Author: Richard Brown

Multiplying by Zero

Richard Brown 4 Comments

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?

Terminating Ambiguity

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I have been working on my paper for my Terminator and Philosophy: I’ll Be Back, Therefore I am volume that I am co-editing with Kevin S. Decker. It is coming along nicely and is nearly ready to be sent to the press. Below is a link to the penultimate version of my paper which is an introduction to the ambiguity issue that we have been discussing around here lately. Any comments are appreciated!

Terminating Ambiguity: The Perplexing case of “The”

What’s the Payoff?

Richard Brown 7 Comments

As some of you may know I am no fan of the ambiguity thesis, which is the claim that definite descriptions like ‘the author of this blog’ are ambiguous as betwee a refferential and attributive use (see here and here). But what hangs on this question? Say it turns out that definite descriptions are ambiguous, what’s the big deal? What do we gain (or loose)? Any thoughts?

Big Brain is Watching

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A new study shows that researchers can tell what has been said and who says it solely by looking at MRIs!

Besides the obvious ethical implications (imagine portable MRIs at every airport scanning passanger’s brains to see if they have recently talked to someone on a terrorist watchlist or you wife checking to see if you talked to an ex, or a mother checking to see if her kid talked to that trouble maker down the street…privacy beware!) this is another fine example of the progress in brain reading (previously discussed here), and another nail in the coffin of those who argue that we will never be able to understand how mental phenomena are physical.

Brain Science and the Soul? As If!

Richard Brown 11 Comments

I just came across this piece over at First Things where the author, a R. R. Reno makes the following ludicrous claim,

We often hear that modern science requires us to reject traditional Christian views of the human person. The argument goes something like this: If we can see the physical process by which ideas are associated or feelings felt or decisions made, then surely we must admit that human beings are nothing more than physical entities. The concept of a soul, so we are told, is irrelevant.

Well, it turns out that science now points us in a different direction…new scientific work on the brain offers an even more interesting and dramatic confirmation of traditional views of the soul. In a recent MRI study, “The Vulcanization of the Human Brain: A Neural Perspective on Interactions Between Cognition and Emotion,” Princeton brain scientist Jonathan D. Cohen has looked at patterns of brain activity while subjects respond to moral dilemmas and make moral decisions. It turns out that the brain patterns related to moral decisions need to be trained. The soul must be disciplined.

There is nothing in Cohen’s work which suggests that materialism is false! Sloppy, sloppy, sloppy. What this provides, if anything, is some vindication of Aristotle’s line of thought that the virtues are learned…it tells us nothing about the nature of the soul! It certainly doesn’t show that there is some non-physical aspect to human beings.

Expressivism and the T-Schema

Richard Brown 6 Comments

Expressivist like Blackburn like to invoke deflationary accounts of truth as a way to save the common sense intuition that moral judgements can be straightforwardly true or false. I have elsewhere argued that this strategy fails to absolve the espressivist from giving an account of justification and, without some kind of modification, the expressivist is committed to relativism. Blackburn’s expressivism collapses into pure autobiography.

Here is another way to make the argument. Take the following claim: Eating meat is immoral. According to the deflationist this will be true just in case eating meat is immoral. This can be put in terms of the T-Schema as so,

“Eating meat is immoral’ is true if and only if eating meat is immoral

But what are to make of the right hand side of this bi-conditional? We cannot take it as naming some fact according to the expressivist. It seems we must, then, give it the expressivist meaning. Doing so yeilds the B-schema

“Eating meat is immoral’ is true if and only if Boo eating meat

This makes it clear that deflationsim about truth cannot help the Blackburns of the world avoid giving a real theory of moral justification.

Or is there some other interpretationof the right hand side of the bi-conditional?

The Ambiguity of ‘That’

Richard Brown 9 Comments

I have previously discussed Devitt’s claim that definite descriptions are ambiguous as between a referntial and an attributive meaning. In my earlier post I gave an argument from Kripke that to my mind is pretty convincing and for which I can’t see a plausible reply.

One of the positive arguments that Devitt gives is a comparison to demonstratives like ‘that’ (argument 3). His point is that the convention by which we express singular thoughts using ‘that’ is straightforwardly a semantic convention (‘if anything is’ as he puts it). Add to this that ‘the’ and ‘that’ are completely interchangable. Anytime that we could use one we can also use the other. So, to take the classic example, if I were to say ‘the murder of Smith is insane’ to express my singular thought about Smith’s murder I could just as well have said ‘that murder of Smith is insane’. This, together with the previous point suggests that ‘the’ has a referential meaning (just like ‘that’).

But if we take the comaprison seriously we will have to postulate an abiguity for ‘that’ as well since there are attributive uses. For insatnce if I am looking at the bloodly murder scene and I say ‘that murder of Smith is insane’ it is clear that I could mean ‘that murder of Smith –whover he is– is insane’. But we have no reason to posit this kind of ambiguity for ‘that’ so we have no reason to postulate it for ‘the’. If anything, what the comparison to demonstratives show is that it isn’t obvious that ‘the’ has the Russellian attributive meaning.

Transworld Saints

Richard Brown 12 Comments

I have been thinking about Plantinga’s free will defense lately for my philosophy of religion course. As is well known central to Plantinga’s argument is teh concept of transworld depravity. A creaturly essence (a person) suffers from transworld depravity just in case there is no possible world in which this creature exists, has morally significant free will and fails to go wrong with respect to at least on morally significant action. Plantinga then suggests that it is possible that we are all transworld depraved. In that case there is no possible world in which there is no evil since any world that God creates will be one where we all go wrong with respect to at least one morally significant action.

But is it really possible for there to be a world where every creature is tranbsworld depraved? Plantinga doean’t really argue for this, he just says that it is possible. But isn’t it just as possible for there to be transworld saints? A transworld saint is a creaturly essence that never goes wrong with respect to a morally significant action in any possible world. For any possible world w the transworld saint always freely chooses to do what is right for all morally significant choices. It is possible that we are all transworld saints. This, I believe, is a nice way to capture Mackie’s claim that God could have made us so that we are free and yet never choose to do evil. There is a possible world where every creature is a transworld saint.

Clearly both worlds can’t really be possible since that would mean that in every world at least one person goes wrong with respect to a morally significant action and no creatures go wrong with respect to any morally significant actions. Is there any reason to think that the Mackie world (one where all creatures are transworld saints) is any less conceivable than the Plantinga world (where all are transworld depraved)?