Bob Allen says:

Hi Perry,

Somehow – you seem to be missing the point of the necessity of taking things slowly so that all of the details find coverage along the way. Obviously, you appear not to want to answer the issue that I raise in Comment 10 on Page 3.

You appear to want to “jump the gun” without going through all of the details of my proof.

I can’t possibly provide you with what you want as “proof” of detail without having the slow, step-by-step agreement or disagreement along the path so that you will be able to see and understand what the detail is. I am trying to remove any and all possibility that you won’t be able to understand the step-by-step process by which one clearly sees that DNA is in fact a naturally occurring code – and just one naturally occurring code that disproves your overall claim.

It is totally up to you if you choose to respond or not respond to my Comment 10 on Page 3. I am only interested in taking the step-by-step approach in dealing with this critical issue of DNA being a naturally occurring code. As I’ve indicated earlier, I have reviewed the entire thread – and have even added comments to the thread – on the FRDB Web site – where you had your famous debate with a number of Atheists. Within that review, I noticed that a great number of folk “jumped the gun” in the discussion – thus a great deal of misunderstanding arose. I don’t want that type of misunderstanding to arise here in this discussion between you and me. That is why the slow and steady, step-by-step process of assembling the details is so important.

Bob Allen

Bob Allen says:

Hi Perry,

I’m glad to see that you agree with me with the 13,700 Million years ago origin of the universe from the Big Bang onward, Planck time, and the synthesis of elements heavier than Hydrogen through numerous Supernova explosions, etc.

There are major two large areas of disagreement between you and I so far. The first is that brought up within my Comment # 14 on page 3. Your response in Comment #15 of page 3 presents the second large area of disagreement. This is where you assert the position that – “Physically speaking I think the universe is a closed system. I believe that the existence of information is proof that it is affected by intelligence outside of that system.”

Your assertion that the “existence of information is proof that it is affected by intelligence outside of that system” does NOT follow current cosmological models. Within the current cosmological models, there is NOTHING outside of the system of the Universe from the Big Bang onward. In the last entry of the discussion inter-change beginning with Comment 5 on page 2, you assert that you accept the current cosmological models of the Universe. In Comment #15 on page 3, you assert that there is Intelligence that exists outside of the Universe from the Big Bang onward.

You and I need to clarify this second area of disagreement prior to being able to discuss anything further about happenings in our Solar system – beginning with the creation of the Sun – about 6,500 Million years ago and the creation of the Earth – about 4,500 Million years ago. I’m assuming that you agree that DNA did NOT exist prior to the appearance of DNA upon the Earth. However, before being able to discuss the appearance of DNA upon the Earth, you and I must deal with the assertion that you make that there is Intelligence outside of the current Cosmological Theories of the Universe from the Big Bang onward.

Bob Allen

Bob Allen says:

Hi Perry,

Now I see that you and I are finally getting to the meat of a number of disagreements between the ways that you and I not only look at the Universe as a whole, but also most importantly, at the way in which the Universe evolves from the Big Bang onward – and the way that evolution happens upon the Earth. Of significant importance in all of this is the basic notion of Information, which wholly finds expression through Symbols and Symbolic Forms.

Of significant importance in the discussion between you and I to date, is that of the issue what comprises the current cosmological models – of Cosmic Evolution from the Big Bang to the moment in time in which the Earth finds creation – about 4,500 Million years ago.

Your contention is that “There HAS to be something outside of the universe; Gödel’s incompleteness theorem guarantees you that.”

My contention is that there IS NOTHING outside of the Universe from the time of the Big Bang until the creation of the Earth about 4,500 Million years ago.

Both you and I agree that DNA most likely did NOT appear anywhere within the Universe until the appearance of DNA upon the Earth – AFTER the creation of the Earth.

Both you and I agree that Information can NOT find derivation from the “Laws of Physics”. In fact, Information and “The Laws of Physics” are what Russell would label as different Logical Types. Of interesting note, Physics exist independently of so-called “laws”, where the “laws” are only descriptions of relationships, which at bottom, tend to be mathematical in scope and substance.

Before you and I will be able to continue the discussion of the significant appearance of DNA upon the Earth, after the creation of the Earth – you and I must FIRST deal with this huge difference in orientation between your contention that there HAS to be something outside of the Universe – and my contention that there IS NOTHING outside of the Universe from the Big Bang onward.

