Dear Banjo,

You obviously misunderstood my TECHNICAL (semantic?) question of whether one should speak of SOMETNIG or a CONCEPT OF SOMETHING as being or not being a figment of imagination.

I think we agree on what is the difference between between us two as far as the basic world-view presuppositions (about what counts for reality) are concerned, no need to defend yours. I was not attacking it or trying to convert you.

Mathematical entities are the best example I can think of where we all agree they “exist outside of time” (and agree with Eugene Wigner about their nevertheless “unreasonable effectiveness” in understanding and handling the physical world).

I mentioned the Mandelbrot set as an example of such, not as an example of a life form or figment of imagination as you seem to suggest.

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Dear George,

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You point out :

« You obviously misunderstood my TECHNICAL (semantic?) question of whether one should speak of SOMETNIG or a CONCEPT OF SOMETHING as being or not being a figment of imagination »
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You are quite right to call me to order, George. I did not misunderstand. I overlooked that point. Sorry about that.

The OED defines “imagination” as “the faculty or action of forming new ideas, or images or concepts of external objects not present to the senses”. Whereas it defines “a figment of the imagination” as “something that someone believes to be real but that exists only in their imagination”.

I guess our mind constructs “concepts” of everything, but when it constructs a concept of something which does not exist, that particular “concept” is “a figment of the imagination”.
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You explain :

« I think we agree on what is the difference between us two as far as the basic world-view presuppositions (about what counts for reality) are concerned, no need to defend yours. I was not attacking it or trying to convert you »

I totally agree. Sorry to give you that impression. It was not intended but simply due to my previous oversight as avowed above.
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You then precise :

« Mathematical entities are the best example I can think of where we all agree they “exist outside of time” (and agree with Eugene Wigner about their nevertheless “unreasonable effectiveness” in understanding and handling the physical world) … I mentioned the Mandelbrot set as an example of such … »

Yes, I understand what you mean, but that is an existentialist problem I am incapable of solving.

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(Continued …)

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(Continued …)

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As I tried to explain in my previous post, the only “time” I am capable of observing is the present. Events are different. Some have already occurred. Others are yet to come. But neither you nor I, nor anybody else – nor any other life form – can live in the past or in the future.

So if “time” is the present, the next question is : “how long is that ?”. An instant ? Then it’s no time at all. But if we consider we live constantly in the present, then the present may be defined as the lifetime of each individual.

However, the birth of an individual is not the beginning of life. It is its continuance. Living cells are constantly renewed, some more frequently than others. Life is relayed by the individual members of each species, in exclusivity, to the next generation of the same species. Life is a self-sustaining process that shows no signs of ceasing.

Perhaps it could be argued that the present is not just limited to the lifetime of each individual but to the process of life itself. In this case, as long as there is life there is time. No life, no time. No past, no present, no future.

Therefore, before we can conclude, as you suggest, that “mathematical entities … exist outside of time” we must determine if “mathematical entities”, as such, exist in nature, independently of all life forms.

Please correct me if I am wrong, but I don’t think they do. According to the OED, “mathematics” is defined as :

« The abstract science of number, quantity, and space, either as abstract concepts (pure mathematics), or as applied to other disciplines such as physics and engineering (applied mathematics) »

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Dear Banjo,

Thanks for an interesting post. Already Augustin of Hippo said “What then is time? If no one asks me, I know what it is. If I wish to explain it to him who asks, I do not know.”

Maybe you are right that my sentence in question should have “concept of God” as you suggested. After all, every concept is a product of imagination (the concept of dog as well as the concept of unicorn), so the accent is on “figment” which entails the verb “exists” that is closely related to what is considered “reality”. Different philosophers see this differently, and apparently so do we two.

I wrote something about that in www.onlineopinion.com.au/view.asp?article=14464 trying to show that the concept of reality is not simple even when one restricts oneself to physical reality. I illustrated this on the three “worlds” of Roger Penrose - physical, mental, and mathematical - that are interconnected by three enigmas.

In particular, there is no unequivocal answer to your question of how mathematical entities “exist” - they are certainly related to our mental processes (do mathematicians discover or invent them?) and also to the physical world - nature, as you call it - with their unreasonable effectiveness.

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Dear George,

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Thank you for the link to your article on “The nature of reality”. An interesting (and amusing) intellectual exercise …

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