Monday, September 24, 2012
Monday, September 17, 2012
Nagel on Plantinga
Thomas Nagel reviews Alvin Plantinga's latest book, Where the Conflict Really Lies: Science, Religion, and Naturalism, here.
Friday, September 7, 2012
Quote of the Day
We understand by a cybernetical machine an apparatus which performs a set of
operations according to a definite set of rules. Normally we "programme" a
machine: that is, we give it a set of instructions about what it is to do in
each eventuality; and we feed in the initial "information" on which the machine
is to perform its calculations. When we consider the possibility that the
mind might be a cybernetical mechanism we have such a model in view; we suppose
that the brain is composed of complicated neural circuits, and that the
information fed in by the senses is "processed" and acted upon or stored for
future use. If it is such a mechanism, then given the way in which it is
programmed -- the way in which it is "wired up" -- and the information which has
been fed into it, the response -- the "output" -- is determined, and could,
granted sufficient time, be calculated. Our idea of a machine is just this, that
its behaviour is completely determined by the way it is made and the incoming
"stimuli": there is no possibility of its acting on its own: given a certain
form of construction and a certain input of information, then it must act in a
certain specific way. We, however, shall be concerned not with what a machine
must do, but with what it can do. That is, instead of
considering the whole set of rules which together determine exactly what a
machine will do in given circumstances, we shall consider only an outline of
those rules, which will delimit the possible responses of the machine, but not
completely. The complete rules will determine the operations completely at every
stage; at every stage there will be a definite instruction, e.g., "If the number
is prime and greater than two add one and divide by two: if it is not prime,
divide by its smallest factor": we, however, will consider the possibility of
there being alternative instructions, e.g., "In a fraction you may divide top
and bottom by any number which is a factor of both numerator and
denominator". In thus relaxing the specification of our model, so that it
is no longer completely determinist, though still entirely mechanistic, we shall
be able to take into account a feature often proposed for mechanical models of
the mind, namely that they should contain a randomizing device. One could build
a machine where the choice between a number of alternatives was settled by, say,
the number of radium atoms to have disintegrated in a given container in the
past half-minute. It is prima facie plausible that our brains should be
liable to random effects: a cosmic ray might well be enough to trigger off a
neural impulse. But clearly in a machine a randomizing device could not be
introduced to choose any alternative whatsoever: it can only be permitted to
choose between a number of allowable alternatives. It is all right to add any
number chosen at random to both sides of an equation, but not to add one number
to one side and another to the other. It is all right to choose to prove one
theorem of Euclid rather than another, or to use one method rather than another,
but not to "prove" something which is not true, or to use a "method of proof"
which is not valid. Any randomizing devices must allow choices only between
those operations which will not lead to inconsistency: which is exactly what the
relaxed specification of our model specifies Indeed, one might put it this way:
instead of considering what a completely determined machine must do, we
shall consider what a machine might be able to do if it had a randomizing device
that acted whenever there were two or more operations possible, none of which
could lead to inconsistency.
If such a machine were built to produce theorems about arithmetic (in many ways the simplest part of mathematics), it would have only a finite number of components, and so there would be only a finite number of types of operation it could do, and only a finite number of initial assumptions it could operate on. Indeed, we can go further, and say that there would only be a definite number of types of operation, and of initial assumptions, that could be built into it. Machines are definite: anything which was indefinite or infinite we should not count as a machine. Note that we say number of types of operation, not number of operations. Given sufficient time, and provided that it did not wear out, a machine could go on repeating an operation indefinitely: it is merely that there can be only a definite number of different sorts of operation it can perform.
If there are only a definite number of types of operation and initial assumptions built into the system, we can represent them all by suitable symbols written down on paper. We can parallel the operation by rules ("rules of inference" or "axiom schemata") allowing us to go from one or more formulae (or even from no formula at all) to another formula, and we can parallel the initial assumptions (if any) by a set of initial formulae ("primitive propositions", "postulates" or "axioms"). Once we have represented these on paper, we can represent every single operation: all we need do is to give formulae representing the situation before and after the operation, and note which rule is being invoked. We can thus represent on paper any possible sequence of operations the machine might perform. However long, the machine went on operating, we could, give enough time, paper and patience, write down an analogue of the machine's operations. This analogue would in fact be a formal proof: every operation of the machine is represented by the application of one of the rules: and the conditions which determine for the machine whether an operation can be performed in a certain situation, become, in our representation, conditions which settle whether a rule can be applied to a certain formula, i.e., formal conditions of applicability. Thus, construing our rules as rules of inference, we shall have a proof-sequence of formulae, each one being written down in virtue of some formal rule of inference having been applied to some previous formula or formulae (except, of course, for the initial formulae, which are given because they represent initial assumptions built into the system). The conclusions it is possible for the machine to produce as being true will therefore correspond to the theorems that can be proved in the corresponding formal system. We now construct a Gödelian formula in this formal system. This formula cannot be proved-in-the- system. Therefore the machine cannot produce the corresponding formula as being true. But we can see that the Gödelian formula is true: any rational being could follow Gödel's argument, and convince himself that the Gödelian formula, although unprovable-in-the-system, was nonetheless -- in fact, for that very reason -- true. Now any mechanical model of the mind must include a mechanism which can enunciate truths of arithmetic, because this is something which minds can do: in fact, it is easy to produce mechanical models which will in many respects produce truths of arithmetic far better than human beings can. But in this one respect they cannot do so well: in that for every machine there is a truth which it cannot produce as being true, but which a mind can. This shows that a machine cannot be a complete and adequate model of the mind. It cannot do everything that a mind can do, since however much it can do, there is always something which it cannot do, and a mind can. This is not to say that we cannot build a machine to simulate any desired piece of mind-like behaviour: it is only that we cannot build a machine to simulate every piece of mind-like behaviour. We can (or shall be able to one day) build machines capable of reproducing bits of mind-like behaviour, and indeed of outdoing the performances of human minds: but however good the machine is, and however much better it can do in nearly all respects than a human mind can, it always has this one weakness, this one thing which it cannot do, whereas a mind can. The Gödelian formula is the Achilles' heel of the cybernetical machine. And therefore we cannot hope ever to produce a machine that will be able to do all that a mind can do: we can never not even in principle, have a mechanical model of the mind.