It’s been quite a while (decades) since I read Hofstadter’s “Gödel, Escher, Bach” and another reading of this excellent work is now in order for me. I do seem to remember though that Gödel’s incompleteness theorem finds focus and limitation upon mathematics and the computer sciences, thus comprising a rather limited set of Symbols and Symbolic Forms.

Of key importance within the discussion between you and I about the issue of the appearance of DNA upon the earth is that of the natural occurrence of DNA from Cosmic evolutionary forces (my contention) or the creation of DNA as an Information carrier from an “Intelligence outside of the system of Cosmic evolution” (your contention) from the Big Bang onwards.

Bob Allen

Bob Allen says:

Hi Perry,

I’ve now gotten about a tenth of the way into Doug Hofstadter’s “Gödel, Escher, Bach” and I’m glad that you have motivated me to pursue a second reading of this fine work. I highly recommend this work to everyone’s attention. Interestingly, this is the second recent read that your web-site has directed me to. Several months ago, I finished Evelyn Keller’s biography of Barbara McClintock – “The Feeling for the Organism: The Life and Work of Barbara McClintock”.

I’ve also gotten some feedback from some friends over on the Freethought & Rationalism Discussion Board on some thoughts they have about Gödel.

One area that Hofstadter covers in the introduction to his work is that of the history of Gödel’s Incompleteness Theorem. Interestingly, this history includes the notable exceptions to Euclid’s geometry in the various discoveries of non-Euclidian geometries within nineteenth-century mathematics – creating havoc within these circles. The English logicians Boole and De Morgan further this havoc, although stability returns with Cantor’s work in the 1880s along the lines of types of infinities brought about by the theory of sets. Canter though is rather particular in differentiating sets from classes, with the Class of Everything being his Omega, so to speak

It wasn’t long before another set of paradoxes arise from set-theory, the most famous being Russell’s paradox – dealing with membership within sets and “self-swallowing” sets (such as the set of all sets) – leading further to possible autological and heterological sets.

Naturally, Russell and Whitehead take on the challenge of bringing order to this chaos with a magnum opus – “Principia Mathematica” – wherein logical types come in to play where the set of the lowest type only contain objects as members of the set – and the next higher type up the line containing only objects and sets of a lowest type as members of the set – and so on to higher and higher logical types.

By expanding Russell and Whitehead beyond mathematics to include the vagaries of Language (language, meta-language, meta-meta-language, etc), one may then create a theory of types that not only deal with the Epimenides paradox (the liar’s paradox) but also an expansion of this paradox – where the next two sentences point to each other. The following sentence is false. The preceding sentence is true.

Russell and Whitehead exorcise self-reference and “Strange Loop” pointers as several of many paradoxes – but do so in such a way that a hierarchy of sets ultimately disallows the formation of a number of sets – such as the set of all non-self-swallowing sets.

This is where Gödel comes into the picture in 1931. Gödel offers a critique of “Principia Mathematica” (P.M.) such that P.M. is not destroyed; however, P.M. is either incomplete or contains self-contradiction. The incompleteness falls within the area of a logical type not being able to say anything about a higher logical type. The self-contradiction falls within the area of once incompleteness finds acknowledgement, then self-reference to internal consistency within a given logical type may only find expression through a statement of inconsistency.

With the above in mind Perry, let’s look at both your statement of – “If you research this closer I think you will find that there is no system of any kind that Gödel’s theorem does not apply to.” – And look at the link that you provided earlier to your web-site – http://www.cosmicfingerprints.com/incompleteness – that purportedly deals with Gödel’s Incompleteness Theorem.

Of significant issue, is that Gödel’s Incompleteness Theorem ONLY applies to systems of formal logic where the particular axioms assert something, generally having importance of some kind – AND – the systems support the rules of mathematics in some way. Thus by definition, all other systems do not have anything to do with Gödel’s Incompleteness Theorem. Thus by definition, there are a plethora of systems that do not find application from Gödel.

For example, any and all analogical systems that find both completeness and non-contradictoriness fall within this category. Let’s take this category as a set – any and all analogical systems where completeness and non-contradictoriness, find existence – and look at a number of objects within this set. Every painting within the American Abstract Expressionist mode comes readily to mind. I’m thinking specifically of Jackson Pollack, but there are a plethora of other Abstract Expressionists. Every Abstract Expressionist painting is complete and non-contradictory on to itself, and does not need reference outside of itself, ever. Naturally, Abstract Expressionism is only one category within a near limitless class of categories.

