2012/5/22 Stephen P. King <stephe...@charter.net> > On 5/22/2012 11:53 AM, Bruno Marchal wrote: > > > On 22 May 2012, at 14:36, Stephen P. King wrote: > > On 5/21/2012 6:26 PM, Russell Standish wrote: > > On Mon, May 21, 2012 at 07:42:01AM -0400, Stephen P. King wrote: > > On 5/21/2012 12:33 AM, Russell Standish wrote: > > On Sun, May 20, 2012 at 12:06:05PM -0700, meekerdb wrote: > > On 5/20/2012 9:27 AM, Stephen P. King wrote: > > 4) What is the cardinality of "all computations"? > > Aleph1. > > > Actually, it is aleph_0. The set of all computations is > countable. OTOH, the set of all experiences (under COMP) is uncountable > (2^\aleph_0 in fact), which only equals \aleph_1 if the continuity > hypothesis holds. > > Hi Russell, > > Interesting. Do you have any thoughts on what would follow from > not holding the continuity (Cantor's continuum?) hypothesis? > > > No - its not my field. My understanding is that the CH has bugger all > impact on quotidian mathematics - the stuff physicists use, > basically. But it has a profound effect on the properties of > transfinite sets. And nobody can decide whether CH should be true or > false (both possibilities produce consistent results). > > > Hi Russell, > > I once thought that consistency, in mathematics, was the indication of > existence but situations like this make that idea a point of contention... > CH and AoC <http://en.wikipedia.org/wiki/Axiom_of_choice> are two axioms > associated with ZF set theory that have lead some people (including me) to > consider a wider interpretation of mathematics. What if all possible > consistent mathematical theories must somehow exist? > > Its one reason why Bruno would like to restrict ontology to machines, > or at most integers - echoing Kronecker's quotable "God made the > integers, all else is the work of man". > > > > > I understand that, but this choice to restrict makes Bruno's Idealism > > > It is not idealism. It is neutral monism. Idealism would makes mind or > ideas primitive, which is not the case. > > > No, Bruno, it is not Neutral monism as such cannot assume any particular > as primitive, even if it is quantity itself, for to do such is to violate > the very notion of neutrality itself. You might like to spend some time > reading Spinoza <http://plato.stanford.edu/entries/spinoza/> and Bertrand > Russell's discussions of this. I did not invent this line of reasoning. >
*Neutral monism*, in philosophy <http://en.wikipedia.org/wiki/Philosophy>, is the metaphysical <http://en.wikipedia.org/wiki/Metaphysics> view that the mental and the physical are two ways of organizing or describing the same elements, which are themselves "neutral," that is, neither physical nor mental. I don't see how taking N,+,* as primitive is not neutral monism. It is neither physical nor mental. > > > > > > even more perplexing to me; how is it that the Integers are given such > special status, > > > Because of "digital" in digital mechanism. It is not so much an emphasis > on numbers, than on finite. > > > So how do you justify finiteness? I have been accused of having the > "everything disease" whose symptom is "the inability to conceive anything > but infinite, ill defined ensembles", but in my defense I must state that > what I am conceiving is an over-abundance of very precisely defined > ensembles. My disease is the inability to properly articulate a written > description. > > > > > especially when we cast aside all possibility (within our ontology) of the > "reality" of the physical world? > > > Not at all. Only "primitively physical" reality is put in doubt. > > > Not me. I already came to the conclusion that reality cannot be > primitively physical. > > You are unclear on what you posit. You always came back to the "physical reality" point, so I don't know what more to say... either you agree physical reality is not ontologically primitive or you don't, there's no in between position. > > > > > Without the physical world to act as a "selection" mechanism for what is > "Real", > > > This contradicts your neutral monism. > > > No, it does not. Please see my discussion of neutral monism above. > Yes it does, reading you, you posit a physical material reality as primitive, which is not neutral... > > > > > why the bias for integers? > > > Because comp = machine, and machine are supposed to be of the type > "finitely describable". > > > This is true only after the possibility of determining differences is > stipulated. One cannot assume a neutral monism that stipulates a > non-neutral stance, to do so it a contradiction. > > Computationalism is the theory that you consciousness can be emulated on a turing machine, a program is a finite object and can be described by an integer. I don't see a contradiction. > > > > > This has been a question that I have tried to get answered to no avail. > > > You don't listen. This has been repeated very often. When you say "yes" > to the doctor, you accept that you survive with a computer executing a > code. A code is mainly a natural number, up to computable isomorphism. Comp > refers to computer science, which study the computable function, which can > always be recasted in term of computable function from N to N. > And there are no other theory of computability, on reals or whatever, or > if you prefer, there are too many, without any Church thesis or genuine > universality notion. (Cf Pour-Hel, Blum Shub and Smale, etc.) > > > I do listen and read as well. Now it is your turn. The entire theory > of computation rests upon the ability to distinguish quantity from > non-quantity, even to the point of the possibility of the act of making a > distinction. When you propose a primitive ground that assumes a prior > distinction and negates the prior act that generated the result, you are > demanding the belief in fiat acts. This is familiar to me from my childhood > days of sitting in the pew of my father's church. It is an act of blind > faith, not evidence based science. Please stop pretending otherwise. > > "evidence based science" ?? > > -- > Onward! > > Stephen > > "Nature, to be commanded, must be obeyed." > ~ Francis Bacon > > -- > 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. > -- All those moments will be lost in time, like tears in rain. -- 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.
