What can be deduced without making presumptions!

[Doctordick]

The critical issue everyone seems to miss is that the meaning of the phrase "without making presumptions". Apparently it is something no one on this forum seems to comprehend.

 I am opening this thread because it seems that responses to my earlier post, "Understanding Reality", have totally degenerated to into silly meaningless garbage without any sign of thought at all. If no one here is capable of comprehending what I am saying I will stop posting my thoughts.

          Please consider the following facts very carefully!

Coming up with an explanation of anything requires comprehension of a language first. If there are readers who believe that is not a fact, I would have them please present an explanation without use of a language of any kind.

My second fact is that any and all languages require symbols (think in terms of concept representations) to represent any specific collection of relevant concepts! If the reader believes this is false, please provide an explanation which requires no means of referring to any concepts relevant to that explanation.

My third fact is, those symbols (if they are known) can be referred to by assigning specific numbers to each and every relevant symbol! The subtle issue of that fact is that, even when the actual assigned numbers are not known, it is still a fact that the concepts can nonetheless be represented by a "specific" collection of numbers and that issue by itself has significant consequences. Anyone who believes that is a false assertion please post a collection of symbols which can be used to represent a language which can not be numerically listed.

          The following constitute my opening assertions.

First, presuming that "the language is known" is itself a direct violation of the constraint "without making assumptions"!! That is, learning the language must first be achieved before even thought of an explanation is possible. Comprehending the relevant language is part and parcel of understanding itself. What I wish to discuss are the underlying facts the solution to any collection of information MUST obey. 

My opening assertion is that there exist relationships within those facts which can be deduced without making any assumptions as to what those facts actually are.

An additional assertion concerns a numerical representation of thoughts, "without making any presumptions" as to the meanings of that specific collection of numbers. Once a specific label is assigned to each and every learned concept (essentially the relevant language elements) that label can be seen as a unique numerical reference (think of an unknown secret code). It follows that, given the specific numerical label for every relevant concept representation in that language, any thought which can be expressed in that language may be expressed by:   [latex] (x_1,x_2 , \cdots ,x_i, \cdots ,x_n) [/latex] ) 

Note that this representation inherently includes what is commonly referred to "context". That is the fact that what those words actually mean can change from case to case depending on the associated meanings of other words in the thought being represented. (Jokes are built from such relationships!)

My point is that such a representation, which makes utterly no assumptions as to what concepts those numbers refer to, must be presumed possible. The possibility of such a representation requires no actual knowledge of either the source of the information (what is quite often referred to as reality) or the actual language being represented! That fact itself has consequences.

          What follows is no more than pure logical analysis of the above proposed circumstance.

The absolute first step in creating the circumstance I wish to analyze is to create a definition of the concept "understanding" without constraining what is to be understood in any way.

          I begin by defining two entities. 

The first entity I will refer to as "the receiver". The receiver is the entity receiving the relevant information from which he (or she) will attempt to learn (or deduce) both the language being represented and the thoughts necessary to explain the reality he (or she) will eventually perceive as standing behind those thoughts. It must be understood that the receiver stands in absolute ignorance except for the actual collection of thoughts, [latex](x_1 ,x_2 , \cdots ,x_i , \cdots ,x_n ) [/latex], he (or she) has presumed to be valid.

The second entity is the source of the relevant issues. Absolutely no information is available about the source except characteristics presumed by the receiver as part of his (or her) deduced explanations of that received information. That is, the presumed truth, of the thoughts as the receiver perceives them to be. (The presumptions he (or she) makes.)

          Deducing fundamental consequences of the above constraints.

I first define "understanding" to be the probability the receiver presumes the source holds a specific represented thought to be true. Note that this assertion is only meaningful within the representation the receiver creates; i.e., it is a consequence of the presumptions the receiver makes. In my analysis (since we are to make no assumptions) no judgements as to the actual truth of the solution the receiver creates can be made. None the less, in the analysis being presented, understanding can represented by the notation: [latex]P(x_1 ,x_2 , \cdots ,x_i , \cdots ,x_n ) [/latex] where "P" stands for the probability the receiver considers the source holds the thought to be true. 

In essence, that thought is presumed to be a true fact.  It should be clear that learning the language represented by the indices xi is the very first part of the problem facing the receiver. The receiver must make presumptions as to what the thoughts being represented are. Internal consistency is the only underlying issue of any understanding achieved. 
That is, knowledge of the relevant information is represented by the supposed truth of the specific thoughts expressed by  [latex]P(x_1 ,x_2 , \cdots ,x_i , \cdots ,x_n ). [/latex]

What is important about my definition of understanding is the fact that adding a single specific arbitrary number (which I will represent by "c") to each and every index used to represent the underlying language makes utterly no change in the meaning of any specified thought. That meaning is deduced from patterns in the received information, not the actual numbers. Adding "c" to each and every index yields internal patterns of the numerically indexed concepts exactly as they were in the original assignments.

