Bruno Marchal wrote: > > > On 20 Feb 2011, at 00:39, benjayk wrote: > >> >> >> Bruno Marchal wrote: >>> >>>> Isn't it enough to say everything that we *could* describe >>>> in mathematics exists "in platonia"? >>> >>> The problem is that we can describe much more things than the one we >>> are able to show consistent, so if you allow what we could describe >>> you take too much. If you define Platonia by all consistent things, >>> you get something inconsistent due to paradox similar to Russell >>> paradox or St-Thomas paradox with omniscience and omnipotence. >> Why can inconsistent descriptions not refer to an existing object? >> The easy way is to assume inconsistent descriptions are merely an >> arbitrary >> combination of symbols that fail to describe something in particular >> and >> thus have only the "content" that every utterance has by virtue of >> being >> uttered: There exists ... (something). >> >> So they don't add anything to platonia because they merely assert the >> existence of existence, which leaves platonia as described by >> consistent >> theories. >> >> I think the paradox is a linguistic paradox and it poses really no >> problem. >> Ultimately all descriptions refer to an existing object, but some >> are too >> broad or "explosive" or vague to be of any (formal) use. >> >> I may describe a system that is equal to standard arithmetics but >> also has >> 1=2 as an axiom. This makes it useless practically (or so I >> guess...) but it >> may still be interpreted in a way that it makes sense. 1=2 may mean >> that >> there is 1 object that is 2 two objects, so it simply asserts the >> existence >> of the one number "two". > > But what is two if 2 = 1. I can no more have clue of what you mean. Two is the successor of one. You obviously now what that means.
So keep this meaning and reconcile it with 2=1. You might get the meaning "two is the one (number) that is the succesor of one". Or "one (number) is the successor of two". In essence it expresses 2*...=1*... or 2*X=1*Y. And it might mean "the succesor of one number is the succesor of the succesor of one number". or 2+...=1+... or 2+X=1+Y. The reason that it is not a good idea to define 2=1 is because it doesn't express something that can't be expressed in standard arithmetic, but it makes everything much more confusing and redundant. In mathematics we want to be precise as possible so it's good rule to always have to specifiy which quantity we talk about, so that we avoid talking about something - that is one thing - that is something - that is two things - but rather talk about one thing and two things directly; because it is already clear that two things are a thing. Bruno Marchal wrote: > > Now, just recall that "Platonia" is based on classical logic where the > falsity f, or 0 = 1, entails all proposition. So if you insist to say > that 0 = 1, I will soon prove that you owe to me A billions of > dollars, and that you should prepare the check. You could prove that, but what is really meant by that is another question. It may simply mean "I want to play a joke on you". All statements are open to interpretation, I don't think we can avoid that entirely. We are ususally more interested in the statements that are less vague, but vague or crazy statements are still valid on some level (even though often on an very boring, because trivial, level; like saying "S afs fdsLfs", which is just expressing that something exists). Bruno Marchal wrote: > >> 3=7 may mean that there are 3 objects that are 7 >> objects which might be interpreted as aserting the existence of (for >> example) 7*1, 7*2 and 7*3. > > Logicians and mathematicians are more simple minded than that, and it > does not always help to be understood. > If you allow circles with edges, and triangles with four sides in > Platonia, we will loose any hope of understanding each other. I don't think we have "disallow" circles with edges, and triangles with four sides; it is enough if we keep in mind that it is useful to use words in a sense that is commonly understood. I think it is a bit authoritarian to disallow some statements as truth. I feel it is better to think of truth as everything describable or experiencable; and then we differ between truth as non-falsehood and the trivial truth of falsehoods. It avoids that we have to fight wars between truth and falsehood. Truth swallows everything up. If somebody says something ridiculous like "All non christian people go to hell.", we acknowledge that expresses some truth about what he feels and believes, instead of only seeing that what he says is false. I believe the only way we can learn to understand each other is if we acknowledge the truth in every utterance. Bruno Marchal wrote: > >> >> I don't think the omnipotence paradox is problematic, also. It >> simply shows >> that omnipotence is nothing that can be properly conceived of using >> classical logic. We may assume omnipotence and non-omnipotence are >> compatible; omnipotence encompasses non-omnipotence and is on some >> level >> equivalent to it. >> For example: The omnipotent God can make a stone that is too heavy >> for him >> to lift, because God can manifest as a person (that's still God, but >> an >> non-omnipotent omnipotent one) that cannot lift the stone. > > That makes the term "omnipotent" trivial. You can quickly be lead to > give any meaning to any sentence. Well I think this makes sense on some level. Language is symbols that are interpreted. There is no absolute rule how to interpret them, so we *can* interpret everything in it (but we