1511 Words7 Pages

An ontological theorist generally begins his discussion with a preconceived notion of what
kind of thing an object will turn out to be. Instead, we will here begin with a Thomassonian
approach to the ontology of mathematics. First, let us consider what happens when we
rst come to determine a mathematical proposition (which I will use synonymously with
'mathematical entitty'). A mathematician does not feel as though he creates mathematical
theories. Pythagoras can hardly be thought to have created the claim that a2 + b2 = c2. It
becomes clear that a mathematical proposition is a discovered one; that is, we would hardly
nd ourselves contending that Pythagoras created his famous theorem. Regardless of who
discovers it, the same mathematical proposition would be discovered. However, what exactly
is Pythagoras discovering when he puts a2 + b2 = c2 to paper (or papyrus)? Pythagoras
is certainly not noting the existence of the formula, but, rather, he is noticing the relation
between a hypoteneuse and its sides. This relationship comes to be expressed in his formula.
So we already see that while a genuine relationship exists between a hypoteneuse and its
sides, a genuine theorem is contingent on language; the language in this case is that of
mathematics.
We are met, then, with two questions. The rst is whether we should consider the terms
of mathematics, such as wo" or four," to abstract or concrete. The second is whether
we should consider the relationships expressed by mathematics, such as one plus one" or
wo sets of two," to be abstract or concrete. A ctional approach, as that suggested by
Harty Field [3], would say that mathematical terms are literally false. So, when we say
1
'a2 + b2 = c2 is true' wha...
... middle of paper ...
...th them [1]. This question aside, it seems
to me that the most plausible candidate for an ontology of mathematics is that of abstract
artifacts. As with all theories, there will likely be problems which will arise, but I believe I
have given ample evidence in the case against constructivism and ctionalism and signicant
evidence for an abstract artifact mathematical theory.
References
[1] Benacerraf, Paul. Mathematical Truth" Journal of Philosophy 70 (1973), pp. 661-80.
[2] Brown, J.R. Constructivism." Philosophy of Mathematics Handout.
[3] Field, Harty. Introduction: ctionalism, epistemology and modality." Realism, Mathe-
matics, and Modality Handout.
[4] McEvoy, Mark. Miscellaneous class notes.
[5] Thomasson, Amie. Fictional Characters as Abstract Artifacts". Fiction and Metaphysics
(Cambridge: Cambridge University Press, 1999), pp. 5-23, 155, 156.

Related

## Mathematical Models of Spacetime in Contemporary Physics and Essential Issues of the Ontology of Spacetime

3252 Words | 14 PagesEssential Issues of the Ontology of Spacetime ABSTRACT: The general theory of relativity and field theory of matter generate an interesting ontology of space-time and, generally, of nature. It is a monistic, anti-atomistic and geometrized ontology — in which the substance is the metric field — to which all physical events are reducible. Such ontology refers to the Cartesian definition of corporeality and to Plato's ontology of nature presented in the Timaeus. This ontology provides a solution to

## The Cartesian Doubt Experiment and Mathematics

3426 Words | 14 PagesThe Cartesian Doubt Experiment and Mathematics ABSTRACT: The view that Descartes called mathematical propositions into doubt as he impugned all beliefs concerning common-sense ontology by assuming that all beliefs derive from perception seems to rest on the presupposition that the Cartesian problem of doubt concerning mathematics is an instance of the problem of doubt concerning existence of substances. I argue that the problem is not 'whether I am counting actual objects or empty images,' but

## Psi and Ontology

2215 Words | 9 Pagesas an epistemic framework in which to house information. Ontology Often times used as a synonym for Aristotle? metaphysics (what he refereed to as first philosophy), ontology can be thought of as the philosophy and/or science of analyzing objects, structures, processes, and other types of entities in such a way as to find relationships between entities within a said domain. While used synonymously with metaphysics, the term ontology (ontologia) was coined by Rudolf Gockel's Lexicon philosophicum