          Thus it must be absolutely true that, no matter what the value of c is,

 [latex]P(x_1 +c,x_2 +c, \cdots ,x_i +c, \cdots ,x_n +c) - P(x_1 ,x_2 , \cdots ,x_i , \cdots ,x_n ) = 0 [/latex]

Now anyone who has any knowledge of mathematics will recognize the fact that if [latex]P(x_1 ,x_2 , \cdots ,x_i , \cdots ,x_n ) [/latex] were a mathematical function, the above assertion would, via standard interpretation, have some very significant consequences.

However, it should also be clear that [latex]P(x_1 ,x_2 , \cdots ,x_i , \cdots ,x_n ), [/latex] as defined in this post, could not possibly be a mathematical function for a number of very important reasons.

   #1 - To begin with, the relevant numbers are not variables; they are constants representing specific concepts in the relevant language.

   #2 - A second problem arises because, in a mathematical expression, "n" would be a fixed number which would be exactly the same in each and every represented thought.

In addition, there are a number of other very serious problems which arise if one attempts to create a representation which can be seen as a mathematical function. However, I will show how a very straight forward conversion in the representation can be made by redefining those indices in a manner which totally avoids making any presumptions whatsoever as to what those indices represent.

If there is anyone interested in conversion of the expression [latex]P(x_1 ,x_2 , \cdots ,x_i , \cdots ,x_n ) [/latex] into a valid mathematical expression I will continue this thread. Note that the proposed conversion, though quite simple, is not a trivial process at all.

If the above is totally beyond your comprehension, don't bother commenting. However, if you can comprehend the problem I have presented, let me know and I will present the details of the required alternate definitions of my indices.

The end result turns out to require exactly the relations standing behind modern physics: i.e., no information whatsoever about actual reality is required to show modern physics is (for the most part) essentially valid.

It also points out a few minor errors in modern physics not realized by the professionals. Those errors clearly arise from invalid presumptions in their hypotheses. In the deductions I produce, quantum mechanics is essentially valid from the word go. Relativity as per Einstein's mathematical relationships falls out implicitly; however, physical interpretation of the results turns out to be quite different. The difference in in interpretation turns out to revolve around some specific solutions to the electromagnetic theory (which also falls out implicitly in my presentation). The specific solutions of interest are rather surprising. As far as I know, those specific solutions have never been examined by the scientific community.

       Thank you for your trouble -- Richard D. Stafford, Ph.D. in Theoretical Physics 1971. 

Sorry about my inability to get LaTeX to work!!!

Edited July 26, 2017 by Doctordick
latex errors

[Area54]

3 minutes ago, Doctordick said:

 Please consider the following facts very carefully!

Coming up with an explanation of anything requires comprehension of a language first. If there are readers who believe that is not a fact, I would have them please present an explanation without use of a language of any kind.

My second fact is that any and all languages require symbols (think in terms of concept representations) to represent any specific collection of relevant concepts! If the reader believes this is false, please provide an explanation which requires no means of referring to any concepts relevant to that explanation.

My third fact is, those symbols (if they are known) can be referred to by assigning specific numbers to each and every relevant symbol! The subtle issue of that fact is that, even when the actual assigned numbers are not known, it is still a fact that the concepts can nonetheless be represented by a "specific" collection of numbers and that issue by itself has significant consequences. Anyone who believes that is a false assertion please post a collection of symbols which can be used to represent a language which can not be numerically listed.

Re your first "fact". As stated, it is not a fact. I can present an explanation of events to myself by visualising it. Perhaps you meant to say that no explanation can be conveyed to another without the use of a language. However, the manufacturers of flat pack furniture can explain to me how to assemble it through a series of photographs. Are you asserting that photographs constitute a language? If so I should like to see some citations from linguists to that effect.

Your second and third facts appear sound.

Since one of your "facts" is thereby invalidated I have not proceeded to consider the notions you build on a flawed foundation.

 

[John Cuthber]

"What can be deduced without making presumptions!"
The traditional answer is "I think therefore I am".

Another possibility is that I can deduce that the OP doesn't know the difference between ? and !

 

[Doctordick]

Area 54 --

In a sense, (that is, with regard to my numeric representation) photographs are certainly a form of communication of presumed facts which can be represented by numerical references. Consider transmission of those photographs with a computer. They are certainly transformed into a numeric code.

Think about it a little. 

John Cuthber,

You have presumed you know what "I" means, what "think" means, what "therefore" and what "am" means. Those are all presumptions!

I have no idea as to what "OP" refers to so I can not respond to that comment.

