Papers I almost Wrote

In celebration of my ten years of blogging I have been collecting some of my posts into thematic meta-posts. The previous two listed my writing on the higher-order thought theory of consciousness and my writing about various conferences and classes I have attended. Continuing in that theme below are links to posts I have written about various things that are not in either of the two previous categories. Some of these I had thought I might develop into papers or something but so far that hasn’t happened!

  1. Freedom and Evil
    • This was written for a debate at Brooklyn College entitled ‘If there is a God, Why does Evil Exist?” sponsored by the InterVarsity Christian Fellowship
  2. There is No Santa
    • Is it wrong to lie to children about the existence of Santa? I think so!
  3. What’s So Unobservable about Causation?
    • This is an excerpt from a paper I wrote while a graduate student at the University of Connecticut
  4. Freedom of Speech Meets Speech Act Theory
    • Freedom of speech means freedom of assertion but not the freedom to perform any speech act one wants
  5. Reason and The Nature of Obligation
    • A discussion of Locke and Hobbes on reason and obligation. I think this was first written for a class I had on social and political philosophy. I argue that both are committed to the view that reason is the source of moral obligation but fear (or some external motivator) is required to get people to conform to reason.
  6. Logic, Language, and Existence
    • I discover the problem of necessary existence, and, as usual, also discover that I have reinvented (a crappier version of) the wheel
  7. Timothy Williamson on Necessary Existents
  8. Stop your Quining!!!
    • Are there any counter-examples to some common analytic truths? I don’t think so
  9. What God Doesn’t Know
    • Can we invent Liar Paradox-type sentences involving God’s knowledge? Spoiler alert: yes!
  10. A Counter-Example to the Cogito?
    • Are you nothing more than an alternate personality of the all-power Evil Genius?
  11. Conceptual Atomism, Functionalism, and the Representational Theory of Mind
    • Can we construct quaility-inversion-type scenarios for the mental attitudes? I give it my best shot.
  12. Did Quine Change His Mind?
    • No he did not. The axioms of logic are revisable but we haven’t got any good reason to revise them (yet)
  13. God v. the Delayed Choice Quantum Eraser
    • one of my most popular posts.
  14. The Evolutionary Argument against Rationalism
    • Evolution may have built certain facts about our local reality into the brain, thus generating a priori justification (of a sort)
  15. The A Priori Argument against Rationalism
    • Is it conceivable that there are no necessary truths?
  16. The Empirical Justification of Mathematics
    • Could there be empirical disconfirmation of basic arithmetic?
  17. Invoking God Doesn’t Save Descartes from Skepticism
    • Doesn’t the case of Job from the bible undermine Descartes’ claim that God is not a deceiver?
  18. The (New) Agnostic’s Manifesto: Part 1 –Preamble
  19. Secular Ethics vs. Religious Ethics
  20. Breaking Promises
    • When is a promise broken versus excused?
  21. Second Thoughts about Pain Asymbolia
  22. Transworld Saints
  23. The Logical Problem of Omniscience
  24. Empiricism and A Priori Justification
  25. Reduction v. Elimination
  26. Why I am not a Type-Z Materialist
  27. Pain Asymbolia and a Priori Defeasibility
  28. Summa Contra Plantinga
  29. The Unintelligibility of Substance Dualism
  30. What is Philosophy that it Sucks so Bad?
  31. Identifying the Identity Theory
  32. Can we think about Non-Existant Objects?
  33. The Zombie Argument Depends on Phenomenal Transparency
  34. Bennett on Non-Reductive Physicalism
  35. News Flash: Philosophy Sucks!
  36. Kant’s response to Hume’s Challenge in Ethics
  37. The Identity Theory in 2-D
  38. Outline of the Case for Agnosticism
  39. Consciousness Studies in 100 words (more) or less
  40. The Argument from Photosynthesis
    • Could humans be photosynthetic? The answer seems to be yes and this i bad news for the problem of evil
  41. The Design Argument for the Simulation Hypothesis
  42. Consciousness as an M-Property (?)
  43. If Consciousness is an M-Property then it is Physical
  44. Do We Live in a Westworld World??
  45. Eliminativism and the Neuroscience of Consciousness

Pretend Numbers

As part of my Cosmology, Consciousness, and Computation course I have lately been thinking a lot about Zeno’s paradoxes and the ‘standard solution’ to them that we get from calculus and thinking about motion as a ‘completed infinity’, limits, etc (next week we start quantum mechanics and I am starting to wonder about how Zeno’s paradoxes might relate or not to that, but one thing at a time!). Take the function g(x)=1/x, as x approaches zero the function trends towards infinity (both positive and negative infinity depending on the direction one is going in). We put this by saying that the function’s limit is ∞ (in both directions), but ‘infinity’ is not a real number. So a different way of putting this point would be to say that there is no real number that is the limit of this function.

This got me to thinking. There may be no real number but does that mean that there is no number at all? Suppose that we introduced them on the lines of imaginary numbers. In homage to this let us call them ‘pretend numbers’. 1/0 will then be equal to some pretend number. I will use ‘Þ’ for pretend numbers, so ‘pretend one’ will be ‘Þ1‘. What is Þ1? It is the pretend number that when multiplied by real 0 will give you real 1. We can then define n/0 as follows:

where N≠0,

N0n,

N⁄Þn=0,

Þnx0=N.

These numbers are not on the real number line, or on the imaginary extension of that line. They are on a further pretend extension. Admittedly 0/0 is still tricky and I am not sure what to say about it but putting that to one side, do pretend numbers exist?