## Personal Statement

1395 Words | 6 Pagesme throughout my graduate studies. They assisted me to decide and pursue the courses and topics that interested me. During my first semester, I took the course Mathematical methods for Intelligent Systems that gave me a strong base for applied mathematics in the field of intelligent systems. Similarly, the research course Computational Neuroscience gave me an insight into applications of statistics, neural networks, and linear dynamical systems in a biological perspective. My keen interest towards

## Ontology And Epistemology

1457 Words | 6 Pagesnotion of innate ideas or innatism (the idea that the mind is born with ideas or knowledge and is not a "blank slate" at birth). 2.Ontology and Epistemology are probably the most complex terms that one might come across while studying philosophy. Ontology and Epistemology are branches of philosophy. Let us try and simplify these complex topics. The word ontology is derived from the Greek words ‘ontos’ which means being and ‘logos’ which means study. It tries to pin point things around us that actually

## Communication Barrier between Science and the Community

1994 Words | 8 Pagescommunity and actual informaticians have a precise answer for the question. Biomedical Ontology: Ontology is the branch of metaphysics that deals with the nature of being (Oxford University Press Southern Africa, 2007). In the biomedical informatics community, the research on ontologies is becoming extensive (Alexander, 2006:252). Alexander (2006:252) explains that the challenges of constructing and maintaining ontologies has become very difficult, resulting in many workers trying to reap the benefits

## Mathematics as Paideia in Proclus

3040 Words | 13 PagesMathematics as Paideia in Proclus ABSTRACT: I examine one aspect of the central role which mathematics plays in Proclus's ontology and epistemology, with particular reference to his Elements of Theology. I focus on his peculiar views about the ontological status of mathematical objects and the special faculties of the soul that are involved in understanding them. If they are merely abstract objects that are "stripped away" from sensible things, then they are unlikely to reorient the mind towards

## Anas Harthieh

1865 Words | 8 Pagesout of rationality, and are utility maximizes (Zey, 1992). With such ontology comes great opportunity to analyse the social. It gives rational choice theory the simplifying factor to create modules, which can lead to empirical proof of the assumptions made. The reason behind such ontology is to factor out anything, which is not physical or quantified (Fearon and Windt, 2012). The first critic to rational choice theory’s ontology comes from the fact that humans are not independent of the society and

## The Attitudes Of Persons Not Pursuing Mathematics

1238 Words | 5 PagesThe attitudes of persons not pursuing mathematics in modern day are more neutral, and this downturn arose due to influences like competitive exams, and peer outlooks in and out of school. There’s the tendency to supposing only right and wrong solutions in mathematics, limiting children’s aptitude in handling diverse problems and helping identify mathematics authority as a continually evolving problem solving tool (Jenner, 1988, pp. 74). However, at foundation levels this can be valuable yet undesirable

## Maria Gaetana Agnesi

505 Words | 3 Pagesand his studies most likely contributed to her own. Nevertheless, Agnesi deserves recognition not only for her mathematical publications but for all she contributed to math, science, and the western world as a whole. She began her studies of mathematics a very early age. In fact, she began studying all subject matters at the tender age of four years old. This was due to many factors. For one, her father, Pietro Agnesi and mother, Anna Brivio were learned people. Pietro was a professor at the

### Mathematical Models of Spacetime in Contemporary Physics and Essential Issues of the Ontology of Spacetime

3252 Words | 14 Pages### The Cartesian Doubt Experiment and Mathematics

3426 Words | 14 Pages### Psi and Ontology

2215 Words | 9 Pages### Personal Statement

1395 Words | 6 Pages### Ontology And Epistemology

1457 Words | 6 Pages### Communication Barrier between Science and the Community

1994 Words | 8 Pages### Mathematics as Paideia in Proclus

3040 Words | 13 Pages### Anas Harthieh

1865 Words | 8 Pages### The Attitudes Of Persons Not Pursuing Mathematics

1238 Words | 5 Pages### Maria Gaetana Agnesi

505 Words | 3 Pages