is the idea that something has no endpoint and goes on forever. The symbol for infinity looks like a sideways 8’ 

https://brilliant.org/wiki/infinity/ 

Cited 

‘Infinity is the concept of an object that is larger than any number. When used in the context "...infinitely small," it can also describe an object that is smaller than any number. It is important to take special note that infinity is not a number; rather, it exists only as an abstract concept. Attempting to treat infinity as a number, without special care, can lead to a number of paradoxes.’  

(End) 

In mathematics and science, infinity is more so an abstract concept. Whereas within much of theistic, philosophy of religion and philosophical theology and biblical theology, God, the first cause, the uncaused caused, is considered an actual, infinite, eternal entity. Apart from more philosophical approaches, this is also revealed within Biblical scripture in what can be named biblical theology as opposed to philosophical theology. 

BLACKBURN, SIMON (1996) Oxford Dictionary of Philosophy, Oxford, Oxford University Press.  

BRYMAN, ALAN (2004) Social Research Methods, Oxford, Oxford University Press.  

DAVIES, BRIAN (1999) ‘Infinity’, in Alan Richardson and John Bowden (eds.), A New Dictionary of Christian Theology, Kent, SCM Press Ltd.  

ERICKSON, MILLARD (1994) Christian Theology, Grand Rapids, Baker Book House.  

KANT, IMMANUEL (1781)(1787)(1998) Critique of Pure Reason, Translated and edited by Paul Guyer and Allen W. Wood, Cambridge University Press, Cambridge.  

KANT, IMMANUEL (1781)(1787)(1929)(2006) Critique of Pure Reason, Translated by Norman Kemp Smith, London, Macmillan.  

KANT, IMMANUEL (1788)(1997) Critique of Practical Reason, Translated by Mary Gregor (ed.), Cambridge University Press, Cambridge.  

KANT, IMMANUEL (1788)(1898)(2006) The Critique of Practical Reason, Translated by Thomas Kingsmill Abbott, London, Longmans, Green, and Co.  

KANT, IMMANUEL (1791)(2001) ‘On The Miscarriage of All Philosophical Trials in Theodicy’, in Religion and Rational Theology, Translated by George di Giovanni and Allen Wood, Cambridge, Cambridge University Press.  

KLEIN, PETER D. (1996) ‘Certainty’, in Robert Audi, (ed.), The Cambridge Dictionary of Philosophy, Cambridge, Cambridge University Press.  

LANGER, SUSANNE K (1953)(1967) An Introduction to Symbolic Logic, Dover Publications, New York. 

Oxford Dictionary of Science, (2010), Sixth Edition, Oxford, Oxford University Press.  

THIESSEN, HENRY C. (1956) Introductory Lectures in Systematic Theology, Grand Rapids, Wm. B. Eerdmans Publishing Company.  

WITTGENSTEIN, LUDWIG (1951)(1979) On Certainty, Basil Blackwell, Oxford.