This conclusion will be highly suspect to some people. They will object first that we cannot have it both that a machine can simulate any piece of mind-like behaviour, and that it cannot simulate every piece. To some it is a contradiction: to them it is enough to point out that there is no contradiction between the fact that for any natural number there can be produced a greater number, and the fact that a number cannot be produced greater than every number. We can use the same analogy also against those who, finding a formula their first machine cannot produce as being true, concede that that machine is indeed inadequate, but thereupon seek to construct a second, more adequate, machine, in which the formula can be produced as being true. This they can indeed do: but then the second machine will have a Gödelian formula all of its own, constructed by applying Gödel's procedure to the formal system which represents its (the second machine's) own, enlarged, scheme of operations. And this formula the second machine will not be able to produce as being true, while a mind will be able to see that it is true. And if now a third machine is constructed, able to do what the second machine was unable to do, exactly the same will happen: there will be yet a third formula, the Gödelian formula for the formal system corresponding to the third machine's scheme of operations, which the third machine is unable to produce as being true, while a mind will still be able to see that it is true. And so it will go on. However complicated a machine we construct, it will, if it is a machine, correspond to a formal system, which in turn will be liable to the Gödel procedure for finding a formula unprovable-in-that- system. This formula the machine will be unable to produce as being true, although a mind can see that it is true. And so the machine will still not be an adequate model of the mind. We are trying to produce a model of the mind which is mechanical -- which is essentially "dead" -- but the mind, being in fact "alive", can always go one better than any formal, ossified, dead, system can. Thanks to Gödel's theorem, the mind always has the last word.
A second objection will now be made. The procedure whereby the Gödelian formula is constructed is a standard procedure -- only so could we be sure that a Gödelian formula can be constructed for every formal system. But if it is a standard procedure, then a machine should be able to be programmed to carry it out too. We could construct a machine with the usual operations, and in addition an operation of going through the Gödel procedure, and then producing the conclusion of that procedure as being true; and then repeating the procedure, and so on, as often as required. This would correspond to having a system with an additional rule of inference which allowed one to add, as a theorem, the Gödelian formula of the rest of the formal system, and then the Gödelian formula of this new, strengthened formal system, and so on. It would be tantamount to adding. to the original formal system an infinite sequence of axioms, each the Gödelian formula of the system hitherto obtained. Yet even so, the matter is not settled: for the machine with a Gödelizing operator, as we might call it, is a different machine from the machines without such an operator; and, although the machine with the operator would be able to do those things in which the machines without the operator were outclassed by a mind, yet we might expect a mind, faced with a machine that possessed a Gödelizing operator, to take this into account, and out-Gödel the new machine, Gödelizing operator and all. This has, in fact, proved to be the case. Even if we adjoin to a formal system the infinite set of axioms consisting of the successive Gödelian formulae, the resulting system is still incomplete, and contains a formula which cannot be proved-in-the-system, although a rational being can, standing outside the system, see that it is true. We had expected this, for even if an infinite set of axioms were added, they would have to be specified by some finite rule or specification, and this further rule or specification could then be taken into account by a mind considering the enlarged formal system. In a sense, just because the mind has the last word, it can always pick a hole in any formal system presented to it as a model of its own workings. The mechanical model must be, in some sense, finite and definite: and then the mind can always go one better.
This is the answer to one objection put forward by Turing. He argues that the limitation to the powers of a machine do not amount to anything much. Although each individual machine is incapable of getting the right answer to some questions, after all each individual human being is fallible also: and in any case "our superiority can only be felt on such an occasion in relation to the one machine over which we have scored our petty triumph. There would be no question of triumphing simultaneously over all machines." But this is not the point. We are not discussing whether machines or minds are superior, but whether they are the same. In some respect machines are undoubtedly superior to human minds; and the question on which they are stumped is admittedly, a rather niggling, even trivial, question. But it is enough, enough to show that the machine is not the same as a mind. True, the machine can do many things that a human mind cannot do: but if there is of necessity something that the machine cannot do, though the mind can, then, however trivial the matter is, we cannot equate the two, and cannot hope ever to have a mechanical model that will adequately represent the mind. Nor does it signify that it is only an individual machine we have triumphed over: for the triumph is not over only an individual machine, but over any individual that anybody cares to specify -- in Latin quivis or quilibet, not quidam -- and a mechanical model of a mind must be an individual machine. Although it is true that any particular "triumph" of a mind over a machine could be "trumped" by another machine able to produce the answer the first machine could not produce, so that "there is no question of triumphing simultaneously over all machines", yet this is irrelevant. What is at issue is not the unequal contest between one mind and all machines, but whether there could be any, single, machine that could do all a mind can do. For the mechanist thesis to hold water, it must be possible, in principle, to produce a model, a single model, which can do everything the mind can do. It is like a game. The mechanist has first turn. He produces a -- any, but only a definite one -- mechanical model of the mind. I point to something that it cannot do, but the mind can. The mechanist is free to modify his example, but each time he does so, I am entitled to look for defects in the revised model. If the mechanist can devise a model that I cannot find fault with, his thesis is established: if he cannot, then it is not proven: and since -- as it turns out -- he necessarily cannot, it is refuted. To succeed, he must be able to produce some definite mechanical model of the mind -- anyone he likes, but one he can specify, and will stick to. But since he cannot, in principle cannot, produce any mechanical model that is adequate, even though the point of failure is a minor one, he is bound to fail, and mechanism must be false.