[John Cuthber]

20 minutes ago, Doctordick said:

 

John Cuthber,

You have presumed you know what "I" means, what "think" means, what "therefore" and what "am" means. Those are all presumptions!

I have no idea as to what "OP" refers to so I can not respond to that comment.

OP = Original Post(er)

That's you, in this thread.

OK 

"What can be deduced without making presumptions!"
Nothing.

That's not a philosophy that will get you very far, but the idea of there being no recognised meaning for words is the inspriration for this.
https://xkcd.com/1860/

 

[Area54]

24 minutes ago, Doctordick said:

Area 54 --

In a sense, (that is, with regard to my numeric representation) photographs are certainly a form of communication of presumed facts which can be represented by numerical references. Consider transmission of those photographs with a computer. They are certainly transformed into a numeric code.

Think about it a little.

You specified "language" and not the more general "communication". Language is a form of communication. Photographs can be used another form of communication. My objection stands. You seem to be attempting a tightly argued thesis, yet you have - in your first substantive assertion - been loose and imprecise in your terminology. That does not bode well for success.

[imatfaal]

I am very good at origami. I tend to do it without thinking and get into an almost meditative state.

A few days before christmas I am sitting at my dining table making little sonobe cubes and other shapes from scraps of wrapping paper to decorate christmas tree - everyone else TBOMK is watching a film.  After about twenty minutes my (frighteningly bright) niece slides a sonobe cube across the table to me that she has made and learned to make by watching me.

There has been no deliberate communication, let alone use of language, as I have never even noticed she was there - I am making sonobe polyhedra not doing anything else consciously (that's the whole point); but the process of making sonobe cubes has been explained ie passed from one individual to a second with no use of language what so ever

I still get sonobe cubes sent to me by my niece - but she never really mastered the complex stuff

 

[Strange]

3 hours ago, Doctordick said:

Coming up with an explanation of anything requires comprehension of a language first. If there are readers who believe that is not a fact, I would have them please present an explanation without use of a language of any kind.

Communicating the explanation may require language but it isn't obvious that coming up with an explanation does.

So you are assuming (I assume you mean "assumption" not "presumption") that thought requires language. Or do you have a reference to support this?

And I can imagine some explanations are sufficiently simple that they don't require language. Just a drawing, for example. 

3 hours ago, Doctordick said:

I first  define "understanding" to be the probability the receiver presumes the source holds a specific represented thought to be true.

What does "truth" have to do with it?

Do you perhaps mean "meaningful"?

You seem to be describing the basic process by which babies acquire language- by analysing probabilities of sounds, words, context, etc occurring together. But none of that content has to be "true" but the baby brain does assume (presume) that there is meaningful relationships / information to be discovered. 

3 hours ago, Doctordick said:

In essence, that thought is presumed to be a true fact.  

Childrenearn language from stories and fairy tales just as much as from "true facts" (whatever that even means). 

In ahort, your argument is full of assumptions that you do not seem to be aware of. I would recommend an introductory course in philosophy so you can tighten up your reasoning. 

Apart from that, I look forward to you using this thread to move some steps beyond where we got before. 

[Doctordick]

3 hours ago, John Cuthber said:

"What can be deduced without making presumptions!"
Nothing.

That's not a philosophy that will get you very far, but the idea of there being no recognised meaning for words is the inspriration for this.
https://xkcd.com/1860/

 

Yes, it is dammed near "Nothing" --- but not quite!!!

And representing experiences without making any assumptions of any kind is quite a difficult thing to achieve. 

3 hours ago, Area54 said:

You specified "language" and not the more general "communication". Language is a form of communication. Photographs can be used another form of communication. My objection stands. You seem to be attempting a tightly argued thesis, yet you have - in your first substantive assertion - been loose and imprecise in your terminology. That does not bode well for success.

I would rather you comprehend that I used the word "language" to specify the means of communication without specifying exactly how that communication is achieved. My central point is the fact that any communication received from the universe is built from concepts which can be labeled. And using that numeric representation, any thought can be represented via collections of those concepts in a form  (x₁,x₂,⋯,x_i,⋯,x_n).

The existence of such a representation is my only assertion. If you disagree present me with a thought which cannot be so represented.

2 hours ago, imatfaal said:

I am very good at origami. I tend to do it without thinking and get into an almost meditative state.

You are simply not concerned with the issue of "explaining" itself. Explanations are the central issue of most all sciences and my point is the fact that John Cuthber's comment, "What can be deduced without making presumptions!" -- Nothing, (though quite close to right), is not absolutely correct!

55 minutes ago, Strange said:

Communicating the explanation may require language but it isn't obvious that coming up with an explanation does.

So you are assuming (I assume you mean "assumption" not "presumption") that thought requires language. Or do you have a reference to support this?