Another object within this set is that of every symphony performance of Wagner, Mahler, Bach, etc. – finding completeness on non-contradictoriness through the performance. Additionally, every symphony performance is different from every other symphony performance – and every performance is complete and non-contradictory on to itself.

Although I am getting way far ahead of myself here, another object from a different set would be that of DNA itself. There is nothing about DNA or Life itself that requires or implies rules of mathematics. Additionally, DNA and Life itself is complete and non-contradictory.

There is even a unique system where a set comprises all truly arithmetic statements in which all of the arithmetic statements are axioms – in which this set is clearly complete and consistent. However, the problem with this unique system – a problem that does NOT find coverage by Gödel – is the problem (that within this unique system) there is no guaranteed way to tell if something is an axiom.

A key component within Gödel’s Incompleteness Theorem is that the axioms need to assert something, thus allowing one to exclude the set of all Irrational Numbers and expressions of Irrational Numbers – which are complete and non-contradictory. Some examples – e (to the power of r) and π (to the power of r) are irrational if r ≠ 0 is rational; e (to the power of n) is irrational; 3π + 2, π + √2 and e√3.

The problems that present themselves with the link that you provided earlier to your web-site that purportedly deals with Gödel’s Incompleteness Theorem (which I’ll refer to below as “your Web-site Gödel area”) – stem largely from your assertion of:

Gödel’s Incompleteness Theorem says:

“Anything you can draw a circle around cannot explain itself without referring to something outside the circle – something you have to assume but cannot prove.”

From my understanding of Gödel’s Incompleteness Theorem – Gödel never talks about drawing a circle around anything. It sounds like you, Perry, are trying to use a circle-analogy to refer to set theory – combining set theory with your understanding of Gödel’s Incompleteness Theorem. It appears to me as though you are using the circle-analogy to indicate a given set – and to differentiate this set from other sets. This is only kinda sorta OK when one attempts to illustrate set theory using Venn Diagrams – however, the Venn Diagrams analogy breaks down when actual set theory involves the discussion of sets and classes and types of classes, etc.

The problem that you present with your circle-analogy is a simple mapping problem, wherein one would need to map the Perry Marshall Circle Incompleteness Theorem to Gödel’s Incompleteness Theorem. The difficulty with this Mapping is that of mapping a formal logic system (the Perry Marshall Circle system) to a physical world system (the Gödel’s system). Mapping of elements to elements is one thing, but mapping statements of logic to elements is something very different – and this something very different sounds exceeding complex – and no doubt leads to a number of paradoxes.

One of the largest areas of misstatements that you make about Gödel’s Incompleteness Theorem is that of EXPANDING Gödel beyond systems of formal logic with these systems supporting the rules of mathematics. Gödel is very careful in limiting his discussions to systems of formal logic and systems that support the rules of mathematics.

There are a large number of paradoxes and simple inaccuracies (within the “your Web-site Gödel area”) that you introduce with the Perry Marshall Circle Incompleteness Theorem – however, I will only address one specifically – because this area is the base for a large disagreement between you and me. This is also the area in which you bring Gödel into the discussion between you and me. In comment # () above, you indicate – “There HAS to be something outside of the universe”.

One paradox that you attempt to bury with the circle-analogy is that of proposing a construct that you label the “biggest circle” – whereby you appear to mean – that one reaches an upper boundary wherein one may no longer draw a circle around something. You appear to use this construct to prevent an infinite expansion of “drawing circles around” various logical types.

In your example from “your Web-site Gödel area” you indicate that one may draw a circle around the Universe (“If there are multiple universes, we’re drawing a circle around all of them too”) – but that then this circle magically becomes the “biggest circle” because whatever is outside of the “biggest circle” is boundless. These are arbitrary statements without any formal proofs offered or explored – and they find a place within the Perry Marshall Circle Incompleteness Theorem – to ward off the paradox of self-reference within a logical type – ala Gödel’s critique of Russell and Whitehead in the P. M.

How would one possibly know that outside of the “biggest circle” that the outside is “boundless” – without “drawing a larger circle” around this “boundless” whatever?

Merely stating that something is “boundless” without proving that something is “boundless” is merely stating an assertion, not proving a proof.

Thus, in the discussion between you and me, Gödel really doesn’t apply to the state of the Universe some 4,500 Million years ago. Thus, there is nothing outside of the Universe some 4,500 years ago – before DNA found creation upon the Earth of our Solar system.