Zombies vs Shombies

Richard Marshall, a writer for 3am Magazine, has been interviewing philosophers. After interviewing a long list of distinguished philosophers, including Peter Carruthers, Josh Knobe, Brian Leiter, Alex Rosenberg, Eric Schwitzgebel, Jason Stanley, Alfred Mele, Graham Priest, Kit Fine, Patricia Churchland, Eric Olson, Michael Lynch, Pete Mandik, Eddy Nahmais, J.C. Beal, Sarah Sawyer, Gila Sher, Cecile Fabre, Christine Korsgaard, among others, they seem to be scraping the bottom of the barrel, since they just published my interview. I had a great time engaging in some Existential Psychoanalysis of myself!

Two Questions Regarding Hume’s Account of Relations of Ideas

I have always had two interpretational questions about Hume’s account of relations of ideas. These issues come up in my into class all the time and I am constantly foiled in my attempt to locate an exact answer either in Hume’s corpus or in the secondary literature. Maybe someone else knows where I should look…

The first question is about Hume’s account of our ideas of numbers. Locke is very clear that the ideas of numbers are what he calls modes. We start with our simple idea of a unity and then form the complex ideas of 2, 3, 4, 5…etc by combing this idea with itself. So the idea of the number three is a complex idea composed of three of the simple ideas of a unity (‘III’). Does Hume accept this account of our ideas of numbers? Or does he have some other account of them? I somehow started to think that he had a set-theoretic accoount but I may be turning him into a logical positivist…

The second question is about the possibility of change in relations of ideas. If the mathematical truths are simply definitional truths defined in such a way as to exclude contradictions then it seems that it should be possible for us to change these definitional relations. Is this what Hume actually thinks or am I turning him into Quine? If he doesn’t think this, then how do the relations get set? And what makes it the case that they can’t be changed?

Does anyone know where in Hume’s work he is more explicit about these issues than he is in the Enquiry? Or the name of a good secondary source that addresses these issues?

Multiplying by Zero

The explanation for why division by zero is undefined often goes like this; To say that 6/3=2 is to say that 3*2=6. Now take 6/0=x we would have to find some number that when multiplied by zero gave us 6 (x*0=6). This we can’t do. So, since division and multiplication are inter-defined in this way (generally a/b=c if and only if c*b=a) we can’t divide by 0.

But another way of talking about the interdefinition is to start from multiplication and work back to division; so we can say that a*b=c if and only if c/b=a and c/a=b (e.g. 3*2=6 if and only if 6/3=2 amd 6/2=3). But this will not work for 5*0=0. One way works fine since 0/5=0, but the other fails since it tells us that 0/0=5. But 0/0 s indeterminate and so cannot equal 5. Therefore 0*5 is indeterminate.

Now it is true in a sense that 0/0=5 since according to our interdefinition this just means that 0*5=0 which is of course true. But the problem is that this will be true for any answer. So, suppose that you thought that 0/0=120. This is a perfectly good answer since 0*120=0. But since any number will do as an answer for 0/0 this is definied as indeterminate and the above argument should go through.

What’s the right answer to this problem?

The Empirical Justification of Mathematics

Things have been quite around here lately, mostly because I have been lost in GTA IV and finishing my dissertation. Well I am making some progress (on both 🙂 ) and so will try to get to some of the comments around here.

In answering the comments on the Refutatioin of Rationalism I started thinking about Quine’s indispensibility argument for the empirical justification of mathematics. The argument starts from Quine’s claim that we are ontologically committed to the things which we quantify over in our best theories. The indispensibility of mathematics to physics means that we are committed to the existence of numbers (but not, obviously, to their non-physical existence). So Quine went on to argue that, since our theories all get confirmed or disconfirmed together as a group, the empirical confirmation of physics is empirical confirmation for mathematics. In this way mathematics is empirically justified.

One problem with this argument is that it depends on confirmation holism. That is, it depends on the claim that all of our theories are confirmed or discomfirmed together. None ‘face the tribunal of experience alone’. I then started thinking about how Rosenthal’s version of this argument avoids this commitment and so is a better argument. Sadly Rosenthal has never published this argument (I heard it in a seminar on Quiene and Sellers he gave) so I will try to recreate it as best as I remember.

The basic idea is: if we ever had empirical evidence that some truth of arithmatic was false we would have to admit that it was false. But if so then mathematics is empirically justified. To make the case he asks us to entertain the following scenerio. Suppose that you had two pens of sheep; one with 6 and one with 7 sheep. Now suppose that you counted the sheep individually in each pen (and got 6 and 7) and then you counted all of the sheep and got 14. Suppose you did it again. 1. 2. 3. 4. 5. 6. Yep six sheep in that pen. 1. 2. 3. 4. 5. 6. 7. Yep seven sheep in that pen. Then all the sheep. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. Suppose that this was repeated by all of your friends with the same results. Suppose that it was on the news and tested scientifically and confirmed. Suppose that this phenomenon was wide spread, observable, and repeatable.

If this were the case we would be forced to admit that 7+6=14 is true therefore mathematics is empirically justified.  

Top 10 Posts of 2008

OK, so the year isn’t over yet…but these are the most view posts so far…

–Runner up– Reverse Zombies, Dualism, and Reduction

10. Question Begging Thought Experiments

9. Ontological Arguments

8. The Inconceivability of Zombies

7. There’s Something About Jerry 

6. Pain Asymbolia and Higher-Order Theories of consciousness

5.  Philosophical Trends

4. A Short Argument that there is no God

3. Has Idealism Been Refuted?

2. God versus the Delayed Choice Quantuum Eraser

1. A Simple Argument Against Berkeley