J. R. Lucas
"Minds, Machines, and Gödel"
Philosophy 36 (1961)
If such a machine were built to produce theorems about arithmetic (in many ways the simplest part of mathematics), it would have only a finite number of components, and so there would be only a finite number of types of operation it could do, and only a finite number of initial assumptions it could operate on. Indeed, we can go further, and say that there would only be a definite number of types of operation, and of initial assumptions, that could be built into it. Machines are definite: anything which was indefinite or infinite we should not count as a machine. Note that we say number of types of operation, not number of operations. Given sufficient time, and provided that it did not wear out, a machine could go on repeating an operation indefinitely: it is merely that there can be only a definite number of different sorts of operation it can perform.
If there are only a definite number of types of operation and initial assumptions built into the system, we can represent them all by suitable symbols written down on paper. We can parallel the operation by rules ("rules of inference" or "axiom schemata") allowing us to go from one or more formulae (or even from no formula at all) to another formula, and we can parallel the initial assumptions (if any) by a set of initial formulae ("primitive propositions", "postulates" or "axioms"). Once we have represented these on paper, we can represent every single operation: all we need do is to give formulae representing the situation before and after the operation, and note which rule is being invoked. We can thus represent on paper any possible sequence of operations the machine might perform. However long, the machine went on operating, we could, give enough time, paper and patience, write down an analogue of the machine's operations. This analogue would in fact be a formal proof: every operation of the machine is represented by the application of one of the rules: and the conditions which determine for the machine whether an operation can be performed in a certain situation, become, in our representation, conditions which settle whether a rule can be applied to a certain formula, i.e., formal conditions of applicability. Thus, construing our rules as rules of inference, we shall have a proof-sequence of formulae, each one being written down in virtue of some formal rule of inference having been applied to some previous formula or formulae (except, of course, for the initial formulae, which are given because they represent initial assumptions built into the system). The conclusions it is possible for the machine to produce as being true will therefore correspond to the theorems that can be proved in the corresponding formal system. We now construct a Gödelian formula in this formal system. This formula cannot be proved-in-the- system. Therefore the machine cannot produce the corresponding formula as being true. But we can see that the Gödelian formula is true: any rational being could follow Gödel's argument, and convince himself that the Gödelian formula, although unprovable-in-the-system, was nonetheless -- in fact, for that very reason -- true. Now any mechanical model of the mind must include a mechanism which can enunciate truths of arithmetic, because this is something which minds can do: in fact, it is easy to produce mechanical models which will in many respects produce truths of arithmetic far better than human beings can. But in this one respect they cannot do so well: in that for every machine there is a truth which it cannot produce as being true, but which a mind can. This shows that a machine cannot be a complete and adequate model of the mind. It cannot do everything that a mind can do, since however much it can do, there is always something which it cannot do, and a mind can. This is not to say that we cannot build a machine to simulate any desired piece of mind-like behaviour: it is only that we cannot build a machine to simulate every piece of mind-like behaviour. We can (or shall be able to one day) build machines capable of reproducing bits of mind-like behaviour, and indeed of outdoing the performances of human minds: but however good the machine is, and however much better it can do in nearly all respects than a human mind can, it always has this one weakness, this one thing which it cannot do, whereas a mind can. The Gödelian formula is the Achilles' heel of the cybernetical machine. And therefore we cannot hope ever to produce a machine that will be able to do all that a mind can do: we can never not even in principle, have a mechanical model of the mind.
This conclusion will be highly suspect to some people. They will object first that we cannot have it both that a machine can simulate any piece of mind-like behaviour, and that it cannot simulate every piece. To some it is a contradiction: to them it is enough to point out that there is no contradiction between the fact that for any natural number there can be produced a greater number, and the fact that a number cannot be produced greater than every number. We can use the same analogy also against those who, finding a formula their first machine cannot produce as being true, concede that that machine is indeed inadequate, but thereupon seek to construct a second, more adequate, machine, in which the formula can be produced as being true. This they can indeed do: but then the second machine will have a Gödelian formula all of its own, constructed by applying Gödel's procedure to the formal system which represents its (the second machine's) own, enlarged, scheme of operations. And this formula the second machine will not be able to produce as being true, while a mind will be able to see that it is true. And if now a third machine is constructed, able to do what the second machine was unable to do, exactly the same will happen: there will be yet a third formula, the Gödelian formula for the formal system corresponding to the third machine's scheme of operations, which the third machine is unable to produce as being true, while a mind will still be able to see that it is true. And so it will go on. However complicated a machine we construct, it will, if it is a machine, correspond to a formal system, which in turn will be liable to the Gödel procedure for finding a formula unprovable-in-that- system. This formula the machine will be unable to produce as being true, although a mind can see that it is true. And so the machine will still not be an adequate model of the mind. We are trying to produce a model of the mind which is mechanical -- which is essentially "dead" -- but the mind, being in fact "alive", can always go one better than any formal, ossified, dead, system can. Thanks to Gödel's theorem, the mind always has the last word.
