Marko Tervio tervio@katk.helsinki.fi sent me his solutions to several of the problems at the end of the last essay. Most of them are excellent. He also posed a new problem that I have added to the list.
Indented regions contain the questions from the last essay. The following text is from Mr. Tervio's letter. Lines in italics are my comments.
1. Paraphrased from Zen and the Art of Motorcycle Maintenance: Scientists say that ghosts don't exist. That is, they only exist in people's minds. Yet the laws of science only exist in people's minds. They cannot be directly perceived in nature. Thus if one is to be completely scientific, one should not accept the existence of either ghosts or the laws of science.If a thing exists in someone's mind, it is a thought. If a thought of something exists in someone's mind it doesn't mean that that something automatically exists as a physical entity in reality. A ghost is an example of this. I think about a ghost, a thought of a ghost exists, a thought being a set of (in this case false) information in my brain. My thinking of it doesn't physically create it from nothing. The laws of science in peoples' minds are information about reality, based on careful and thoroughly investigated perceptions of reality. The laws of science are explanations for the behavior of actual physical objects in reality. This behavior can be perceived in reality while ghosts can not be perceived in reality. The writer of Zen has confused the identity of physical objects and of sets of information; thoughts.
Excellent answer.
2. From one of logician Raymond Smullyan's books: "Santa Claus exists if I am not mistaken. This sentence is certainly true and hence, I am not mistaken and therefore Santa Claus exists."If R.S. is not mistaken about the truth of the first sentence, he may still be mistaken about other things, such as the existence of Santa Claus. What he really states in the first sentence is not clear, the sentence has no truth value. Mistaken about what ?
Precisely. First the phrase ``I am not mistaken'' refers to the first half of the first sentence. Later it refers to the entire sentence.
3. God is that being than which no greater entity can be conceived. Now either God exists or he does not. If He does not then a greater entity than God can be conceived, namely one identical except existing. Thus God exists. (Classic.)The third sentence is most illogical. If something does not exist its properties can not be compared with others' since it has none. The first sentence can't be claimed to be true unless the existence of God is proven first. And why should there be a limit to how great entities can be conceived. So you can conceive a God, well I can always conceive of a bigger God! If a certain entity can be conceived it doesn't turn that concept into a real physical entity. I can, by the way, conceive of a 7-headed dragon that eats gods for breakfast...
Since the term ``god'' has not yet been given precise meaning (in fact it does not yet have any meaning at all), the law of the excluded middle cannot validly be applied to it. Thus the second sentence is also in error. Again we say, as emphasized in previous essays, that laws of logic cannot be applied when meaning is excluded.
It is very dangerous to compare existent entities to non-existent non-entities. To form a comparison between two things it must first be established that they both are, in fact, things. Non-existent non-entities do not qualify.
If you feel whimsical you can always respond as follows:
``Consider a being greater than god. This being clearly cannot
exist because god is the greatest being that exists. So here we have a
being greater than god that doesn't even exist!''
4. God is the most perfect entity imaginable. Perfection includes existence. Thus He must exist. (Classic -- a variant of above.)Explain why and how God is the most perfect entity imaginable. Perfect in what? I can imagine a circle and it is most perfectly round, actually it is indefinitely perfectly round, how could anything be more perfect in anything than a circle is in its absolute roundness? Is circle God? The word imaginable is important here. If something is imaginable (everything is) that only makes it a thought. If He is to you the most perfect entity imaginable than he does exist, and he is a thought in your imagination, a number of brain cells turned on and off in a certain pattern, information. Perfection of an imaginable entity includes existence as an imaginable entity.
Good. An analysis of the intended usage of the word ``perfect'' shows that the question of god's existence is being begged.
5. From one of Raymond Smullyan's books: ``Surely there are unicorns, in concept, but are there existent unicorns? Well, either existent unicorns exist or they do not. But it is impossible for existent unicorns not to exist. Hence they do.''This is a lot like (1). The existence of a concept, a thought and the existence of a physical entity are deliberately confused here. It would be impossible for existent unicorns not to exist. The fact that this sentence is true does not in any way create existent unicorns, although R.S. seems to think so. He's just trying to show what kind of sentences illogic can produce, isn't he?
R.S. presents this as erroneous reasoning.
The statement ``existing unicorns exist'' is a tautology stating only that before an entity can be considered an ``existing unicorn'' it must first be established that it exists. This does not mean that any entities so qualify.
Consider the phrase, ``A car has doors.'' This means all cars (or, if you prefer, cars in general) have doors. Arguably, this sentence would be vacuously true if no cars existed. Now consider the following, ``A car is in my garage.'' This means at least one car is in my garage. This sentence could not be true if no cars existed. Even the word ``an'' can be misused!
8. How do you know that you exist? (Classic)Only existent entities can have properties. Nonexistence can't have properties. Consciousness is a property that I have since I am thinking about this question. Therefore I exist. How do self-transcenders refute this?
Excellent. I don't know how self-transcenders refute this. They try, though. Mostly they just say that self-transcendence is one of those truths that defies human understanding. I agree with them, except for the inclusion of the word ``truth''.
