# The Challenge of the Ultimate Prime Number

Andreassen characterizes my previous discussions with him concerning eliminative materialism (the doctrine that nothing but matter exists) in this way:

I am happy to present the evidence and argument that convinced me, if only we could get past the jeer of “Meat robot!” that silences all serious discussion of the point.

Sir, if the only thing halting serious conversation on this topic is alleged untoward antics on my part, let me ask you ten questions on the topic. I make no statements and propose no arguments, and leave you free to answer however you will. They are questions, pure and straightforward.

Question One: Is there or is there not an Ultimate Prime number? That is to say, is there a prime number of which there is no higher number on the number line which is also a prime?

If there is no Ultimate Prime, is there an infinity of primes, such that given any prime number there is always another prime number higher than it?

Question Two: If you know the answer to question one, by what means do you know it?

Did you make an observation with your eyes at a particular time and place; or did you make a deduction from axiomatic first principles; or do you know the answer by some other means?

Question Three: If you made an observation at a particular time and place of the infinity of primes, please tell me where and when you stood, and what you looked at, so that I may look at this infinity of numbers with my own eyes for myself, and count them as you have done, and so confirm your observation.

If on the other hand, it is not an observation, is it something known by deduction from self evident first principles?

(For your reference, and in case you ask, I myself hold that the nonexistence of an Ultimate Prime is a formal truth which is deduced from self evident first principles. The argument can be found here: http://aleph0.clarku.edu/~djoyce/java/elements/bookIX/propIX20.html If you came to this same conclusion by this same or a similar argument, you need not give it in full, merely refer to it.)

Question Four: If it is true that there is an infinity of primes, is this true in all times and all places and under all conditions? Or are there times and place and conditions where it is not true?

Question Five: If you answered that there are an infinity of primes under all conditions and in all times and places, does this include times and places and conditions which neither you nor I nor any human being nor any rational being whatsoever has observed or can possibly observe?

Question Six: Can a truth about a time or place or condition no observer has or can observe be confirmed by empirical observation?

Or, in other words, are there non-empirical truths?

Question Seven: If materialism is true, is it not the case that every fact is material fact?

In other words, is it true that if materialism is true, then there are no non-material facts, no non-material truths?

Question Eight: If it is true that all truths are material truths, and if empirical observation is the only means of gaining knowledge of material truths, then does it follow that all truths are empirical?

In other words, is it true that there are no truths known only through deduction from self evident first principles?

Question Nine: If the statement “there is an infinity of primes” is true and if no true statements can be made about nonexistent things, about what existing things is the statement true?

Does the subject of the statement (the infinity of primes) exist in the physical and material sense that the rocks underfoot and stars overhead exist?

I am including my question all prime numbers, including any unimagined prime numbers no human brain has thought nor contemplated as yet.

Does the infinity of primes have material existence, that is, do the prime numbers display mass, location, extension, duration, and other material properties?

Question Ten: Do you agree that if the infinity of primes has material extension, that is, if they occupy space, either brain space or outer space, then these primes, being endless in number, no matter how small their volume nor where located, would fill up all the space in the universe?

If so, does this describe the universe we see empirically around us?

If any questions are based on some unspoken axiom you do not grant, I am happy to discuss that axiom once you identify it.

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A word of explanation to Andreassen:

Perhaps you forget, sir, that the last time I tried to ask you about your beliefs using the Socratic method, your sole reply was to say it was insulting of me to ask you questions.

Your past behavior shows you lack the will to have a conversation on philosophical matters. You have voiced scathing contempt for philosophy, so your repeated attempts to discuss such topics is odd.

Your answers in previous conversations have been flippant and irrelevant, leading me to believe that you neither understand the issues, nor admit when you do not understand, nor are curious enough to ask.

Worse, when trapped by an awkward question, rather than admit anything damaging to your case, you make claims you simply know not to be true.

You claim to have measured the width of the line of demarcation of the horizon at sea; you claim to have measured the duration of the abstract and formal concept of checkmate; you claim to be able to see into my head and to know what I can and cannot visualize; you claim your thoughts fly around your desk, and have mass; you claim access to a sense impression unknown to the rest of mankind which allows you to sense the mass and position of atoms inside your skull.

None of these are honest mistakes. You cannot honestly think you performed a careful experiment last October to measure the width of the line of demarcation of the horizon with a spectrometer, when actually you were just staring at the ceiling and imagining what such an experiment might produce were it performed.

These are all your opinions of what empirical experiment would produce if metaphysical materialism were true, but not an honest report of a real empirical experiment.

Past experience argues that it is vain to engage you yet again on this wearisome topic. But out of an exaggerated and chivalrous respect for justice, merely because you allege not to have been given a full and fair chance to air your views, I will make the gesture of reopening the conversation.

What I will not do is answer any replies which resort to your usual tactics, so please stick to the topic and be straightforward. Anything less than sober answer to the actual questions asked, I reserve the right to ignore or delete.

Frankly, my time is short, so I would prefer you not to reply, but honor requires I make this gesture.