A second objection will now be made. The procedure whereby the Gödelian formula is constructed is a standard procedure -- only so could we be sure that a Gödelian formula can be constructed for every formal system. But if it is a standard procedure, then a machine should be able to be programmed to carry it out too. We could construct a machine with the usual operations, and in addition an operation of going through the Gödel procedure, and then producing the conclusion of that procedure as being true; and then repeating the procedure, and so on, as often as required. This would correspond to having a system with an additional rule of inference which allowed one to add, as a theorem, the Gödelian formula of the rest of the formal system, and then the Gödelian formula of this new, strengthened formal system, and so on. It would be tantamount to adding. to the original formal system an infinite sequence of axioms, each the Gödelian formula of the system hitherto obtained. Yet even so, the matter is not settled: for the machine with a Gödelizing operator, as we might call it, is a different machine from the machines without such an operator; and, although the machine with the operator would be able to do those things in which the machines without the operator were outclassed by a mind, yet we might expect a mind, faced with a machine that possessed a Gödelizing operator, to take this into account, and out-Gödel the new machine, Gödelizing operator and all. This has, in fact, proved to be the case. Even if we adjoin to a formal system the infinite set of axioms consisting of the successive Gödelian formulae, the resulting system is still incomplete, and contains a formula which cannot be proved-in-the-system, although a rational being can, standing outside the system, see that it is true. We had expected this, for even if an infinite set of axioms were added, they would have to be specified by some finite rule or specification, and this further rule or specification could then be taken into account by a mind considering the enlarged formal system. In a sense, just because the mind has the last word, it can always pick a hole in any formal system presented to it as a model of its own workings. The mechanical model must be, in some sense, finite and definite: and then the mind can always go one better.
This is the answer to one objection put forward by Turing. He argues that the limitation to the powers of a machine do not amount to anything much. Although each individual machine is incapable of getting the right answer to some questions, after all each individual human being is fallible also: and in any case "our superiority can only be felt on such an occasion in relation to the one machine over which we have scored our petty triumph. There would be no question of triumphing simultaneously over all machines." But this is not the point. We are not discussing whether machines or minds are superior, but whether they are the same. In some respect machines are undoubtedly superior to human minds; and the question on which they are stumped is admittedly, a rather niggling, even trivial, question. But it is enough, enough to show that the machine is not the same as a mind. True, the machine can do many things that a human mind cannot do: but if there is of necessity something that the machine cannot do, though the mind can, then, however trivial the matter is, we cannot equate the two, and cannot hope ever to have a mechanical model that will adequately represent the mind. Nor does it signify that it is only an individual machine we have triumphed over: for the triumph is not over only an individual machine, but over any individual that anybody cares to specify -- in Latin quivis or quilibet, not quidam -- and a mechanical model of a mind must be an individual machine. Although it is true that any particular "triumph" of a mind over a machine could be "trumped" by another machine able to produce the answer the first machine could not produce, so that "there is no question of triumphing simultaneously over all machines", yet this is irrelevant. What is at issue is not the unequal contest between one mind and all machines, but whether there could be any, single, machine that could do all a mind can do. For the mechanist thesis to hold water, it must be possible, in principle, to produce a model, a single model, which can do everything the mind can do. It is like a game. The mechanist has first turn. He produces a -- any, but only a definite one -- mechanical model of the mind. I point to something that it cannot do, but the mind can. The mechanist is free to modify his example, but each time he does so, I am entitled to look for defects in the revised model. If the mechanist can devise a model that I cannot find fault with, his thesis is established: if he cannot, then it is not proven: and since -- as it turns out -- he necessarily cannot, it is refuted. To succeed, he must be able to produce some definite mechanical model of the mind -- anyone he likes, but one he can specify, and will stick to. But since he cannot, in principle cannot, produce any mechanical model that is adequate, even though the point of failure is a minor one, he is bound to fail, and mechanism must be false.
J. R. Lucas
"Minds, Machines, and Gödel"
Philosophy 36 (1961)
Saturday, August 25, 2012
Tuesday, August 21, 2012
For your viewing pleasure...
...C. S. Lewis through the Shadowlands, the BBC version which I prefer to the Hollywood version. Having said that, the Hollywood version has much higher production values, and honestly, I don't remember it very well.
Monday, August 20, 2012
Saturday, August 18, 2012
Friday, August 3, 2012
Roaming Rover
I'm not posting much, but some things are too important to not mention. On Sunday, the new Mars Rover will land on Mars, filming on the way down. So so so cool.
Update (7 Aug): First pictures. Including this one
which reminds me of this one from the Phoenix landing.
Update (7 Aug): First pictures. Including this one
which reminds me of this one from the Phoenix landing.
Thursday, July 19, 2012
Folks,
once again, I apologize for not posting much of late. I have PhD stuff going on. I'll probably experience a burst of activity once I turn in my dissertation.
Monday, July 9, 2012
More Favorite Movie Scenes
The Shawshank Redemption
Open Range
Aliens
Falling Down
Eternal Sunshine of the Spotless Mind
The Commitments
The Commitments - Try a Little Tenderness par algizdk
The Rock
Evil Dead 2
On Her Majesty's Secret Service
Robocop 2
Gran Torino
The Untouchables
Blade Runner
Open Range
Aliens
Falling Down
Eternal Sunshine of the Spotless Mind
The Commitments
The Commitments - Try a Little Tenderness par algizdk
The Rock
Evil Dead 2
On Her Majesty's Secret Service
Robocop 2
Gran Torino
The Untouchables
Blade Runner
Tuesday, July 3, 2012
High Noon in Space
That's how my dad described the 1981 science-fiction movie Outland with Sean Connery. I just saw it again on YouTube and for the life of me I don't understand why this movie isn't more well-known. I'm probably biased, but I just love it -- apart from the absurd claim that being exposed to vacuum makes people immediately explode. Maybe I shouldn't link it, but you can watch the whole thing here. My dad thought the chase/fight scene that starts around 48:30 was one of the best chase scenes ever filmed.
Thursday, June 28, 2012
Proof Positive
Last night I left a few comments on another blog that reported the news that a German court had declared it illegal to circumcise children under the age of consent. The comments on the blog veered to several side issues, one of which was condemnation of religions that practice circumcision. This led to a couple of commenters making the claim that atheism is not disbelief in God, it's merely the absence of belief in God. I've written about that before so I challenged them to define what the "absence of belief" is and how it's different from withholding belief (agnosticism) and disbelief (atheism as it has been understood historically and today). The "absence of belief" position was popular in the mid to late 20th century among some atheist philosophers, but they eventually abandoned it because they couldn't define it. Their motive for suggesting it was that if one simply lacks a belief then they (allegedly) do not share any burden of proof: the burden is entirely on the person who claims that God exists. If you assert that God does not exist, however, then you're making a claim to knowledge and so must shoulder the burden of proof just as much as the theist does. So the "absence of belief" position is basically an attempt to think whatever you want without having to go to the trouble of having reasons or evidence for it.
