Fesapo
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Thanks. I'm sure that eventually I'll get to a printed version, but since I'm travelling for work at the moment, online is the easiest way to get a headstart on the reading. I was unsure of #5 because the Bpage number doesn't seem to match what you had. As to marginal notes, I have MORE room for that by printing off an online copy  I can make it fit into as small a column as I wish. But I agree that a printed version with footnotes is superior. I'm just trying to make some structural sense of what is available with me here. I'll have another read through it and try to mark out your weekly readings. Actually, the online version seems pretty good by online standards. They seem to have done it right by including the B numbers. And they have the A version available as well.

I did what I planned and read the preface this weekend. I wonder if anyone has the translations to the Latin. Specifically, these: 1. Nil actum reputans, si quid superesset agendum. 2. ens reasissimum 3. Quod mecum nescit, solus vult scire videri. Finally, returning to the issue of the six footnotes: Is most of this preface footnotes? I count 4 pages prior to the first footnote (per above). Does the text interveen again? Or is the completion of the text this: "...after having for so many centuries been nothing but a process of merely random groping.

This was quite helpful and informative. Together with the other poster's comments, I was able to determine that in fact all the footnotes appear to be there. In the online Kemp, there appear to be some markings, which might relate back to the first edition interleaving.(It is marked "P 020n", and I assume that the 'n' refers to 'note') These are in the correct place, except for # 5 above. We have, then: 1. P 020n "I am not, in my choice of examples, tracing the exact course of the history of the experimental method; we have indeed..." 2. "This method, modelled on that of the student of nature, consists in looking for the elements of pure reason in what admits of confirmation or refutation by experiment." 3. Bxxi "This experiment of pure reason bears a great similarity to what in chemistry is sometimes entitled the experiment of reduction, or more usually the synthetic process" 4. Bxxiii ... <snipped one paragraph> ... "Similarly, the fundamental laws of the motions of the heavenly bodies gave established certainty to what Copernicus had at first assumed only as an hypothesis, and at the same time yielded proof of the invisible force..." 5. <???I'm unsure about this one???> Bxxvii ...<snipped one short paragraph>... "To know an object I must be able to prove it's possibility, either from it's actuality as attested by experience, or a priori by means of reason." 6. P 034n "The only addition, strictly so called, though one affecting the method of proof only, is the new refutation of psychological idealism..." I would appreciate if someone could compare the online version with theirs, on #5 at least. This should be a simple text search on the phrases above. And the next question is ... why are there "Bx" numbers? What the devil is "B" anyway? That isn't a Roman numeral. And finally, why is there a P 023 style number embedded all over the place? Is that the page number from the first edition?

It seems like quite a good edition otherwise. The german page numbers are clearly embedded into the text on the right hand side at various points. I'm somewhat puzzled that this footnote is missing. It has both the first and second edition available online.

Fesapo started following Kant's CPRB Preface

I'm commited to participation, although I fall into the novice category wrt Kant. My interest in Kant is medium, because I prefer to spend my time on things that I can positively learn from, rather than focusing on critical examination of pathologies, but, nevertheless, I think it would be worthwhile to examine Kant in some more depth. I want to participate because I'm interested in improving my ability to think critically about philosophy and also to articulate those thoughts well. I particularly like the fact that you require wouldbe participants to make a clear decision and commitment to actually study the passage and participate. Since I got your approval I downloaded the text in English translation by Norman Kemp Smith and in German (although I'm severly rusty and never was that great at German). Apparently the translation by Smith (online) is lacking the blasted "long footnote." Anyone else locate a better online version? The URL's I found were: http://humanum.arts.cuhk.edu.hk/Philosophy...r/cpropen.html http://gutenberg.spiegel.de/kant/krvb/krvb001.htm I plan to have a leisurely read through the entire contents this weekend. Then I'll let it stew for a while. ###

The substanative issue of about "Originialism" is interpretive. Is the "original intent" a proper consideration for interpreting the constitution? Or, as another group formulates it, is "original meaning" a proper consideration for interpreting the consitution. Some have argued that the author's intent is a subjective consideration and that one should go by the objectively written. I believe Harry Binswanger holds to the original meaning form of originalism. If you've gotten to your notes could you give us a better update?