I suppose their next question in response to ``consciousness is a property I have since I am thinking about this question'' would be ``how do you know that you are thinking about this question?'' There is just no pleasing some people.
I would answer the original problem as follows:
``Only existent entities can question, know, reason, and think. Since I do all of these, I exist. The knowledge that I exist is implicit in every percept or concept that I have. All of this is obvious upon introspection and directly available to any human being. If you claim that you do not know this, you are either lying or hopelessly muddled.''
11. One of Zeno's classic paradoxes of motion: ``In a race between the fleet Achilles and the slow Tortoise, we give the Tortoise a small head start. Now, when we begin the race, Achilles must reach the Tortoise's starting position prior to overtaking him. At this point, the Tortoise will have moved ahead a small distance and the original situation has returned. Thus Achilles can never catch up to or pass the Tortoise.''This paragraph includes the unstated assumption that the Tortoise moves at a constant speed, whereas Achilles slows down more the closer he gets to the Tortoise. If both the Tortoise and Achilles move at a constant speed and Achilles is faster then the total distance run by Achilles exceeds the total distance run by the Tortoise at a constantly growing length. Ultimately, that length equals and exceeds that of the Tortoise's head start.
I think this is Mr. Tervio's weakest response.
I don't see where the paragraph makes the assumption of variable speed
for Achilles. Both Achilles and the Tortoise move at different but
constant speeds. When Achilles reaches the Tortoise's starting position,
the Tortoise will have moved ahead some small but finite amount. Now
Achilles, still travelling at his original speed, must reach the Tortoise's
new position before he can overtake the Tortoise, but by the time he
gets there, the Tortoise has moved ahead. The original situation keeps
recurring.
Achilles can only pass the Tortoise after he has performed an infinite
number of such catch-ups -- if we accept the mathematical model implied
in the problem.
This problem is an example of what I call ``eating the recipe.'' The mathematical model of motion used herein (continuous motion in continuous time) is valid so long as it does not give results that conflict with reality. Here it does. Do we question reality or the model?
Some philosophers with a well-justified abhorrence of existent infinities indeed could find no resolution other than to declare motion impossible -- an illusion of the senses. Such a leap is not required.
Let us postulate an alternate mathematical model of motion that is consistent (to my knowledge) with all currently known physical theory and observation. Time flows in tiny quanta (a tiny fraction of a trillionth of a second) and motion takes place in tiny jumps (a tiny fraction of a trillionth of an atomic radius). One quantum length per quantum time equals the speed of light.
Now, Achilles moves forward a quantum length a greater percentage of quantum times than the Tortoise. At any given point he is an integral number of quantum lengths behind. At some point, he will be one quantum length behind. At each subsequent quantum time there is an increasing probability that the two will wind up at the same `point' next quantum time. Now Achilles has caught up and after further quantum times, he will move ahead.
A mathematical model of motion (or anything else) should be retained so long as it gives correct results. When it fails, reject it not reality. To do otherwise it to eat the recipe.
I am not saying that my specific quantum model should be accepted as fact. There is simply not enough evidence available. Yet, the continuous model certainly should not -- it contradicts observation and requires the acceptance of existent infinities, a self-contradictory notion. Imagine if the Greeks had used Zeno's paradox to predict `atomistic' quantized motion! They would have postulated quantum theory and reality considerations could have justified it.
Let me briefly address the mathematical finite-sum-of-an-infinite-series answers: Those answers only replace the problem of how Achilles will pass the Tortoise with the equally difficult problem of how Achilles is expected to actually complete an infinite number of steps to reach that finite sum. We understand that a series approaches a limit; it does not ever reach it and pass it! It was precisely to clean up much nonsense about infinitesimals and actual performance of an infinite number of operations that calculus was rigorized.
12. [Peikoff on Quantum Electrodynamics]If a theory can be accurately used to predict phenomena it still doesn't mean that the theory is absolutely correct. That the sun orbits the earth once every 24 hours was an excellent theory in its time. It was able to accurately predict the time of sunrise and sunset for millennia. From a certain, limited viewpoint of men it seemed to be true, the same can be true with Quantum Electrodynamics today.
There are aspects at the subatomic level that man can not yet understand or maybe even perceive fully. While scientists don't know all the things behind the phenomena they can see many of its consequences and create working theories based on the observations they've been able to make. If a particle appears to be in two locations at the same time then are we sure that we fully understood and knew the nature of that particle in the first place when it was all in one location?
Very good.
Concepts such as ``position'' (as an X, Y, and Z coordinate) and ``velocity'' (as a numerical speed and a direction) are mathematical models. ``Existence'' and ``identity'' are not. If our naive notions of position and velocity turn out to be only approximations and not valid on a micro scale, we will replace them with better ones. If QED tried to claim that electrons did not exist, had no nature, or were whatever people wanted them to be, then philosophers would need to have a word with them!
