User:LGreg/sandbox/Approaches to Knowledge (LG seminar)/ Group 2/Truth/Mathematics, (blank), and (blank)
Truth in Mathematics[edit | edit source]
General truth in Mathematics[edit | edit source]
On the whole, the concern of pure mathematics regarding truth is that it is consistent throughout the discipline. Paul Benacerraf states that "any philosophically satisfactory account of truth, reference, meaning, and knowledge must embrace them all and must be adequate for all the propositions to which these concepts apply. An account of knowledge that seems to work for certain empirical propositions about medium-sized physical objects but which fails to account for more theoretical knowledge is unsatisfactory-not only because it is incomplete, but because it may be incorrect as well, even as an account of the things it seems to cover quite adequately."[1] In short, truth in pure mathematics must be standard so that new discoveries can be found, proven, evaluated and applied in the same way as long-standing mathematical concepts so as to provide continuity. This is not to say that mathematical methodology has stayed stagnant - on the contrary, a very common method of proof which secondary school students often learn is proof by mathematical induction, which has developed over centuries up to the 1800s, which is more or less the form we use it in today - but merely to stress the importance that the language of mathematics is kept consistent, so as to aid the student's understanding.
Various debates over the nature of mathematical truth[edit | edit source]
Inductive vs Empirical[edit | edit source]
Although it seems immediately obvious that a lot of mathematics comes from inductive reasoning, there are many who argue that mathematics as a discipline is, in fact, much more empirical than it seems at first glance. Partly due to the generality of its subject matter, and the flexibility with which it can be applied to other discipline and, through its application, be tested and proved empirically[2], but also in pure mathematics.[3]
Platonism vs Realism[edit | edit source]
Many mathematicians believe that the mathematical discoveries we make are just that - discoveries. These theorems and truths have existed before humans, and we have just happened upon them and observed them. This school of thought toward mathematical truth is Platonist, but as Stanislas Dehaene states, "for the modern neurobiologist, however, the Platonist position seems hard to defend".[4] Øystein Linnebo addresses further challenges of an epistemological nature to mathematical Platonism.[5]
Truth in Economics[edit | edit source]
1. What are its truths (if it has any)?
Positive statement Normative statement Empirical methods
2. How does it come to realize/evaluate truth?
'As a social science, economics analyzes the production, distribution, and consumption of goods and services. The study of economics requires the use of mathematics in order to analyze and synthesize complex information.'
3. is truth important to the discipline?
The various fields Economics can be applied to.
Truth in Art[edit | edit source]
The concept of truth in Art
While the definition of what Art constitutes is widely debated, it can be generally considered to be a discipline which does not make judgement on what is and is not true, but instead aims to demonstrate truths through the artistic process. However, there are still many differing opinions on the degree of success to which this is achieved in Art.
Methods of realising/evaluating truth in Art
Plato was certain that art was an imitation of life and hence was the furthest from "truth" that anything could be; his idea was that ‘Truth’ refers to the idea that the purest existence of any given thing lies not in the physical manifestation of the thing itself, but rather in its invisible and eternal ‘Form’ [6] So for this example, Art is considered to be a discipline which does not deal with truth at all.
Aristotle shed a more promising light on the arts. "The aim of art is to represent not the outward appearance of things, but their inward significance". He believed that objects contain their own eternal truths different in nature from their universal Forms. These are not the esoteric truths that Plato refers to, but are the products of the human psyche which all humans experience. Aristotle invites us to realise that although artistic depictions may be based on an “outward appearance”, these depictions are a means to communicate an artist’s “inward” experience of the physical world. [7]
The importance of truth in Art
The concept of truth in Art is not important for the understanding of whether what the Art depicts is "true" or not, but it is important with the philosophical consideration of what "truth" is in itself. Truth is not valued for its objectivity as it would be in a discipline such as Mathematics, but it is its subjectivity that is considered in Art.
References[edit | edit source]
1. Geoff Riley Positive and Normative Economic Statements, Available at: https://www.tutor2u.net/economics/reference/positive-and-normative-statements (Accessed: 24th October 2019).
2. LARS P. SYLL (2016) What is truth in economics?, Available at: https://larspsyll.wordpress.com/2016/10/27/what-is-truth-in-economics/ (Accessed: 24th October 2019).
3. Economic Models, Available at: https://courses.lumenlearning.com/boundless-economics/chapter/economic-models/ (Accessed: 24th October 2019).
4. Economics, Available at: https://en.wikipedia.org/wiki/Economics (Accessed: 24th October 2019).
- ↑ Benacerraf, Paul. “Mathematical Truth.” The Journal of Philosophy, vol. 70, no. 19, 1973, pp. 661–679. JSTOR, www.jstor.org/stable/2025075.
- ↑ C. G. Hempel (1945) On the Nature of Mathematical Truth, The American Mathematical Monthly, 52:10P1, 543-556, DOI: 10.1080/00029890.1945.11999203
- ↑ Putnam H. (1975) What is mathematical truth? Harvard, Historia Mathematica 2, 529-533.
- ↑ Dehaene S. (2005) How a Primate Brain Comes to Know Some Mathematical Truths. In: Changeux JP., Damasio A.R., Singer W., Christen Y. (eds) Neurobiology of Human Values. Research and Perspectives in Neurosciences. Springer, Berlin, Heidelberg
- ↑ Linnebo, Ø. Philos Stud (2006) 129: 545. https://doi.org/10.1007/s11098-004-3388-1
- ↑ https://www.florenceacademyofart.com/the-truth-in-art-and-the-art-in-truth/
- ↑ https://www.florenceacademyofart.com/the-truth-in-art-and-the-art-in-truth/