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‘The superultramodern doubt’ is the first and the most basic principle of my ‘Superultramodern science / philosophy’.

Theorem:
Anything may be possible.

1. That which could otherwise be believed to be absolutely (or 100%) certainly impossible at present could be possible as the intellectual capacities of the believer may be limited. That is, the proposition/s, for example, that are otherwise thought to be absolutely certainly true could be false.

Controversy:

1. Cartesian doubt vs. Superultramodern doubt

The Cartesian doubt is the doubt raised by Rene Descartes on everything except his own existence as he is a thinking, specifically doubting, substance. Thus, the Cartesian doubt is the principle that ‘anything may be possible, except the impossibility of one’s own existence as one is a thinking, specifically doubting, substance’. The Cartesian doubt thus contradicts the superultramodern doubt.

Let’s for a moment agree with the Cartesian inference that ‘I think (specifically doubt) therefore I am’. But still it could be that it is a wrong way of thinking. I naturally think that as there is a doubt there has to be someone who doubts. But it could be a wrong inference. My language, for example, always refers to ‘I’ because I cannot think otherwise. But I can very well think that I could be wrong. The basic thought involved in the justification of the theorem of the superultramodern doubt appears to be more fundamental than the thought mainly involved in the Cartesian doubt.

The Cartesian doubt is also referred to as ‘Universal Doubt’. However, Cartesian doubt is not really universal as it is not applicable to itself or one’s own existence. The superultramodern doubt is universal as it is even applicable to itself or one’s own existence.

2. Certain universal doubt vs. Uncertain universal doubt

‘Certain universal doubt’ would be the principle that ‘anything is possible’. In contrast to it, the principle of superultramodern doubt that ‘anything may be possible’ would be ‘uncertain universal doubt’. Now, quite apparently, as a universal doubt is all-inclusive, it applies to itself (or is self-referential), and thus should be uncertain.

Philosophical Implications of the Superultramodern Doubt:

1. All axioms as 99.99% certainly true

All of the propositions which otherwise appear to be 100% (or absolutely) certainly true should now be supposed to be 99.99% certainly true. In other words, it should be believed that it is 0.001% likely that those axiomatic propositions are false. An example of such propositions would be ‘if p implies q, and q implies r, then p implies r’.
This 0.001% slightest margin in the belief system should be reserved/retained for the sake of the superultramodern doubt.

2. No belief in a proof

Implication 1 implies that there should be no belief in a (mathematical) proof. Something may actually have been proved, but it would be irrational for one to believe that it has been proved. (Here the term ‘proof’ means definite, absolute, or certain resolution of a problem.)

3. All mathematics as philosophy

Implication 2 implies that all mathematics is hypothetical and thus philosophical.

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In continuation of my discussion on infinity and its implications with the divine, I should mention that the concept of there existing infinities beyond imagination is quite difficult to comprehend. If you read my poem, “How Can this Be? you read in verse the proof that shows clearly that there is no such thing as one kind of infinity. (See my ezine article “How Can this Be”) The extension of this most curious fact is that there are actually an infinite number of infinities!

Occasionally I wax metaphysical in conversations with my uncle and the other evening we were discussing some points regarding the spiritual realms. In passing, I brought up the topic of infinity and I asked him his impression of it. His response, which is typical of most people, is that infinity is just thatinfinity: something that never ends. But how do we make this vague notion somewhat more concrete? I pointed my uncle’s attention to the set of natural, or counting numbers. This set comprises the familiar numbers {1, 2, 3, …}. The numbers go on and on, falling like dominoes, and never reaching a “biggest one.” This process is easy to grasp and presents no ordinary difficulty for the average person. What does become difficult to understand is why the infinity typified by this set of numbers is not unique.

Now let’s delve a little more deeply into this curious set of numbers and the topic of infinity in general. This set of counting numbers obviously never ends. If you have ever seen a chronometer counting hundredths of a second, then you have seen how fast the digits representing the hundredths of a second whiz by, not appearing for any length of time sufficient to allow recognition of the appropriate digit. And this is for hundredths of a second. Imagine the same chronometer counting off thousandths of a second. Now imagine this going on from, let us say, ten thousand years ago and continuing for another ten thousand years, starting with 1 and such that each thousandth of a second would represent the next sequential counting number. Think of how far along in the set of counting numbers you would be. We could actually compute the number but we are only interested in trying to conceptualize how large potential infinity could be.

Now that we have this huge number in hand, we could do whatever we wanted with it to project ourselves much further out in the set of counting numbers. We could multiply it by itself ten times (the mathematical way of saying we can raise the number to the tenth power); we could multiply it by itself a hundred times, a thousand times, and so on. We could then take the largest product and do the same process all over again. How big is this set?

This set is so largenever ending in factthat we should be able to use it to compare to anything else that is infinite, right? Wrong. And in a continuing article on this most fascinating subject, I will discuss how this notion of one universal infinity is completely wrong. Thus, if sets of numbers can shatter our preconceived notions of a concept like infinity, which is more or less universally accepted as something that is real, what more can we uncover by plunging into the mysteries of numbers and mathematics in general? Stay tuned……

Joe is a prolific writer of self-help and educational material and an award-winning former teacher of both college and high school mathematics. Under the penname, JC Page, Joe authored Arithmetic Magic, the little classic on the ABC’s of arithmetic. Joe is also author of the charming self-help ebook, Making a Good Impression Every Time: The Secret to Instant Popularity, the original collection of poetry, Poems for the Mathematically Insecure, and the short but highly effective fraction troubleshooter Fractions for the Faint of Heart. The diverse genre of his writings (novel, short story, essay, script, and poetry)?particularly in regard to its educcational flavor? continues to captivate readers and to earn him recognition.&

Joe propagates his teaching philosophy through his articles and books and is dedicated to helping educate children living in impoverished countries. Toward this end, he donates a portion of the proceeds from the sale of every ebook. For more information go to http://www.mathbyjoe.com

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