On 17 Jan 2012, at 20:06, Stephen P. King wrote:

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On 1/17/2012 5:08 AM, Bruno Marchal wrote:SNIP- I disagree that set theory might be more primitive thanarithmetic. Why? First because arithmetic has been proved moreprimitive than set theory, and less primitive than logic. Withlogic we cannot define numbers. with set, we can define numbers,even all of them (N, Z, Q, ... octonions, etc.). The naturalnumbers are often defined by the von Neuman finite ordinal:0 = { } 1 = {{{}}} = {0} 2 = {{}, {{}} } = {0, 1} 3 = {{}, {{}},{{}}},,{{} ,{{}} } } = {0, 1, 2} ... n = {0, 1, 2, ..., n-1} etc.And you can define addition by the disjoint union cardinal, andmultiplication by the cardinal of cartesian product,and then, you can *prove* the laws of addition and the laws ofmultiplication. With arithmetic you cannot recover any axioms ofset theory, except for the hereditarily finite sets.I am confused. It seems to me that you are admitting that setsare more primitive than Arithmetic since what you wrote here is ademonstration of how numbers supervene on set theoretic operations.The fact that we can define the natural numbers via the von Neumanfinite ordinals is the equivalent of claiming that the naturalnumbers emerge from the von Neuman finite ordinals (up toisomorphism!), so I am confused by what you are claiming here! Butwhichever is the most primitive, it is not more primitive than theneutral foundation of existence in itself.

`I just meant that sets are more complicated that natural numbers, so`

`by assuming sets you assume more than by assuming just the natural`

`numbers. With comp we have that assuming arithmetic is enough. Sets,`

`real numbers and the physical world are recovered in the epistemology`

`of relative natural numbers (that is a number + a universal numbers).`

`I have no clue what you mean by "neutral foundation of existence in`

`itself".`

`I have another problem with set theories. There is no clear "standard`

`model". For arithmetic there is. The set of Gödel number of true`

`arithmetical sentences is a highly complex set, but it is still well`

`defined. That is not the case for the set of Gödel numbers of set`

`theoretical sentences. I cannot be realist about sets.`

`Yet another problem: in the quantified self-reference logic on set`

`theory, B(P(x)), or [ ] P(x) has no easy meaning, and suffer from all`

`the Quine-Marcus critics of quantified model logic, where on the`

`contrary in the quantified self-reference logic on arithmetic BP(x) is`

`crystal clear, and defeat all those critics, by showing transparent`

`counter-example.`

`I will confess you, Stephen, that I have never really believe in Set`

`Theories. Set theories looks just like quite imaginative Löbian`

`numbers to me. But I know well ZF, and appreciate it as an interesting`

`logical object.`

- As I said, I don't take the word "Existence" as a theory. I haveno clue what you mean by that. I was asking for a theory. You saythat by taking (N, +, *) as a primitive structure, I am no moreneutral monist, due to the use of + and *. This is not correct. Itwould make neutral monism empty. We alway need ontological terms(here 0, s(0) etc.) and laws relating those terms (here additionand multiplication).No, I am not making Existence as a theory, it is merely apostulate of my overall theory

`Theories are made of postulates. I don't see a postulate. Existence of`

`what?`

(if you can call what I have been discussing a "theory"). I am usingthe notion of Existence as it is defined in ObjectivistEpistemology. For example, as explained in this video lecture: http://www.youtube.com/watch?v=GfOS7xfxezA&feature=player_embeddedNeutral monist takes is empty in the sense that it shows thecoherent implication that the most basic ontological level cannot beconsidered to have some definite set of properties to the exclusionof others.

`This does not make sense for me. Sorry. (I am not a philosopher). You`

`might have to elaborate.`

`Something primitive without any property cannot explain anything. That`

`is why physicist postulate particles and forces, and mathematicians`

`postulate numbers and laws or operations, or set and belonging`

`relations.`

- All you arguments with the term "physical" are going through inarithmetic, given that you agree that "physical" is not primitive.For example, the physical world is not required to make sense ofwhat is a universal machine. It is required for human chatting onthe net, but such a physical world is provided by arithmetic.Including concurrency.WE simply might have to agree to disagree.

`You cannot disagree with a theorem in a theory. You have to find a`

`flaw in the proof, or you have to disagree with the premise. If you`

`disagree with what I say above, I take it that you say "no" to the`

`digitalist doctor, and defend a non computationalist theory of mind.`

- I don't do philosophy. I offer you a technical result only. Istill don't know if you grasped it, or if you have any problem withit.You result has deep philosophical implications and as a studentof philosophy I am very interested in it.

I do think that genuine philosophers should appreciate it :)

If you agree to assume that the brain works like a materialmachine, then arithmetic is enough and more than arithmetic isnecessarily useless: it can only make the mind body problemunecessarily more complex. Primitive matter (time, space) becomeslike invisible horse. Not epiphenomena, but epinomena.Again, we have to agree to disagree on this. The necessity ofphysical implementation cannot be dismissed otherwise the scientificmethod itself is empty and useless.

`"physical" is what I attempt to explain in a non circular way. That is`

`why, even before studying comp, I did not postulate an ontological`

`physical reality. I don't see at all why the scientific methods need`

`an ontological physical reality. Its existence is not a fact, or show`

`me a paper proving its existence. It is only a tradition since`

`Aristotle. The founders of science, the greeks, where actually taking`

`some distance with what is only an animal extrapolation from`

`experience. Comp shows that such an extrapolation is not sensical.`

Without the definiteness that the physical world

`With QM, such definiteness can be doubted. But comp explains`

`completely (up to the comparison with facts) that there is no`

`ontological physical reality. The physical implementations does not`

`disappear, but are themselves made definable in arithmetic (or better`

`through arithmetic, because it refers to the non arithmetical notion`

`of arithmetical truth).`

`Again, it would be more efficacious to read UDA and point on where you`

`think a non valid step might have been made, given that what I say is`

`just the UDA conclusion.`

`I think that if you are set realist, the step-8 might not be`

`necessary, or could be simplified. Perhaps.`

offers us is accepted there can be only idle speculation, we sawthis kind of thinking in the Scholastics and know well how that wassuch a terrible waste of time. So why are you advocating a return tothat? Ideal monism was pushed hard by Bishop Berkeley and failedback in the 18th century, its flaw - that the material world becomescausally ineffective epiphenomena - is not solved by your result, itis only more explicitly shown. You seem to think that it is avirtue. No, sorry, it is not a virtue for the simple reason that itmakes the falsification of the theory impossible thus rendering ituseless as an explanation.

`Physics is entirely given by the logic Z1* and X1*, so it is hard to`

`imagine something more refutable than that. And Z1* and X1* are`

`derived from comp (by UDA) + the classical theory of knowledge. Even`

`if that theory is not correct, it provides a counter-example on what`

`you say above. Comp is empirically refutable. This does not mean that`

`we take the empirical reality as a primary given (it is not even for`

`biological reason)`

`Also, all that talk contradicts your neutral monism, given that you`

`too don't take the physical as primitive. It looks like you contradict`

`yourself a little bit.`

My alternative hypothesis

`I don't see it. I still don't see what you take as primitively`

`existing, and what you derive from that.`

`You have to find a way to express your idea so that simple minded`

`scientist can understand them especially when you refer to scientists`

`theories or math.`

has the chance of being falsified as it predicts that the physicalworlds actually observe must be representable as Boolean algebras(up to isomorphisms).

`This is even weirder coming from someone who insists nature is not`

`boolean (?).`

Bruno http://iridia.ulb.ac.be/~marchal/ -- You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.