Such concepts as ``position'', ``momentum'', ``mass'', and so on are not necessarily valid outside the sphere in which they were created, that is, they are not automatically valid in every new situation without weighing evidence. Such postulates as "existence", ``identity'', and ``consciousness'' are already proven beyond all doubt and no contrary evidence has ever appeared or can appear. Such evidence `appearing' would itself subsume all three postulates! Existence, identity, and consciousness are the very preconditions for the presence of evidence.
As our sphere of experience grows, some of our concepts will need refinement. If we ever encounter other sentient life forms, for example, it is possible that our concepts ``man'', ``intelligence'', and ``sentient'' may need refinement to be useful in this new sphere of experience. They will still be fully valid in the sphere in which they were derived.
Mr. Tervio included the following `argument' that he heard from a theist. Consider it problem number 13:
``I've heard Him while I've been asleep. He spoke to me in a dream. So God is not unknowable to me. He is unknowable to you however, since you refuse to believe in Him. The only way He affects this world is that he tells truly believing people how to live right. In that way He is unknowable to non-believers. Only after you die will He affect you directly, in the other world. The other world can not be directly perceived from here, only the other way around. I don't claim that believing in God and praying will make you win the lottery or save your this life in a plane crash, all I claim is that it would make you happier in the afterlife.You may deny that I have been contacted by God in dreams since dreams can't be documented. But you can never prove the non-existence of God and the afterlife. Why would the information that my (and many other peoples', too) hearing sense has received be viewed less credibly than others?' You haven't seen the moonflights yourself either and yet you believe in them.''
He also suggested that it would be reasonable for me to believe in God ``just in case'' he exists (!), if he doesn't I'll just have lived a righteous life and if he does then I'll be better off after death...
Beautiful! What a potpourri of errors. Where to start?
One may find it ``reasonable'' to believe in god ``just in case'' he exists, but is it possible? Can a human being truly twist himself into believing something because he wants to or calculates it beneficial for him to do so? I certainly cannot!
Analyze how the word `believe' is being used. You are being asked to embrace concepts not just without evidence but without meaning. Where does that leave the rest of your intellectual life, your self-esteem, and your ability to employ reason effectively?
In other words, this argument only works once it is agreed that it is meaningful to discuss the possibility of god's existence. It is impossible to believe something that you do not understand -- unless verbal assent to meaningless words is all that you require of `belief'!
As far as living that way being ``a righteous life,'' the question of god's existence and attributes has been begged. If god exists and he is all good and he told us how to live a righteous life accurately then, if you follow god accurately you will lead a righteous life. Since you presently do not believe any of those things, you cannot be convinced that a belief in god will lead you to a righteous life.
When I discuss morality, you will see what I consider to be a righteous life and why. You will find that it disagrees with the morality of all religions (altruism) in many respects. Since it is derived from reality, and god's claims conflict with it, we have clear reason to doubt assertions of omniscience and omni-benevolence. Those who advocate a morality that is valid and based on reason have no need to appeal to a god or justice in an after-life to buttress it.
There remain many errors in logic and reason to address in this beautiful submission. Some possibilities:
Objectivism, incidentally, does not devote much attention to the question of the existence of god. It regards the entire matter as a non-issue -- an academic exercise of analyzing an error in reasoning.
If, for example, a claim is made that the universe requires a creator, the response `if god is self-created why not the universe' is an implicit demand for infusion of content into the otherwise non-concept ``god''. If this cannot be done, as is always the case, what is left to discuss?
Objectivists would rather devote their time and energies to the many meaningful, powerful, and relevant considerations that evolve from the underlying premises of Objectivism. They prefer to devote time to positives rather than negatives -- to issues with true relevance to man's existence.
Incidentally, men of religion are not bothered by heated disavowals of god's existence. One theologian has openly stated that god will finally be dead when man becomes indifferent to the issue of his existence or non-existence.
Mr. Tervio included a profile of himself that I thought the rest of you might find interesting:
I'm afraid as a first year College student I don't yet have all the time and effort that a thorough learning from this mailing list would probably take... I am however puzzled by the fact that I'm reading my first real introduction to any philosophy from this marginal (?) but reasonable school of thought. I always thought that philosophers are generally weirdos who have lost contact with reality and who aren't even sure whether they exist or not. I've often kept my mouth shut because they're such respected historical figures. The few philosophic statements I've heard had made me avoid all philosophy, but now I think I'll take a Philosophy course or two next year and challenge the teachers with the principles and methods that I hopefully will learn from this list. (Don't worry, I won't claim to represent `objectivism').
Don't worry about ``representing objectivism''. Represent meaning, reason, and reality -- no Objectivist could do more.
Unfortunately, a lot of philosophers are weirdos who have lost contact (more precisely, never acknowledged contact) with reality. I always wondered what it was they claimed their arguments referred to.
Give 'em hell, Mr. Tervio!
One word of warning though: I wouldn't advise anyone to take a class when they expect to disagree with the professor openly. It just annoys the rest of the class; most only want to get a good grade and don't care what's true and what's false -- what's true is what the professor will grade as truth. If you cannot keep silent, make your comments brief and powerful, then try to shut up.
Finally, Mr. Tervio included the following, excellent signature:
Ask not what you can do for your country
Ask what you can do for you
And how your country can stop preventing you from doing that