This led to someone else making a statement that is popular among atheist laymen. He wrote, "You can't prove a negative." I responded, "You can't? Why not? I can prove negatives. Who told you that you can't prove a negative?" Really, negatives are proven all day long and are very easy: you can prove that there is no full-sized elephant in your room right now. You can prove that, under normal conditions, if you drop a pencil, it will not fall up instead of down. These are perhaps silly examples, but proving negatives is one of the most common things to prove. Here's a more realistic case. Many scientists and philosophers of science follow Popper in claiming that science cannot prove anything it can only falsify. Science cannot prove "if A --> B" because A and B may just be occuring together by coincidence. However science can falsify "if A --> B" by finding an example of A occurring without B. If we accept this account then not only is it possible to prove a negative, it means that science only proves negatives.
Now I suspect the atheist who says you can't prove negatives is really thinking something else. Perhaps he's thinking that while you can prove negatives about observables you can't prove negatives about unobservables, like God. But of course this is false as well: you can prove that God did not just create a full-sized elephant in your room right now. The atheist may counter-respond that if we appeal to God we can make any absurd qualification we want. Maybe God just created a full-sized invisible elephant in your room right now. If you object that part of your anti-elephant proof is that your room is not big enough for an elephant, you can maybe qualify it further. But these attempts are non-starters. Absent the specific qualification that the elephant is invisible (or any other ad hoc qualification) the phrase "a full-sized elephant" by itself would mean that the elephant in question is visible (or lacks the ad hoc qualification). I think the people who make this objection are thinking something along the lines of: the concept of God has been repeatedly qualified to render it immune to disproof. It used to refer to a physical person-like object, but then when that became philosophically and scientifically untenable it was upgraded to a non-physical person-like object, etc. This seems to presuppose a naive view of the origin and development of religion which was common in the second half of the 19th century. Certainly, the theistic concept of God has developed -- as it should -- but it is not clear to me that this has been a series of ad hoc qualifications like, "Well, well, maybe he's just invisible!" At any rate, atheism is guilty of the same thing, so it strikes me as a tu quoque argument.
Or perhaps the atheist is thinking you can't prove a universal negative. That's a more respectable claim: to say there are no X's would seem to require that one had searched all of reality and determined that no X's exist. Even more, it would seem to require that one had searched all of reality simultaneously: otherwise, perhaps the X's were somewhere other than where you were looking at each particular moment; maybe they moved around so that they were always behind you or something. Unfortunately, this claim is still false. It assumes the only way you can prove something is via observation, that is, through scientific methods. This is scientism and scientism is a naive and foolish position. To make the most obvious point, you can prove things via logic -- specifically you can prove universal negatives via logic. If something contradicts a law of logic then it is impossible and cannot exist anytime, anywhere. If the atheist challenges the laws of logic we can simply point out that science presupposes the laws of logic. Once you've abandoned logic you've abandoned science (not to mention knowledge and rationality). However, this has a limited application. That's why this objection is more respectable: in many cases you can't prove a universal negative. It's only when the universal negative contradicts a law of logic that it can be disproven.
A third possibility: perhaps the atheist is defining "prove" in the logical sense. You can give an argument for something, you can demonstrate that something is more likely true than false, you can even show that it is very probably true. But a logical proof is an absolute proof. It cannot fail to be true (or, conversely, fail to be false). It holds of all possible worlds. But of course, this was already dealt with: to prove a universal negative via logic is to prove it absolutely.
Finally, I would just like to point out that the claim "You can't prove a negative" is a negative. So by its own lights, it can't be proven. This doesn't necessarily render it invalid, since there are many things we can know that we can't prove. However, it does mean, at the very least, that the person who claims you can't prove a negative must give us a reason for thinking why you can't prove a negative. This is likely to lead to one of the three possibilities above.
(Updated to add a point and clean up some awkward phrasings.)
Update, 12 July: Defining ignorance.
(cross-posted at Quodlibeta)
This led to someone else making a statement that is popular among atheist laymen. He wrote, "You can't prove a negative." I responded, "You can't? Why not? I can prove negatives. Who told you that you can't prove a negative?" Really, negatives are proven all day long and are very easy: you can prove that there is no full-sized elephant in your room right now. You can prove that, under normal conditions, if you drop a pencil, it will not fall up instead of down. These are perhaps silly examples, but proving negatives is one of the most common things to prove. Here's a more realistic case. Many scientists and philosophers of science follow Popper in claiming that science cannot prove anything it can only falsify. Science cannot prove "if A --> B" because A and B may just be occuring together by coincidence. However science can falsify "if A --> B" by finding an example of A occurring without B. If we accept this account then not only is it possible to prove a negative, it means that science only proves negatives.
Now I suspect the atheist who says you can't prove negatives is really thinking something else. Perhaps he's thinking that while you can prove negatives about observables you can't prove negatives about unobservables, like God. But of course this is false as well: you can prove that God did not just create a full-sized elephant in your room right now. The atheist may counter-respond that if we appeal to God we can make any absurd qualification we want. Maybe God just created a full-sized invisible elephant in your room right now. If you object that part of your anti-elephant proof is that your room is not big enough for an elephant, you can maybe qualify it further. But these attempts are non-starters. Absent the specific qualification that the elephant is invisible (or any other ad hoc qualification) the phrase "a full-sized elephant" by itself would mean that the elephant in question is visible (or lacks the ad hoc qualification). I think the people who make this objection are thinking something along the lines of: the concept of God has been repeatedly qualified to render it immune to disproof. It used to refer to a physical person-like object, but then when that became philosophically and scientifically untenable it was upgraded to a non-physical person-like object, etc. This seems to presuppose a naive view of the origin and development of religion which was common in the second half of the 19th century. Certainly, the theistic concept of God has developed -- as it should -- but it is not clear to me that this has been a series of ad hoc qualifications like, "Well, well, maybe he's just invisible!" At any rate, atheism is guilty of the same thing, so it strikes me as a tu quoque argument.
