Hi Bruno Marchal  

Cool. Shows you how little I know. 


Roger Clough, rclo...@verizon.net 
11/7/2012  
"Forever is a long time, especially near the end." -Woody Allen 


----- Receiving the following content -----  
From: Bruno Marchal  
Receiver: everything-list  
Time: 2012-11-07, 12:05:11 
Subject: Re: Peirce's concept of logical abduction-- a possible moneymaker 




Hi Roger Clough, 


Hi Bruno Marchal  

Yes, by new I mean contingent. But Kant, although his examples  
are debatable, at least sought a synthetic a priori,  
which of course would be a gold mine, or perhaps a stairway  
to the divine.  

Pragmatism rejects the idea of there being any  
such universals, but I think by abduction strives  
to obtain completly new results (if actually new I can't say).  
I think that's why Peirce came up with the concept of abduction.  
The concept is very seductive to me for its possible 
power of discovery of something unknown or new.  
If comp could do this, I'd not spend a moment more on  
simulating the brain. Such a program might be worth a lot of  
money in venues such as AI, the defense industry, medicine 
and criminal investigation a la Sherlocki Holmes. 





Abduction is just one technic among many to do inductive inference (predicting 
theories from fact, synthesizing programs from input-output sequences,  finding 
explanations from data, etc.). 


The mathematical theory of inductive inference is a very large subfield of 
theoretical computer science and theoretical artificial Intelligence, or 
Learning theory. AI is the practice and/or experimental part of it. 


Behavioral Comp is the idea that machines can emulate all 3p aspect of 
experience and consciousness. 
STRONG AI is the thesis that machine can have 1p experience. 
COMP is the thesis that *you* are emulable by a computer. 


Famous theorem in theoretical learning theory: 


Roughly speaking we measure the "intelligence" (really competence) by the 
largeness of the class of computable processes recognized (explained, inferred) 
by a machine, or by the number of such classes (or comobinations). 


What is *much* more clever than a machine? Answer: two machines. It is the non 
union theorem of Blum and Blum. Actually, and in general, the gap of 
intelligence is incomputably big. 


A machine which can change its mind n times is also incomputably  more "clever" 
than a machine which changes its mind m times, if m < n. (Case and Smith) 


A surprising result: a machine which is able to change its mind, despite he got 
a correct theory, is again *much more* clever than a machine which sticks on 
the correct theory!  (Case and Smith). 


Case & Al. refuted also a form of strict Popperianism. Machines able to infer 
irrefutable theories can learn larger classes, and more classes, of computable 
process. 


Most result are, as we could expect, non constructive. No machine can really 
construct a machine and prove that such machine is more clever than herself. 
But of course machine can do that serendipitously, and machine can build other 
hierarchies, close to form of biological self-extension.  


References below. 


Theoretical computer science is a *very* large part of mathematical logic. With 
both a deductive and an inference inductive part. 


Computer are very peculiar objects. They seem close to what you say about the 
supreme monads, but the supreme monads are not Gods, they are only God 
reflector, or God mirror. God is more like the whole truth, I mean the whole 
arithmetical truth, which contains the many truth concerning many universal 
numbers and universal relation between numbers. The monads are windows through 
which God can take a look at itself, but the supreme-monads the universal 
numbers, are window enough large so that God can begin to "recognize" itself, 
so to speak. 


Bruno 






BLUM L. & BLUM M., 1975, Toward a Mathematical Theory of Inductive Inference.  
Information and Control 28,.pp. 125-155. 


CASE J. & SMITH C., 1983, Comparison of Identification Criteria for Machine 
Inductive  
Inference. In Theoretical Computer Science 25,.pp 193-220. 


CASE J. & NGO-MANGUELLE S., 1979, Refinements of inductive inference by 
Popperian  
machines. Tech. Rep., Dept. of Computer Science, State Univ. of New-York, 
Buffalo.  











http://en.wikipedia.org/wiki/Abductive_reasoning  


"Abduction[1] is a form of logical inference that goes from data description of 
something to a  
hypothesis that accounts for the reliable data and seeks to explain relevant 
evidence.  
The term was first introduced by the American philosopher Charles Sanders 
Peirce (1839?1914) as 
"guessing".[2] Peirce said that to abduce a hypothetical explanation from an 
observed surprising circumstance  
is to surmise that may be true because then would be a matter of course.[3] 
Thus, to abduce  
from involves determining that is sufficient (or nearly sufficient), but not 
necessary, for [b, unclear symbol].  

For example, the lawn is wet. But if it rained last night, then it would be  
unsurprising that the lawn is wet. Therefore, by abductive reasoning, the  
possibility that it rained last night is reasonable. (But note that Peirce did  
not remain convinced that a single logical form covers all abduction.)[4]  
Peirce argues that good abductive reasoning from P to Q involves not simply  
a determination that, e.g., Q is sufficient for P, but also that Q is among the 
 
most economical explanations for P. Simplification and economy are what call 
for the 'leap' of abduction.[5] In abductive reasoning, unlike in deductive  
reasoning, the premises do not guarantee the conclusion. Abductive reasoning  
can be understood as "inference to the best explanation".[6]  
There has been renewed interest in the subject of abduction in the  
fields of law,[7] computer science, and artificial intelligence research.[8] " 



Roger Clough, rclo...@verizon.net  
11/7/2012  
"Forever is a long time, especially near the end." -Woody Allen  


----- Receiving the following content -----  
From: Bruno Marchal  
Receiver: everything-list  
Time: 2012-11-07, 09:07:59  
Subject: Re: (mathematical) solipsism  


On 06 Nov 2012, at 15:30, Roger Clough wrote:  

> Hi Bruno Marchal  
>  
> OK. That's analytic uncertainty.  