Bob Allen

Bob Allen says:

Hi Perry,

Thanks for responding to my rather long entry in this New Evolution section about my thoughts on Gödel’s Incompleteness Theorem – and how they relate to the ongoing conversation that you and I are having about the issue of DNA being or not being a Naturally Occurring happening, stemming from the ongoing Evolution of Life upon the Earth. My orientation is that DNA is Naturally Occurring. Your orientation is that DNA is a Code, carrying information, created by an Intelligence, and therefore is NOT Naturally Occurring. I realize that the previous sentence is a rather short summary of both my and your orientation – however, I do believe that I am accurately reporting both the summary and the differences in orientation between you and me.

I also wish to point out that currently the discussion between you and me generally finds agreement on the happening of the Big Bang, some 13,700 Million years ago (although you and I disagree on Randomness at Planck Time), the creation of the Sun some 6,500 Million years ago, and the creation of the Earth some 4,500 Million years ago. You and I agree that the creation of both the Sun and the Earth are Naturally Occurring happenings derived from the explosions of countless numbers of Super Nova throughout the course of the development of the Universe from the Big Bang onward. You and I also agree that DNA appears to be a unique occurrence within the Universe, limited to the Earth, sometime after the creation of the Earth.

You, Perry, then bring Gödel’s Incompleteness Theorem into this discussion as – “There HAS to be something outside of the universe; Gödel’s incompleteness theorem guarantees you that.” You then you further indicate – “If you research this closer I think you will find that there is no system of any kind that Gödel’s theorem does not apply to.”

This is the point at which I wrote my response above dealing with my thoughts on Gödel’s Incompleteness Theorem. Other pressing reading has torn me away from Hofstadter’s “Gödel, Escher, Bach” – however on this second reading of Hofstadter, I’m better than 200 pages into the second read. I highly recommend Hofstadter to your reading attention.

Of significant importance is that Gödel’s Incompleteness Theorem initially applies to Russell and Whitehead’s “Principia Mathematica” (PM) – and as I put it above – “This is where Gödel comes into the picture in 1931. Gödel offers a critique of “Principia Mathematica” (P.M.) such that P.M. is not destroyed; however, P.M. is either incomplete or contains self-contradiction. The incompleteness falls within the area of a logical type not being able to say anything about a higher logical type. The self-contradiction falls within the area of once incompleteness finds acknowledgement, then self-reference to internal consistency within a given logical type may only find expression through a statement of inconsistency.”

Thus, Gödel’s Incompleteness Theorem – (again quoting from my earlier entry above) “ONLY applies to systems of formal logic where the particular axioms assert something, generally having importance of some kind – AND – the systems support the rules of mathematics in some way. Thus by definition, all other systems do not have anything to do with Gödel’s Incompleteness Theorem. Thus by definition, there are a plethora of systems that do not find application from Gödel.”

THIS is what Gödel says – as opposed to the Perry Marshall interpretation of what Gödel says – particularly in the area of NOT asserting the notion that one may draw circles around things, as you, Perry, do elsewhere on your Web-site and in your recent comments above. Please review my comments above about the “circle around things” orientation that you have about Gödel.

The reason that I mention Impressionist Paintings, Abstract Expressionism, and performances of Symphonic works, above, is that each of these areas represent sets – that are complete and non-contradictory on to themselves – thus present systems in which Gödel does NOT apply. I am taking issue with your earlier assertion, Perry , that – “….there is no system of any kind that Gödel’s theorem does not apply to”. There is a plethora of such systems – and I’m NOT talking about the number of molecules within a painting. I am speaking of works complete and non-contradictory within themselves. This equally applies to any given Symphonic performance – each performance is complete and non-contradictory on to itself – and is collaboration between composer, conductor, and musicians – such that each performance is also unique on to itself.

I am pleased to note that you agree with me in your latest comment above – “The universe is not a formal mathematical statement”. Thus, everything that you assert in the following six paragraphs (starting with your Postulate) has NOTHING to do, whatsoever, with Gödel’s Incompleteness Theorem. Obviously, you as a Theist assert the existence of a God. I, as an Atheist, assert that there is no room in the Universe for a God.

I’ll end this entry as I ended my last entry above – “Thus, in the discussion between you and me, Gödel really doesn’t apply to the state of the Universe some 4,500 Million years ago. Thus, there is nothing outside of the Universe some 4,500 years ago – before DNA found creation upon the Earth of our Solar system.”

I trust Perry, that you and I may now move on to the issue of DNA upon the Earth – the creation of which occurred 4,500 Million years ago. This is where the discussion between you and me left off prior to you bringing Gödel into this discussion.

Bob Allen