Godel on Philosophy of Mathematics

About: ... or what i got from Godel:


The axioms of a system are outside of the system.  There is no such thing as a system in which all of its axioms can be proven.   So once you choose some axiom or belief, it will be true within that belief network ... and cannot be questioned ... and must be taken on Faith as  true within that system.   You can only unchoose that belief by literally getting out of the system. 

I am sure i can find better ways to say that ... but i wanted to get the essence of my belief here written out.  Godel, of course, did not prove all of that ... no he just proved it for arithmetic.   But many of us take it to be true in general ... even though it is probably impossible for us to prove it within our human mental capacity.  Of course, we can just choose it to be so ... and then, within our mind, it will be so. 

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  1. godel
  2. belief
  3. faith
  4. item 17989

Comments


Eiamyme says
I grok is mostly that way ... & hold it that it is a matter of focus & the a priori & a posteriori thingy. We need axioms  as a priori so that we can focus on expanding beyond what is obvious.
One can carry doubt only so far out of the Cosmos back into the chaos.


Eiamyme says
Another way of saying it is one has to hold something still or find a viewpoint and look to study it.


Eiamyme says
Yet interesting is 17112 which I ran into while looking for the picture above.


Seth says

* Picture from this continuously scrolling journal about The Whole is More than the Sum of its Parts

source: mark
... & hold it that it is a matter of focus & the a priori & a posteriori thingy.

I hold it pretty much the same.  

I look at any system ... any network of relationships and interaction ... as having at its core beliefs and rules and/or habits and assumptions or axioms ... which are then connected to the consequential world only on its edges. 

When i talk about a individual human mind ... that is how i picture it ... the sensations impinging on the sense organs (consequential or spiritual) being the outside edges ... those sensations happening at the boundary between inside the system (mind) and outside it.

Yet we need not apply that model only to individual human minds ... we can also apply it to any network or institution which is somewhat isolated from its environment ... usually by "in groups" and privacy. 

Perhaps Quine said substantially the same thing with much more authority ... yet not as simply and directly.

source: Willard Quine Two Dogmas of Empiricism

     The totality of our so-called knowledge or beliefs, from the most casual matters of geography and history to the profoundest laws of atomic physics or even of pure mathematics and logic, is a man-made fabric which impinges on experience only along the edges. Or, to change the figure, total science is like a field of force whose boundary conditions are experience. A conflict with experience at the periphery occasions readjustments in the interior of the field. Truth values have to be redistributed over some of our statements. Re-evaluation of some statements entails re-evaluation of others, because of their logical interconnections -- the logical laws being in turn simply certain further statements of the system, certain further elements of the field. Having re-evaluated one statement we must re-evaluate some others, whether they be statements logically connected with the first or whether they be the statements of logical connections themselves. But the total field is so undetermined by its boundary conditions, experience, that there is much latitude of choice as to what statements to re-evaluate in the light of any single contrary experience. No particular experiences are linked with any particular statements in the interior of the field, except indirectly through considerations of equilibrium affecting the field as a whole.
I actually have this essay and studied it around the turn of the century under provocation from Longley who thinks he is the greatest philosopher of modern history. 

One reason i like this model of mind is that it explains a lot of why we have so many troubles communicating in words.


Seth says
Eiamyme 2014-12-04 12:20:38 17989
Yep, but it is only a MODEL! - an abstraction.

yep.  

the use of a model is that you can alter something in the model and predict how the corresponding thing will react in reality .... if, of course, the model correctly represents the reality. then if you do not find corresponding changes, you adjust the model accordingly ... finding better and better truths as you go .  That is, if you think about it, the essence of the scientific method. 

For example, this model predicts that we are going to have disconnects in our communications ... why, well just because your internal network at its core has quite different assumptions than mine.  Me thinks the trick to imrove it is try to teas out those assumptions that differ.  Nobody need change their beliefs, but we will understand each other better if we know that something said was based upon a differing assumption ... that way one can simulate the other network better inside their own. 

Mark de LA says
seth 2014-12-05 20:00:16 17989
Eiamyme 2014-12-04 13:38:19 17989
seth 2014-12-04 12:58:48 17989
Eiamyme 2014-12-04 12:20:38 17989
Yep, but it is only a MODEL! - an abstraction.

yep.  

the use of a model is that you can alter something in the model and predict how the corresponding thing will react in reality .... if, of course, the model correctly represents the reality. then if you do not find corresponding changes, you adjust the model accordingly ... finding better and better truths as you go .  That is, if you think about it, the essence of the scientific method. 

For example, this model predicts that we are going to have disconnects in our communications ... why, well just because your internal network at its core has quite different assumptions than mine.  Me thinks the trick to imrove it is try to teas out those assumptions that differ.  Nobody need change their beliefs, but we will understand each other better if we know that something said was based upon a differing assumption ... that way one can simulate the other network better inside their own. 
Enjoy!  I doubt you will ever grok a mind or soul that way, but you might have a pleasing model to yourself & your network.


Well, obviously, a model of something is never the actual experience of it.  I don't know why you continually point that out to me. 
You always come back with models & mind chatter.

Eiamyme says
That is not to say that there are not interesting things to play with in pattern recognition & metaphors in language & neural neural networks. One might or could have to say that AI arrives at the idea that a neural network is conscious if it can perform complex human tasks without coaching. OTOH that is just stopping at a point & forgetting that consciousness has many dimensions not all confined to the human brain nor residing in the physical anatomy.


Eiamyme says
... & human behavior is quite variable & infinite.

