The ultimate tactics of self-referential systems by Christine Cordula Dantas

Dear Sylvain Poirier,

1) You wrote: "(...)it seems that you are just making your "conjecture" that "Mathematics is irreducible to anything else that is not itself mathematically expressible" trivially true by the mere fact that everything that exists would be mathematically expressible, so that of course, everything which exists, such as mathematics, will be irreducible to any non-existing thing."

You seem to be making a confusion between object and property. I wrote on page 3:

"When a physical law is expressed mathematically, no evidence for the "truth" regarding the law actually surfaces, but only a guarantee for the logical foundation of the outcomes resulting from the implemented assumptions. In fact, any application of mathematics (seen as a form of language) to physical problems just brings forth a relative valorization of their logical evidence, but not the evidence, per se, of their truth."

The observational fact that everything can be mathematically expressed does not imply that everything is fundamentally mathematical. Such observations only make evident a phenomenological recognition made by our brains that sensible objects are logically intelligible, hence mathematically expressible. But to claim that there is an ultimate reality that is mathematical because everything that we perceive can be mathematically expressed is not implied, as far as I see. My conjecture does not make any reference to that.

2) "Do you mean, then, that the circularity problem you point out with defining mathematics in mathematical ways, is a problem that probably cannot be resolved ?"

I only claimed it to be very hard.

3) "I recognize the difficulty of making a clear and short essay, however I do not consider it a justification for writing nonsense; I cared myself to be clear in my own essay(...)

Congratulations to you for having succeeded. You have the right to claim that my essay is nonsense, and I am trying my best to respond to your criticisms. However, I am not unexperienced nor malicious. I would never waste my time or that of potential readers by submitting "nonsense".

I wrote: "The proposed conjectures are philosophical, a fact that could be unattractive to some readers. However, these ideas could eventually be expressed in a more concrete or formal way, so they should be regarded as preliminary for the purposes of the present essay."

I have clearly stated that my ideas are preliminary, under development, and are not presented in a formal way. You have the right to criticize my essay, to dislike it and call it nonsense. However, I find your tone a diminishing one, and unfortunately I do not see how we can continue in a constructive way. Thank you for removing my name from your site.

Regards,

Christine

Hi Christian,

It's very nice to meet you again, my near-namesake fellow! I look forward to read your essay, it was already in my list. Thank you for reading my essay with the right "spirit" and for placing your comments here.

I think you saw the point of my essay (equally valid to previous contests): to bring forth some unusual ideas (at least, I think they are unusual). I do not see the point of participating in the FQXi contests if one cannot bring unusual, different ideas, even if they are not fully developed. If they are fully developed, there is no place for them in a FQXi contest, at least the way I see it. So it is true that I sacrifice rigor but I think it is worthy to a point. Thanks a lot to have understood that. I also think you share the same ideal in your essays, so I am looking forward to reading yours opportunely.

As for your question #4, it is implicit, deep down in what I wrote, that this must be a result from an autonomy property, and deeper down, it is about freedom. I do not make this clear, as I cannot develop such ideas any further, not in the present moment. This relates to free-will.

Good luck!

Christine

Dear Joe,

No need for apologies, so please do not worry about it at all. You may place your criticisms to my essay here any time at your discretion and if you think there are connections to your essay, you can also mention them by giving the specific points.

Take care and good luck.

Christine

I would like to add this fine quote by Fichte:

The highest interest, and hence the ground of all other interest, is that which we feel for ourselves. Thus with the Philosopher. Not to lose his Self in his argumentation, but to retain and assert it, this is the interest which unconsciously guides all his Thinking. Now, there are two grades of mankind; and in the progress of our race, before the last grade has been universally attained, two chief kinds of men. The one kind is composed of those who have not yet elevated themselves to the full feeling of their freedom and absolute independence, who are merely conscious of themselves in the representation of outward things. These men have only a desultory consciousness, linked together with the outward objects, and put together out of their manifoldness. They receive a picture of their Self only from the Things, as from a mirror; for their own sake they cannot renounce their faith in the independence of those things, since they exist only together with these things. Whatever they are they have become through the outer World. Whosoever is only a production of the Things will never view himself in any other manner; and he is perfectly correct, so long as he speaks merely for himself and for those like him. The principle of the dogmatist is: Faith in the things, for their own sake; hence, mediated Faith in their own desultory self, as simply the result of the Things.

But whosoever becomes conscious of his self-existence and independence from all outward things--and this men can only become by making something of themselves, through their own Self, independently of all outward things--needs no longer the Things as supports of his Self, and cannot use them, because they annihilate his independence and turn it into an empty appearance. The Ego which he possesses, and which interests him, destroys that Faith in the Things; he believes in his independence, from inclination, and [seizes] it with affection. His Faith in himself is immediate.

--Fichte,

Introduction to Fichte's Science of Knowledge

http://en.m.wikisource.org/wiki/Introduction_to_Fichte%27s_Science_of_Knowledge

Dear Thomas,

Thank you for the kind words... I am flattered! Yes, I have read several books and short stories by Jorge Luis Borges, including Bioy Casares, I enjoy Latin American Fantastic Fiction. Yes, I'll be reading your essay as soon as time allows. Good luck and best wishes,

Christine

Dear Michel,

Thank you for reading my essay and posting your comments. It is perfectly fine to be not satisfied, I certainly am not myself, as what I wrote was just some tentative first steps into my investigation. My points are completely compatible with different kinds of mathematics, in fact I firmly believe that is possible and even quite natural. I need more time in order to write a more detailed comment, though. As for your point on Tegmark, I disagree. See my last answer (point # 1) to Sylvain a few comments above.

Best wishes,

Christine

Dear Christophe,

Thanks for reading and for your question.

In an extrinsic view (but see last paragraph below), a self-referential object X would be equipped with a series of maps to itself, the endomaps {a}, and its evolution to another self-referential state, Y, with endomaps {b}, would be carried out by some extrinsic map, say, f: X -> Y, wherein the composition f o a = b o f holds, for all a and b.

But for an intrinsic view, the {a} have a new meaning within the system: a map a_i operates with itself and this must result in a "change of state" within X. That is, the composition a_i o a_j = a_k (not necessarily i=j) results in a new state Y, with self-referential operators {b}, mixed from the original ones {a}, which I suppose to be countably infinite. This requires an "autonomy" for the evolution, which is fed by a combinatorial, potentially non-exhaustive, set of endomaps. This self-characterization acquires an internal meaning as "active", and externally as "autonomous".

On the other hand, the external map f has no meaning inside the self-referential object. So it is difficult (or impossible) to characterize it-- a different mathematics, perhaps?

Best,

Christine

Dear James,

Yes, time runs... And my reading list is late. Hope to be able to read yours and others! :/

Best,

Christine

I've read it many years ago. It's one of my favorite books.

Regards,

Christine