don't have to!). In most cases it is most useful to interpret some quite specific meaning into a sentence (if you don't want to act madly), but as we use more broad and vague terms there are more and more ways to interpret what is said. So in this case omnipotency is trivial. It might just be open for too many interpretations to say anything really useful. Bruno Marchal wrote: > > Did you confess that you killed your wife? yes, sure, but by "I killed > my wife" I was meaning that "I love eggs on a plate". > This will not help when discussing fundamental issues. Right, but I am not saying we *should* talk in a way that is impossible for others to understand. We should talk as clearly as possible. For this reason saying 1=2 or "I killed my wife" while meaning that "I love eggs on a plate" is mostly not a good idea. But that it is impractical to speak in a in an incomprehensible way can be reconciled with that it still makes sense on some level. Bruno Marchal wrote: > >> >> >> Bruno Marchal wrote: >>> >>>> >>>> >>>> Bruno Marchal wrote: >>>>> Like in Plotinus, the ultimate being (arithmetical platonia) is >>>>> not a >>>>> being >>>>> itself (nor is matter!). >>>> Could you explain what you mean with that? >>> >>> Platonia, the platonia of Plato, is the Noûs, [...] >> Many thanks for your effort to explain this to me. :) >> >> Honestly your non-technical explanation is a bit vague for me and your >> technical explanation is simply way to technical for me. Some things >> seem to >> make sense, but overall it's still quite mysterious to me. >> Frankly I am a bit afraid to ask questions concerning your technical >> explanation, because I'm not sure if you can answer them succintly or >> whether I understand your explanations and I don't want you to waste >> your >> time explaining it to me in great detail and then still be not much >> more >> smarter. > > There are good book on self)-reference, but they need some familiarity > in mathematical logic. An excellent book on Logic is the book by > Elliot Mendelson, another one is by Boolos, Jeffrey and Burgess. Thanks. :) I will consider buying one of them. Bruno Marchal wrote: > >> Maybe I will try searching some terms that I don't understand (or >> that I >> don't understand the context of) on the list or in the web. > > You will find the best and the worst. Podnieks' page is not too bad. > http://www.ltn.lv/~podnieks/ It looks interesting, though a bit disorganized. Bruno Marchal wrote: > >> >> A have a few questions regarding the non-technical part of >> explanation, >> though: >> >> What does it mean that the soul falls, falls from what? > > From Heaven. From Platonia. From the harmonic static state of the > universal consciousness to the state with death and taxes. How come that we don't have memories of falling from heaven? Bruno Marchal wrote: > >> >> How can the One / matter be outside of existence? I have no clue >> what this >> could mean. Is the "outside" of existence not existence as well? > > It is a bit like in most set theories, the set of all sets is not a > set. For example usually the set of all subsets of a set is bigger > than the set itself, and if the collection of all sets is a set, then > the set of the subsets of the set of all sets is bigger than the set > of all sets. This makes sense, since there might be something outside of sets. But existence seems to be all-encompassing. What would the One be, if not existent? It isn't non-existent, surely? Bruno Marchal wrote: > > God cannot create itself, in most conception of Gods. Because he already is himself, right? Bruno Marchal wrote: > >> >> Is the one conscious? What you write seems to imply it is (eg "the >> ONE and >> the Divine Intellect are overwhelmed by the Universal Soul,"), but I >> thought >> only the universal soul can experience? > > I thought that too, but my mind evolves on this. Plotinus is himself > full of doubts on that question. I really don't know. I would still > say that the ONE is not a person, but I am less sure. Technically, any > set of sentences defined a canonical believer/person, which is the one > believing exactly those sentences. And what is sure is that it is not > a Löbian person, so what is is? There is a need of a 'truth theory" or > meta-truth-theory, but none in the literature, a part of Tarski > theory, satisfies me, in the comp setting. Okay, I probably imagined that there is clearer picture of the ONE or the universal soul is. Bruno Marchal wrote: > >> Why does >> the one let matter eminate at all then? > > Matter is defined by what God cannot control. It is the border of God. > God is not so much powerful in Neoplatonism. The idea that God is > omnipotent has been added by the Christians, I think. God is good, > sure (in Plato, Plotinus), but, well, he does its possible but he is > limited, notably by logic and mathematics. Does god ever had control? Control seems only possible if we can make sense of the future or of consequences, but since God is the source of both future and consequences, he's more like bomb. God is limited by logic and mathematics? This seems strange since the ONE is that which everything emanates of, which seems to mean God is the source of all limitations - and how could this be if God is already limited? -- View this message in context: http://old.nabble.com/Platonia-tp30955253p30976699.html Sent from the Everything List mailing list archive at Nabble.com. -- You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to firstname.lastname@example.org. 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.