Phil 160D2
Mind, Matter and God

D2L Website

1. Introductory Paragraph:
   1. In this paragraph, provide a very brief introduction describing Socrates’ demonstration of innate mathematical knowledge presented in the Meno.
   2. Keep this paragraph brief.
   3. Avoid trite phrases and avoid providing historical background.
   4. You simply want to present an explanation of Socrates’ demonstration that provides the key features of the demonstration, and this is the only thing you want to present in this introduction---keep your paper very focused!
   5. You will want to end this introduction paragraph with 1 or 2 sentences explaining your answer to the two-part question that is the focus of this paper topic.

                                                            i.      In other words, you want to provide an initial summary of at most two sentences answering the two following questions:

1.    Why do you think mathematical knowledge is more likely to be known innately?

2.  What is the best argument against the view that Socrates’ demonstration shows mathematical knowledge is known innately?

3.  As an element in the introduction to your paper, your initial summary should not include any explanation of why you arrived at your answers since this explanation will be developed in the body of your paper.

 

2. Development of your Position (consisting of roughly two pages and including several paragraphs)
   1. Immediately after your introduction paragraph, you should address the first half of the paper topic. Namely, explain your answer to why mathematical knowledge is likely to be innate.
   2. In providing your explanation, think of the following:

                                                              i.      The ways in which mathematical knowledge is often more certain than other kinds of knowledge.

1.    For example, do I know that a particular flower is red the same way and with the same certainty that I know that 2 + 2 = 4?

2.  Is the latter a better case of knowledge than the former?

                                                           ii.      Although it may happen to be true that the particular flower is red, it might have been false

                                                         iii.      It is also true that 2 + 2 = 4, but might that have been false?

1.    Does this suggest that mathematical truths are necessarily true whereas many truths about physical objects, such as flowers, are not necessarily true?

2.  Does the necessity of a mathematical truth enable us to know it with certainty?

3.  Does the lack of necessity in the case of a truth about a particular physical object’s color prevent us from knowing this truth with certainty?

4.  I might have various perceptual experiences that might disconfirm my prior judgment of the flower’s color, but could any experience disconfirm my judgment that 2 + 2 = 4?

5.  How might the kind of certainty associate with knowing mathematical truths indicate that such mathematical knowledge is innate?

                                                          iv.      Discuss the way in which mathematical knowledge is acquired.

1.    I can come to know that the flower is red by perception.

2.  I can come to know that salt is soluble in water by experimentation.

3.  Is mathematical knowledge acquired by perception or experimentation?

a.      Can we acquire mathematical knowledge by experience?

b.     It may be tempting to think it can be acquired by experience since you have had classroom experiences that produced mathematical knowledge, i.e., the experience of being told that 2 + 2 = 4, but considering such classroom experiences only pushes the question back. How did your teachers come to acquire that knowledge? How did their teachers before them come to acquire their knowledge? And so on.

                                                            v.      Consider the ways in which mathematical knowledge is often claimed to be woven into the way we think.

1.    It appears to be impossible genuinely to imagine that 2+2 is not equal to 4

2.  It is certainly possible genuinely to imagine a red flower to be yellow

3.   This suggests that it is impossible for us to conceive of arithmetic as false

4.  Does this fact about us and how we think about arithmetic suggest that our knowledge of arithmetic (and mathematics generally) is innate?

                                                          vi.      Consider the fact that mathematical truths are universal in the sense that they are true forever and everywhere

1.    When we know a mathematical truth we thus know something that, since it is universally true, transcends our temporally and spatially limited experience.

2.  Does this fact suggest that it is impossible for us to know mathematics through experience?

3.  If so, then, since we do know universal mathematical truths, is our knowledge of them innate?

 

3. Critique of Socrates’ Demonstration in the Meno  (roughly 2 pages)
   1. In the second half of your paper, you should address the second half of the paper topic. Namely, explain what you take to be the best argument against Socrates’ demonstration that the slave possessed mathematical knowledge innately.
   2. In providing your explanation, think of the following:

                                                              i.      A common response to Socrates’ demonstration is that Socrates is providing ‘leading questions’ to the slave boy.

                                                           ii.      If you think this is right, you must explain what this means.

1.    What is a leading question? Give an example of someone providing leading questions in a different context (hint: think of how this might happen in playing games like trivial pursuit).

2.  Cite an instance where Socrates gives a leading question and explain how it is just like your example of a leading question.

3.  Finally, make sure you address why providing ‘leading questions’ undermines Socrates’ claim that he has provided a demonstration of the slave possessing mathematical knowledge innately.

3. You are encouraged to think of other problems with the demonstration besides the “leading question” objection

                                                              i.      However, if you do cite some other problem with his demonstration, make sure that you

1.    fully explain what the problem is

2.  give an example to illustrate the problem in other contexts,

3.  cite exactly where the problem occurs in Socrates’ demonstration, and

4.  explain how the problem undermines Socrates’ conclusion that the slave possessed innate knowledge.

 

4. Conclusion
   1. In one brief paragraph of at most half of the final page summarize the central arguments of your paper
   2. Indicate whether your position agrees or disagrees with Socrates’ position on innate knowledge
   3. State whether you think additional questions need to be addressed completely to address the topic of innate knowledge and briefly state these questions