Or perhaps the atheist is thinking you can't prove a universal negative. That's a more respectable claim: to say there are no X's would seem to require that one had searched all of reality and determined that no X's exist. Even more, it would seem to require that one had searched all of reality simultaneously: otherwise, perhaps the X's were somewhere other than where you were looking at each particular moment; maybe they moved around so that they were always behind you or something. Unfortunately, this claim is still false. It assumes the only way you can prove something is via observation, that is, through scientific methods. This is scientism and scientism is a naive and foolish position. To make the most obvious point, you can prove things via logic -- specifically you can prove universal negatives via logic. If something contradicts a law of logic then it is impossible and cannot exist anytime, anywhere. If the atheist challenges the laws of logic we can simply point out that science presupposes the laws of logic. Once you've abandoned logic you've abandoned science (not to mention knowledge and rationality). However, this has a limited application. That's why this objection is more respectable: in many cases you can't prove a universal negative. It's only when the universal negative contradicts a law of logic that it can be disproven.
A third possibility: perhaps the atheist is defining "prove" in the logical sense. You can give an argument for something, you can demonstrate that something is more likely true than false, you can even show that it is very probably true. But a logical proof is an absolute proof. It cannot fail to be true (or, conversely, fail to be false). It holds of all possible worlds. But of course, this was already dealt with: to prove a universal negative via logic is to prove it absolutely.
Finally, I would just like to point out that the claim "You can't prove a negative" is a negative. So by its own lights, it can't be proven. This doesn't necessarily render it invalid, since there are many things we can know that we can't prove. However, it does mean, at the very least, that the person who claims you can't prove a negative must give us a reason for thinking why you can't prove a negative. This is likely to lead to one of the three possibilities above.
(Updated to add a point and clean up some awkward phrasings.)
Update, 12 July: Defining ignorance.
(cross-posted at Quodlibeta)
Wednesday, June 20, 2012
Quote of the Day
The other motive which prompts Naturalism in its attempt to deny the efficiency of mind is of a more positive and ambitious sort. It is, namely, the desire to make all forms of matter, of motion, and of energy susceptible to the same sort of description, explanation, and prediction; the wish to get a single world formula under which everything that happens may be subsumed. "We have achieved the impersonal point of view," hymns one of the most ecstatic of the behaviorists, "in the interpretation of stars and stones and trees and bacteria and guinea pigs. Our next step is to achieve it for the phenomena of human behavior." Thus shall we at length achieve that consummation devoutly to be wishes, that thoroughly scientific point of view, from which we shall be unable to find in man anything essentially different from what we observe in stones, bacteria, and guinea pigs. There is, to be sure, absolutely no evidence to show that such an achievement is possible, no argument to indicate that the actual world is such as to submit to such a formula; but the great longing heart of Naturalism demands that it shall be so, and the naturalistic philosopher solemnly declares that it is so -- it is so because it must be so. It would be impossible to find in the most sentimental and unreasoning forms of religious experience a more extreme case of the pious wish or the Will to Believe. Nor can the annals of Scholastic Philosophy or of Protestant Theology give us a more admirable example of dogma, pure and undefiled. No evidence that Galileo could give as to the motion of the earth had any influence upon his judges; the earth did not move because it could not move. In similar fashion we are assured that the mind cannot move nor influence the movements of the body -- to say that it does so is heresy, for so one would deny the universality of physical law. -- E pur si muove!
Here is the real issue of the mind-body problem, here is the only important question. And looking back over our course with this fact in mind we can now see that there are not, as we had supposed, three or four chief views of this problem, but only two, namely Interaction and its rivals. The various forms of Materialism, of Parallelism, and of Behaviorism are only different ways of saying pretty much the same thing, only varied attempts to prove the same thesis. The aim of all is identical, namely, to write down and explain the whole of reality in physical formulæ, to deny to mind any influence whether direct or indirect upon matter and motion. The first expression of this naturalistic thesis is the blatant form of Materialism. The difficulties to which this gives rise are too patent to permit of its acceptance, so they are later disguised under the gentlemanly costume and the idealistic mask of Parallelism. But the splendid promises of Parallelism lead to disillusion at the end, and the mask which it wore is easily torn from its face. No one weeps its fall, for few besides Fechner and Paulsen were ever very much interested in it except as a means of defeating Interaction and establishing Naturalism. So its old upholders rapidly desert it to give in their allegiance to Behaviorism. Behaviorism, also, would like to avoid the blatancy of Materialism. It has many brave words as to the nobility and the significance of intelligence. But when we get at the real meaning of the words we learn that intelligence is simply a specific form of activity and set in nerves, muscles, and glands. Thus, Behaviorism, in common with its predecessors and allies, is merely a specially devised way of denying the efficiency of consciousness.
And when one stops to face squarely this proposition that mind has no effect on conduct, -- when, I say, one stops to face it squarely, and leaving aside pet theories, gives it serious consideration int he light of all that one knows of oneself and of other men and of human history and civilization -- the proposition reveals itself to the steady gaze as unspeakably preposterous. In the words of Professor Lovejoy, "Never, surely, did a sillier or more self-stultifying idea enter the human mind than the idea that thinking as such -- that is to say, remembering, planning, reasoning, forecasting, -- is a vast irrelevancy having no part in the causation of man's behavior or in the shaping of his fortunes -- a mysterious redundancy in the cosmos which would follow precisely the same course without it."