Yes indeed. Almost the opposite of the comp indeterminacy. With comp  
we get many form of indetermlinacies and uncertainties.  



>  
> And analytic deduction cannot really tell us anything new,  
> it can only give us a fresh perspective.  

Yes. But nor can a God, or a universe. I am not sure what you mean by  
"new".  


>  
> But a new thing can be created with synthesis  
> (intuiition,inference, induction, abduction),  
> which is the trick that Einstein performed when  
> he showed (very simply) that time is relative.  

OK, but this happens in arithmetic too, even without comp. And more  
easily shown with comp.  



> This was invented I think, entirely new, not deduced.  

So by new, you mean contingent. But arithmetic is full of many  
contingencies. Even many type of very different sort of contingencies.  



>  
> I suppose this might be construed as a form of nominalism,  
> and if so, realism can be expanded with intuition.  

Tell me what you mean by nominalism, as this term is often used  
differently by different people.  

Bruno  



>  
>  
>  
> Roger Clough, rclo...@verizon.net  
> 11/6/2012  
> "Forever is a long time, especially near the end." -Woody Allen  
>  
>  
> ----- Receiving the following content -----  
> From: Bruno Marchal  
> Receiver: everything-list  
> Time: 2012-11-06, 07:48:07  
> Subject: Re: (mathematical) solipsism  
>  
>  
> On 05 Nov 2012, at 13:48, Roger Clough wrote:  
>  
>> Hi Bruno Marchal  
>>  
>> Isn't strong AI just an assumption ?  
>  
> Yes. Comp too. The existence of the moon also.  
>  
> The fact that I am conscious, can only be an assumption for you, and  
> vice versa.  
>  
> The only thing which is not an assumption is private consciousness.  
> All the rest are assumptions.  
> Strictly speaking.  
>  
> Science uses only assumption and develop only *relative* certainty. A  
> difficulty comes from the fact that the brain wired in us already many  
> assumptions, which we are not conscious of the hypothetical nature.  
> for example some birds assumes that the first things they see moving  
> after birth is their parent, and we tend to do the same. But having  
> parent is of the type "theoretical hypotheses".  
>  
> Bruno  
>  
>  
>  
>>  
>>  
>> Roger Clough, rclo...@verizon.net  
>> 11/5/2012  
>> "Forever is a long time, especially near the end." -Woody Allen  
>>  
>>  
>> ----- Receiving the following content -----  
>> From: Bruno Marchal  
>> Receiver: everything-list  
>> Time: 2012-11-04, 09:43:16  
>> Subject: Re: (mathematical) solipsism  
>>  
>>  
>>  
>>  
>> On 03 Nov 2012, at 13:00, Stephen P. King wrote:  
>>  
>>  
>> On 11/3/2012 5:39 AM, Bruno Marchal wrote:  
>>  
>> [SPK] In the absence of a means to determine some property, it is  
>> incoherent and sometimes inconsistent to claim that the property has  
>> some particular value and the absence of all other possible values.  
>>  
>>  
>> In math this is called (mathematical) solipsism.  
>>  
>>  
>> Dear Bruno,  
>>  
>> How is it solipsism? Solipsism is: "Solipsism is the  
>> philosophical idea that only one's own mind is sure to exist. The  
>> term comes from the Latin solus (alone) and ipse (self). Solipsism  
>> as an epistemological position holds that knowledge of anything  
>> outside one's own mind is unsure. The external world and other minds  
>> cannot be known, and might not exist outside the mind. As a  
>> metaphysical position, solipsism goes further to the conclusion that  
>> the world and other minds do not exist."  
>>  
>> My point is that numbers, by your notion of AR, are solipsistic  
>> as there is literally nothing other than the numbers. I reject AR  
>> because of this! Numbers alone cannot do what you propose.  
>>  
>>  
>>  
>> Comp entails Strong AI, which attributes consciousness to machines,  
>> and thus to others. You argument is not valid because it beg the  
>> question that number (related through the laws of + and *) emulated  
>> computation to which comp attribute consciousness. So comp is not  
>> solipsism.  
>>  
>>  
>> Bruno  
>>  
>>  
>>  
>>  
>>  
>>  
>>  
>>  
>>  
>> This post argues similar to my point: 
>> http://mathforum.org/kb/message.jspa?messageID=5944965  
>>  
>> "Conventional solipsism is a logical philosophy whose underlying  
>> views  
>> apply equally to mathematical philosophies of neopythagoreanism and  
>> neoplatonism as well as mathematical realism and empiricism  
>> generally.  
>>  
>> The well established philosophical principle of solipsism is that  
>> only  
>> the individual is or can be demonstrated to exist. But the problem is  
>> that if this principle were actually demonstrably true it would also  
>> make it false because the "truth" established would ipso facto make  
>> the principle beyond control of any individual.  
>>  
>> Nobody really thinks solipsism is true. But the difficulty is no one  
>> can prove or disprove the concept because no one can prove the  
>> foundations of truth in absolute, necessary, and universal terms."  
>>  
>>  
>> This article 
>> http://digitalcommons.macalester.edu/cgi/viewcontent.cgi?article=1020&context=philo
>>   
>> argues against the claim that Intuitionism is solipsistic. I reject  
>> Intuitionism as a singular coherent theory of mathematics, but I do  
>> accept it as a member of the pantheon of "interpretations" of  
>> mathematics.  
>>  
>> --  
>> Onward!  
>>  
>> Stephen  
>>  
>>  
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>> http://iridia.ulb.ac.be/~marchal/  
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