Seth says
choy 2014-12-06 00:51:35 17989
seth 2014-12-05 20:00:16 17989
Eiamyme 2014-12-04 13:38:19 17989
seth 2014-12-04 12:58:48 17989
Eiamyme 2014-12-04 12:20:38 17989
Yep, but it is only a MODEL! - an abstraction.

yep.  

the use of a model is that you can alter something in the model and predict how the corresponding thing will react in reality .... if, of course, the model correctly represents the reality. then if you do not find corresponding changes, you adjust the model accordingly ... finding better and better truths as you go .  That is, if you think about it, the essence of the scientific method. 

For example, this model predicts that we are going to have disconnects in our communications ... why, well just because your internal network at its core has quite different assumptions than mine.  Me thinks the trick to imrove it is try to teas out those assumptions that differ.  Nobody need change their beliefs, but we will understand each other better if we know that something said was based upon a differing assumption ... that way one can simulate the other network better inside their own. 
Enjoy!  I doubt you will ever grok a mind or soul that way, but you might have a pleasing model to yourself & your network.


Well, obviously, a model of something is never the actual experience of it.  I don't know why you continually point that out to me. 
You always come back with models & mind chatter.

well models are just recognized patterns ... Gestalts .... Wallabies ... they are just representations of what i observe and experience.   I think about them ... twist them around in my mind ... and here i try to communicate them to you in language ... on the if-come that they will also be gestalted similarly over there. 

Obviously, the experiences themselves cannot be communicated from mind to mind ... at best we can expect that some instructions communicated would yield similar experiences for both of us.   Of course  for either of us to know that we detected a similar pattern in our private affairs, we would need to tell the other about it ... er, in language.

So i am still at a loss to know what alternative you are expecting.  Maybe you will tell me ... maybe not. 

Seth says
Eiamyme 2014-12-06 11:06:48 17989
seth 2014-12-06 10:57:32 17989
choy 2014-12-06 00:51:35 17989
seth 2014-12-05 20:00:16 17989
Eiamyme 2014-12-04 13:38:19 17989
seth 2014-12-04 12:58:48 17989
Eiamyme 2014-12-04 12:20:38 17989
Yep, but it is only a MODEL! - an abstraction.

yep.  

the use of a model is that you can alter something in the model and predict how the corresponding thing will react in reality .... if, of course, the model correctly represents the reality. then if you do not find corresponding changes, you adjust the model accordingly ... finding better and better truths as you go .  That is, if you think about it, the essence of the scientific method. 

For example, this model predicts that we are going to have disconnects in our communications ... why, well just because your internal network at its core has quite different assumptions than mine.  Me thinks the trick to imrove it is try to teas out those assumptions that differ.  Nobody need change their beliefs, but we will understand each other better if we know that something said was based upon a differing assumption ... that way one can simulate the other network better inside their own. 
Enjoy!  I doubt you will ever grok a mind or soul that way, but you might have a pleasing model to yourself & your network.


Well, obviously, a model of something is never the actual experience of it.  I don't know why you continually point that out to me. 
You always come back with models & mind chatter.

well models are just recognized patterns ... Gestalts .... Wallabies ... they are just representations of what i observe and experience.   I think about them ... twist them around in my mind ... and here i try to communicate them to you in language ... on the if-come that they will also be gestalted similarly over there. 

Obviously, the experiences themselves cannot be communicated from mind to mind ... at best we can expect that some instructions communicated would yield similar experiences for both of us.   Of course  for either of us to know that we detected a similar pattern in our private affairs, we would need to tell the other about it ... er, in language.

So i am still at a loss to know what alternative you are expecting.  Maybe you will tell me ... maybe not. 
Something that indicates that you got to the heart of a matter sans just mind chatter & how you got there!  But arguing further along your current line is not it. I know what models are.


I actually am pretty good at silencing mind chatter .... i do Za Zen where what is uppermost in my attention is only my breathing ... now breathing in ... now breathing out.   Still  nothing that i will call "out of body" shows up ... yet i am still aware of a background for potential attention way too vague to describe ... like waves to a body of literature or experience too ambiguous to form what could be called a thought; and, lacking the intent to focus, wave away.   That background varies radically with my emotional state.  If something is irritating me, then of course its material will be there in the background luring me to form a thought about it.  For example, the last time i did za zen, the material for this paragraph was there in the background.  Hence i let it show up now as i write it here.  So I think the trick to a better za zen is to do it when there is nothing already irritating.  ... or even being anticipated, like for example the expectation of something spiritual.

I do "out of body" stuff quite literally ... i let other bodies bring it up. 



 

Mark de LA says
Nice! I don't do za-zen much.  Sometimes only to clear the chatter.   I hold a question & contemplate & get to a more interesting kind of consciousness.  I am not looking for out-of-body stuff or any other pre-determined result just more light on my question. Consciousness seems to be to be more light on the matter at hand; not necessarily of the visual kind.


Seth says
choy 2014-12-07 09:05:43 17989
Nice! I don't do za-zen much.  Sometimes only to clear the chatter.   I hold a question & contemplate & get to a more interesting kind of consciousness.  I am not looking for out-of-body stuff or any other pre-determined result just more light on my question. Consciousness seems to be to be more light on the matter at hand; not necessarily of the visual kind.
cl

many times, as you probably have noticed, i use this blog to focus on a single thought ... reading it back ... editing it ... taking out extraneous matters and cloying self consciousness and rwg  ... trying to get its tone correct ... and allowing it to bond more completely to the background of my mind.  i use the words on the screen to help with my fleeting attention and wigging memory. 

Sometimes "more interesting" other stuff does show up as i mediate on the sentences ... somtimes i detect contradictions and delete the entire comment ... sometimes  i can realate it to something not habitually connected ... and sometimes things show up from your reactions to it.

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