Mathematics, Logic, Set Theory, and Objectivism
Fesapo replied to PhilE.Stein's topic in Physics & Mathematics
So you are suggesting that I not stick so rigorously to understanding each step in the causal chain, as it builds up? I guess that what bothers me about doing that is just that I want to really understand this and the feedback I'm getting indicates that I'm missing something right at this point. But you're the teacher. If you think that I need to jump ahead, I'll take a look at it. 
Mathematics, Logic, Set Theory, and Objectivism
Fesapo replied to PhilE.Stein's topic in Physics & Mathematics
Happy New Year! I'm ready to start back in on Landau, if you are. I'm still stuck on why it is valid to define addition using an implicit formula. Shouldn't they go ahead and do the development in order to be able to give an explicit definition as I described it? 
Mathematics, Logic, Set Theory, and Objectivism
Fesapo replied to PhilE.Stein's topic in Physics & Mathematics
I think I have finally clarified what bothered me about this definition. I'll restate what I think to be the case and see if you can confirm/disconfirm my understanding. This first part I have no problem with as a definition of "x+1": x+1 = x' This defines "addition of one" as succession. And, then, chaining these togther we get: 1. x+1 = x' 2. x+1+1 = x'' 3. x+3 = x''' 4. x+4 = x'''' . . . . . . y. x+y = xy#of' [x with the y number of succesors applied] y+1. x+y+1 = (xy#of')' [another recursive application of (1)] y+1. x+y' = (x+y)' [substituting the equality in (y) into (y+1)] So, as written above, the "chaining" of cases leads to a definition where x+y is defined in terms of succession. This is then extended one case further to cover the case which defines x+y' in terms of succession applied to the summation. I guess the problem I had was in thinking that the definition ought to end at the case y, rather than at y+1. I do remember that in other demonstrations, such as with series, one specified them as follows: 1, 2, 3, 5, 8, 13, .... n, n+1 And the formulation in Landau follows that by offering the cases (1) and (n+1), or rather, (y+1). What had troubled me about claiming that x+y' = (x+y)' was part of the definition of addition as a recursive function, is that it seemed to be an implicit definition of x+y. I still think that this is the case and that my version which defines x+y as "withynumberofsuccessions" is a more directly defining one. But I suppose that one can properly say that x+y is defined such that those two endpoints are met, and this is also a valid definition. 
Mathematics, Logic, Set Theory, and Objectivism
Fesapo replied to PhilE.Stein's topic in Physics & Mathematics
Oh, I looked further ahead in Landau and see what you mean. You're talking about section 3 ("Ordering"), where ordering is proven by induction. right? 
Mathematics, Logic, Set Theory, and Objectivism
Fesapo replied to PhilE.Stein's topic in Physics & Mathematics
You are arguing that Landau's axiom 5, the axiom of induction, is invalid, because it isn't fundamental: it is derived from the principle of being wellordered. But I just took it to be an expression or formalization of the principle that natural numbers are wellordered. As Aristotle pointed out with the axiomatic method: you have to start somewhere. You can't have an infinite regress. Thus, you have to "presuppose certain properties of the natural numbers", which are the axioms. Then, you can go on to prove other properties on the basis of those presupposed axioms. 
Mathematics, Logic, Set Theory, and Objectivism
Fesapo replied to PhilE.Stein's topic in Physics & Mathematics
Are you saying that my description was OK, except that there is no problem with association? Otherwise, how would I go symbolically from: (((x+1)+1))+1 = ((x')')' = x''' to x + y' = (x+y)' In other words, I'm pretty clear on the left hand side, but not on getting the right hand side from x'''' inductively to (x+y)' . Maybe thats the key ... I'm musing online here ... is it that x'''''' (of however many repetitions of succession) is equivalent to (x +y)', since y *is* that repetition of successions. Wow, can that thought even be understood? Is there a simpler way to express the abstraction of a given number of recursions of the succession? 
I hate to point it out, but during the Rodney King riot, it was announced in advance that the National Guard would not be carrying ammunition. So, the P.C. rot is well in place here as well.

Mathematics, Logic, Set Theory, and Objectivism
Fesapo replied to PhilE.Stein's topic in Physics & Mathematics
That either makes it completely intelligible, or I'm completely missing it. I think that what this means is that after you chain them together: (x+1)+1 = (x')' ((x+1)+1)+1 = ((x')')' (((x+1)+1)+1)+1 = x'''' you can then regroup the "1"s so that a variable number, say "y" of them plus one falls as an instance under the prior definition of x' = x + 1. Putting this portion of the "1"s into brackets we have: (x+ [1] )+1 = (x')' ((x+ [1)+1)] +1 = ((x')')' (((x+ [1)+1)+1)] +1 = x'''' Then, replacing the bracketed succession of additions with the symbolic "y"on the left side, allows us to reduce the left hand side to a general formula: (x+ [y] )+1 = ??? And then by the same dfn. of x + 1 = x' applied taking x+y as an instance of x, we get the right hand side: (x + y)+ 1 = (x+y)' Finally, by regrouping the left hand side we have: x + y' = (x+y)' But this all depends upon the associative law of addition. And that hasn't been proven yet. So where did I go wrong? 
Mathematics, Logic, Set Theory, and Objectivism
Fesapo replied to PhilE.Stein's topic in Physics & Mathematics
It's been quite a while and I haven't been idle. I've looked at this at least five separate times and I still just can't quite get it. I still don't see how one constructs a recursive definition of addition. I'm pretty confident that I understand the proof that a similar structure ends up being equivalent. How do you get to a definition of (x+y) in terms of a recursive definition of a succession function? This problem is tantallizing, and that is part of why I haven't posted again. Each time I start to look at it I think, "OK, I see that x' ought to be usable to define x+y so that y simply get collapsed as some form of x' and then the whole thing boils down to the fact that x' is another way of saying x+1. But I just can't seem to make all the symbolic forms come together to do that. What am I missing here? If I have a function a(x) and b(x) and they are the same recursive structure, how do I get a(b((x))=x+y?