We are told we must deny the efficiency of consciousness because of the difficulty in believing in any exceptions to the action of mechanical law and the difficulty of imagining how mind can act on matter. I submit that to be so nice with little difficulties, and so omnivorous with monstrosities that approach the mentally impossible is a case of straining at one poor gnat and swallowing a whole caravan of camels. Like others I find it difficult to imagine an idea affecting a brain molecule; but I think I am also like nearly everybody else when I find it impossible to believe that thought and purpose have had nothing to do with building up human civilization and creating human literature and philosophy. How the opponents of Interaction manage to believe these things I confess I find it very difficult indeed to imagine.
I know this is not decisive. I know indeed what the upholder of Naturalism will probably reply. His reply, in fact, will be in substance not very different from that of the Red Queen to Alice, after Alice had told her there were some things she couldn't believe. "Can't you?" said the Queen in a pitying tone. "Try again; draw a long breath and shut your eyes."
"There's no use trying," said Alice, "one can't believe impossible things."
"I dare say you haven't had much practice," said the Queen. "When I was your age I always did it for half an hour a day. Why, sometimes I've believed as many as six impossible things before breakfast."
When one remembers the materialistic assertions that consciousness is matter and that logic is ground out by mechanical processes, the parallelistic thesis that the non-existent brain determines wholly the existent mind, the neo-realist denial of all reality to the subjective, the behaviorist identification of thought with the action of the larynx, one sees that Naturalism, like the Red Queen, has had some practice in believing the impossible; that in fact it would be stating its case with great moderation, not to say modesty, if it should claim that sometimes it had believed as many as half a dozen impossible things before breakfast. Moreover, the Red Queen's formula for belief is the one which must necessarily be adopted if we are to imitate successfully the remarkable achievements of Naturalism in the arousal of faith in the impossible, -- namely, "Draw a long breath and shut your eyes!"
I too can believe a good many things with my eyes shut; but if I keep them persistently open I becomes less and less impressed with the ambitious claims and the false dignity of Naturalism. And by Naturalism I mean, of course, not natural science but the unempirical philosophy, the a priori theory, which would extend the formulæ of natural science into spheres in which the true scientist has no ambition to advance. Taken in this sense Naturalism appears to me the great hoax of our times. Its seemingly adamantine fortifications, with their tremendous and terrifying guns, are mostly camouflage. Its walls are enormously impressive; but like those of Jericho they will fall before whosoever has the courage coolly to examine their foundations -- and to blow upon the trumpet.
This being the case, I must also say frankly that Interaction seems to me the inevitable outcome of our argument. It is the only view that makes history and human life really intelligible. Indeed if we were right in believing (and we have seen no reason for doubting) that Materialism, Parallelism, Interaction, and the denial of the mind-body relation are the only answers to our problem worth serious consideration; and if we were justified also in our conclusion that the relation is a real one, and that neither Materialism nor Parallelism is tenable, and that the alleged difficulties of Interaction are much slighter than at first they seem, it follows that we are plainly compelled by the very process of elimination to conclude that Interaction is the true doctrine and that mind has an independence and a power of its own. And now we can begin to understand the wild attempts of Materialism, Parallelism, Neo-Realism, and Behaviorism to invent some method by which Interaction might be avoided. Not for nothing were the strange twistings and writhings of these theories. For if Interaction be accepted a momentous turn has been taken in our philosophy. We shall namely have given in our assent to a Dualism of Process with the universe.
The consequences of such a Dualism of Process are fateful and endless. There is no time to deal with them this afternoon and they must be postponed for consideration to our final lecture. But we can, I think, already begin to form some notion of what is involved in this Dualism of Process, to which, by the force of logic and of experience, we seem to have been driven. Such a world view will mean a profound, if not a fundamental, distinction between matter and spirit. It will mean the return of all sorts of possibilities against which the iron gates of Naturalism were forever closed. It will mean that perhaps Plato and Christianity were right after all.
James Bissett Pratt
Matter and Spirit: A Study of Mind and Body in Their Relation to the Spiritual Life (1922)
(footnotes omitted)
Here is the real issue of the mind-body problem, here is the only important question. And looking back over our course with this fact in mind we can now see that there are not, as we had supposed, three or four chief views of this problem, but only two, namely Interaction and its rivals. The various forms of Materialism, of Parallelism, and of Behaviorism are only different ways of saying pretty much the same thing, only varied attempts to prove the same thesis. The aim of all is identical, namely, to write down and explain the whole of reality in physical formulæ, to deny to mind any influence whether direct or indirect upon matter and motion. The first expression of this naturalistic thesis is the blatant form of Materialism. The difficulties to which this gives rise are too patent to permit of its acceptance, so they are later disguised under the gentlemanly costume and the idealistic mask of Parallelism. But the splendid promises of Parallelism lead to disillusion at the end, and the mask which it wore is easily torn from its face. No one weeps its fall, for few besides Fechner and Paulsen were ever very much interested in it except as a means of defeating Interaction and establishing Naturalism. So its old upholders rapidly desert it to give in their allegiance to Behaviorism. Behaviorism, also, would like to avoid the blatancy of Materialism. It has many brave words as to the nobility and the significance of intelligence. But when we get at the real meaning of the words we learn that intelligence is simply a specific form of activity and set in nerves, muscles, and glands. Thus, Behaviorism, in common with its predecessors and allies, is merely a specially devised way of denying the efficiency of consciousness.
