3. Using your three sources and your assembled thoughts above as deep background, compose a paragraph (@ 200 words each) that describes that specialized philosophy area that you have been researching in Research 1 and now in Research 2. This will be your own account of the philosophy of [ Art ) and Philosophy of( Mathematics). Do not write it as a course description—that was just your source material—write an objective account of that philosophy of [….]. Avoid self-references, “I think”, “my opinion”, etc. I will provide my three sources for each one. one of them is philosophy of Art. The other one is Philosophy of Mathematics. Using the sources I’m providing you need to write an account of the philosophy. 200 words each.

philosophy_of_art_and_mathemathics.pdf

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Shahin Sadeghi

Professor Ortega

6 January 2019

Research 1

Philosophy of Mathematics

#1 UCSD University

124 Philosophy of Mathematics

Christian Wu ̈thrich

Winter 2014

wuthrich@ucsd.edu

Course Description

What is the nature of mathematical knowledge, as compared to knowledge of the natural world?

What, if any, is the connection between the two? What role does mathematics play in empirical

sciences such as physics? What role does philosophy play in clarifying the foundations of

mathematics? Do abstract objects, such as numbers, exist? Is mathematics somehow true of our

world, or is it merely an ingenious language devised by humans to address all sorts of problems?

In this class, we will address these questions and study how leading philosophers and mathe- maticians

have attempted to answer them, giving special attention to the influential schools of logicism, formalism,

and intuitionism. No prior college mathematics or philosophy is pre- supposed, although both will be

helpful. Since it offers a focal point for many issues raised in the class, I will give a self-contained

introduction to set theory.

https://philosophy.ucsd.edu/courses/syllabi/14winter/phil124wi14.pdf

#2 Stanford University

Instructor: Thomas Donaldson; Winter Quarter, 2015

tmed@stanford.edu

Course Description

This course is a general survey of the philosophy of mathematics; we’ll focus on epistemological

issues. We begin with a survey of some basic concepts (proof, axiom, definition, number, set,

…). Some of this discussion will be historical in character. We then discuss some mind-bending

theorems about the limits of our current mathematical knowledge: Gödel’s Incompleteness

Theorems, and the independence of the continuum hypothesis from the current axioms of set

theory. We then discuss some of the major philosophical accounts of mathematics, proceeding

more-or-less in chronological order:

Logicism

Intuitionism

Hilbert’s program

Quine’s empiricism

Field’s program

Structuralism

We finish with a discussion of Eugene Wigner’s ‘The Unreasonable Effectiveness of

Mathematics in the Natural Sciences’.

This is a course on philosophy, not mathematics – students won’t be expected to prove

theorems or complete mathematical exercises. However, students will have to read some

material of a technical nature.

https://philosophy.stanford.edu/sites/default/files/courses/syllabus/phil162-262.pdf

#3 NYU

Syllabus: Philosophy of Applied Mathematics

Instructors:Cian Dorr and Hartry Field Fall 2015

Course Description

In science and everyday life, theories are often expressed using so-called ‘mixed’ predicates—predicates (or function symbols) which relate concrete objects or properties of concrete

objects to mathematical objects such as natural numbers, real numbers, vectors at points, and coordinate systems. For example:

● We use natural numbers to talk about how many things there are of a certain kind, e.g. to

say that the number of concrete objects of a certain kind is greater than seven, or even, or

prime.

● We use real numbers to talk about quantities like mass, e.g. when we say that a ma- terial

object has a certain mass in grams, or that the masses of two material object stand in a

certain ratio.

● We use vectors to talk about quantities like velocity, e.g. when we say that a certain

vector at a spacetime point gives the velocity of some fluid through that point.

● We use co-ordinate systems to talk about the geometrical structure of physical spa- ces,

e.g. when we characterise the differential structure of spacetime in terms of a

distinguished class of smooth co-ordinate systems.

● These practices have prompted philosophers to engage in two kinds of reconstructive

projects. The first project is to provide definitions of ‘mixed’ predicates in terms of ‘pure’

predicates all of whose arguments are concrete (like ‘equally massive’), together with

certain especially basic mathematical predicates (like set-membership), thereby

sustaining the natural thought that the relevant relations between the concrete and

mathematical realms are explained by the intrinsic structure of the concrete world. The

second project is to state theories entirely about the concrete world, which can in some

way substitute for, or explain the efficacy of, theories expressed in the usual way using

‘mixed’ vocabulary and quantification over mathematical objects. In this course, we will

discuss several possible motivations for engaging in projects of these kinds—including,

but not limited to, the nominalist thesis that there aren’t any mathematical objects. We

will also delve in to some of the details about the execution of particular projects of these

kinds, with particular attention to cases where the projects have been used to mo- tivate

controversial claims about the ontology of concrete objects, such as the existence of

spacetime points.

● The seminar will not presuppose any prior familiarity with the philosophy of

mathematics, although some background in logic will be helpful. Its topics will overlap

metaphysics and the philosophy of science as well as the philosophy of mathematics.

http://www.nyu.edu/projects/dorr/teaching/AppliedMathSyllabus.pdf

Yasaman Bakhtjoo

Professor Ortega

Philosophy 1

6 January 2019

“ Philosophy of Art ”

1. University of Pennsylvania

Professor Elisabeth Camp

Email: campe@sas.upenn.edu

Course Description

This course will investigate what art is and what role it plays in our lives. Is there a

distinctive quality or function which all works of art possess and which makes them art?

Do they have a distinctive kind of meaning? What determines an artwork’s meaning?

Can it be expressed in other terms? Why do we care about an artwork’s originality and

authenticity? How should we evaluate art? Can it make us better or worse people? In

asking these questions, it’s important that we test our views against actual works of art.

https://www.sas.upenn.edu/~campe/Courses/Camp80SyllF06.pdf

2. University of New Hampshire

Professor William Seeley

Course Description

What is Art? What makes a photograph on the wall at the Museum of Modern Art

different from the one on the front page of the Daily News? What makes a landscape

painting more (or less!) interesting than a snapshot? Our commonsense understanding of

art tells us that artworks are in some way special. Art is often beautiful. It is sometimes

provocative and controversial. But it is notoriously difficult to identify just what it is that

makes artworks unique. In fact, it is sometimes difficult to understand why particular

artworks are considered special at all. Philosophy of Art is a branch of philosophy

concerned with answers to just these types of questions. In this course we will examine

four broad issues that have defined philosophical aesthetics: What is the relationship

between art and representation? What does it mean to say that an artwork expresses an

emotion? What role does the formal structure of artworks play in explanations of art?

What is an aesthetic experience, and what role, if any, does our knowledge of a culture

play in shaping these experiences? We will also discuss a range of philosophical issues

associated with particular art forms. Finally, despite disagreements about the nature of art

most would agree that art must be experienced to be understood. Therefore, throughout

the course we will both make art and look at particular artworks as illustrations of the

views discussed.

https://courses.unh.edu/sites/courses.unh.edu/files/syllabus/part-f16_syllabus.pdf

3. Oregon University

Professor Mark Johnson

Course Description

We will examine five basic views about the nature of art and aesthetic experience that

have been dominant in the Western philosophical tradition. These include conceptions of

art as (1) imitation, (2) emotional expression and communication, (3) form, (4)

institutionally-defined artifacts, and (5) consummation of human meaning and

experience. Texts will range historically from the Greeks up through the 21st century.

Examples of arts will be drawn from painting, sculpture, poetry, literature, architecture,

and music.

https://pages.uoregon.edu/uophil/files/PHIL_322_syll2012.pdf

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