And when one stops to face squarely this proposition that mind has no effect on conduct, -- when, I say, one stops to face it squarely, and leaving aside pet theories, gives it serious consideration int he light of all that one knows of oneself and of other men and of human history and civilization -- the proposition reveals itself to the steady gaze as unspeakably preposterous. In the words of Professor Lovejoy, "Never, surely, did a sillier or more self-stultifying idea enter the human mind than the idea that thinking as such -- that is to say, remembering, planning, reasoning, forecasting, -- is a vast irrelevancy having no part in the causation of man's behavior or in the shaping of his fortunes -- a mysterious redundancy in the cosmos which would follow precisely the same course without it."
We are told we must deny the efficiency of consciousness because of the difficulty in believing in any exceptions to the action of mechanical law and the difficulty of imagining how mind can act on matter. I submit that to be so nice with little difficulties, and so omnivorous with monstrosities that approach the mentally impossible is a case of straining at one poor gnat and swallowing a whole caravan of camels. Like others I find it difficult to imagine an idea affecting a brain molecule; but I think I am also like nearly everybody else when I find it impossible to believe that thought and purpose have had nothing to do with building up human civilization and creating human literature and philosophy. How the opponents of Interaction manage to believe these things I confess I find it very difficult indeed to imagine.
I know this is not decisive. I know indeed what the upholder of Naturalism will probably reply. His reply, in fact, will be in substance not very different from that of the Red Queen to Alice, after Alice had told her there were some things she couldn't believe. "Can't you?" said the Queen in a pitying tone. "Try again; draw a long breath and shut your eyes."
"There's no use trying," said Alice, "one can't believe impossible things."
"I dare say you haven't had much practice," said the Queen. "When I was your age I always did it for half an hour a day. Why, sometimes I've believed as many as six impossible things before breakfast."
When one remembers the materialistic assertions that consciousness is matter and that logic is ground out by mechanical processes, the parallelistic thesis that the non-existent brain determines wholly the existent mind, the neo-realist denial of all reality to the subjective, the behaviorist identification of thought with the action of the larynx, one sees that Naturalism, like the Red Queen, has had some practice in believing the impossible; that in fact it would be stating its case with great moderation, not to say modesty, if it should claim that sometimes it had believed as many as half a dozen impossible things before breakfast. Moreover, the Red Queen's formula for belief is the one which must necessarily be adopted if we are to imitate successfully the remarkable achievements of Naturalism in the arousal of faith in the impossible, -- namely, "Draw a long breath and shut your eyes!"
I too can believe a good many things with my eyes shut; but if I keep them persistently open I becomes less and less impressed with the ambitious claims and the false dignity of Naturalism. And by Naturalism I mean, of course, not natural science but the unempirical philosophy, the a priori theory, which would extend the formulæ of natural science into spheres in which the true scientist has no ambition to advance. Taken in this sense Naturalism appears to me the great hoax of our times. Its seemingly adamantine fortifications, with their tremendous and terrifying guns, are mostly camouflage. Its walls are enormously impressive; but like those of Jericho they will fall before whosoever has the courage coolly to examine their foundations -- and to blow upon the trumpet.
This being the case, I must also say frankly that Interaction seems to me the inevitable outcome of our argument. It is the only view that makes history and human life really intelligible. Indeed if we were right in believing (and we have seen no reason for doubting) that Materialism, Parallelism, Interaction, and the denial of the mind-body relation are the only answers to our problem worth serious consideration; and if we were justified also in our conclusion that the relation is a real one, and that neither Materialism nor Parallelism is tenable, and that the alleged difficulties of Interaction are much slighter than at first they seem, it follows that we are plainly compelled by the very process of elimination to conclude that Interaction is the true doctrine and that mind has an independence and a power of its own. And now we can begin to understand the wild attempts of Materialism, Parallelism, Neo-Realism, and Behaviorism to invent some method by which Interaction might be avoided. Not for nothing were the strange twistings and writhings of these theories. For if Interaction be accepted a momentous turn has been taken in our philosophy. We shall namely have given in our assent to a Dualism of Process with the universe.
The consequences of such a Dualism of Process are fateful and endless. There is no time to deal with them this afternoon and they must be postponed for consideration to our final lecture. But we can, I think, already begin to form some notion of what is involved in this Dualism of Process, to which, by the force of logic and of experience, we seem to have been driven. Such a world view will mean a profound, if not a fundamental, distinction between matter and spirit. It will mean the return of all sorts of possibilities against which the iron gates of Naturalism were forever closed. It will mean that perhaps Plato and Christianity were right after all.
James Bissett Pratt
Matter and Spirit: A Study of Mind and Body in Their Relation to the Spiritual Life (1922)
(footnotes omitted)
Monday, June 18, 2012
On Anti-Semitism in Europe
Walter Russell Mead has been blogging a lot on European anti-Semitism recently: see here, here, here, here, here, here, and here (and actually read them; Mead is a voice of deep moral clarity). On one of those posts I left a comment regarding something I experienced last month. I was getting off a train at Brussels-Midi and, while waiting for the train to stop, stood by a door that had the "danger: electricity" sign on it to warn passengers not to open it. Under the sign, someone had scrawled, "Only Jews inside".
I stood there staring at it for about half a minute as it sank in. I was standing on a train in western Europe looking at a casual statement wishing death to Jews. It made me sick to my stomach.
I stood there staring at it for about half a minute as it sank in. I was standing on a train in western Europe looking at a casual statement wishing death to Jews. It made me sick to my stomach.
Sunday, June 17, 2012
Popular media finally gets around to covering medieval philosophy
I Want a New Left points to an article on Ibn Rushd a.k.a. Averroës. I wrote my M.Phil. thesis on Averroës and originally planned to do my Ph.D. dissertation on him, Ibn Bajjah (Avempace), Ibn Tufail, and Ibn Sina (Avicenna), and how they were influenced by Alexander of Aphrodisias. I still hope to be able to come back to that and write it someday.
Subscribe to:
Posts (Atom)