And I can imagine some explanations are sufficiently simple that they don't require language. Just a drawing, for example. 

What does "truth" have to do with it?

Do you perhaps mean "meaningful"?

You seem to be describing the basic process by which babies acquire language- by analysing probabilities of sounds, words, context, etc occurring together. But none of that content has to be "true" but the baby brain does assume (presume) that there is meaningful relationships / information to be discovered. 

Childrenearn language from stories and fairy tales just as much as from "true facts" (whatever that even means). 

In ahort, your argument is full of assumptions that you do not seem to be aware of. I would recommend an introductory course in philosophy so you can tighten up your reasoning. 

Apart from that, I look forward to you using this thread to move some steps beyond where we got before. 

I am not concerned with the issue of "coming up with an explanation", I am concerned with "communicating an explanation"! I am looking at that communication as referring to what the receiving individual has to work with: i.e., the universe he (or she) experiences. And most all of our beliefs are built upon presumptions built on presumptions. The only real defense of those beliefs are self consistency with our experiences. The real issue I am concerned with is "do there exist explanations which we have not thought of?"

Have you no interest in "truth"? I suspect "meaningful" is no more than requiring that self consistency I just referred to above.

You are presuming I am talking about those beliefs being "true". I am not, I am concerned with the "receiving individual's" belief that they are true (that the source is not feeding them invalid information), an issue central to whatever conclusions are arrived at.

No, my argument is not full of assumptions. Your reading of it is embedded in assumptions as to what you think I am saying and/or where you think I am going!

Read what I have written carefully and if you can comprehend the constraints I want to work with let me know. 

 

My first step in redefining those indices is to add ignorance to the representation. I do this by setting n equal to the largest value required by the largest possible thought. This makes n the same in all represented thoughts.

Thank you for reading this -- DoctorDick

[swansont]

5 hours ago, Doctordick said:

Coming up with an explanation of anything requires comprehension of a language first. If there are readers who believe that is not a fact, I would have them please present an explanation without use of a language of any kind.

I take it you've never assembled an Ikea product

[John Cuthber]

8 minutes ago, swansont said:

I take it you've never assembled an Ikea product

Has anyone ever assembled an ikea product?

 

Seriously, without assumptions about what words (or pictures or symbols) mean, you can't put any idea across. So you can't really deduce anything, because there's nothing on which to base any deduction.

 

[Doctordick]

I have a couple quotes which might (or might not) clarify what I am talking about!

"Too often it is said that there is no absolute truth, but only opinion and private judgment; that each of us is conditioned, in his view of the world, by his own peculiarities, his own taste and bias; that there is no external kingdom of truth to which, by patience and discipline, we may at last obtain admittance, but only truth for me, for you, for every separate person. By this habit of mind one of the chief ends of human effort is denied, and the supreme virtue of candor, of fearless acknowledgment of what is disappears from our moral vision. Of such skepticism mathematics is a perpetual reproof; for its edifices of truths stands unshakable and inexpungable to all the weapons of doubting cynicism."

Bertrand Russell, 1872­-1970
 

"As a conscious being I am involved in a story.  The perceiving part of my mind tells me a story of a world around me. The story tells of familiar objects.  It tells of colours, sounds, scents belonging to these objects; of boundless space in which they have their existence, and of an ever-­rolling stream of time bringing change and incident.  It tells of other life than mine busy about its own purposes.  As a scientist I have become mistrustful of this story."

Sir Arthur Eddington, 1934 

These men have played a large roll in my thoughts.

Thank you --- DoctorDick

[Strange]

1 hour ago, Doctordick said:

I am not concerned with the issue of "coming up with an explanation", I am concerned with "communicating an explanation"!

I can only comment on what you write, not what you (later) claim to be concerned with. You said "coming up with an explanation".

Quote

And most all of our beliefs are built upon presumptions built on presumptions.

ASSUMPTION. ASSUMPTION.

Yes, all our beliefs and knowledge are based on various assumptions and axiomatic ideas. And your idea is also based on lots of assumptions. I have pointed out some, other people have noted some others.

But I really don't think that is relevant. I just want you to get to the point instead of all this faffing about.

Quote

Have you no interest in "truth"?

Not really, no. Which is why I am interested in science. (If I was interested in "truth" I would be hanging around on religion forums.)

Quote

You are presuming I am talking about those beliefs being "true".

Again, I can only respond to what you actually say. If you mean something different then I can't comment on that.

Quote

I am concerned with the "receiving individual's" belief that they are true (that the source is not feeding them invalid information), an issue central to whatever conclusions are arrived at.

But the receiver doesn't have to think they are true. Children can learn language from fairy tales. They (probably) know that the stories are not true. That doesn't stop them (a) using the input to extend/strengthen their knowledge of language and (b) understanding the story.

So your assumption that truth is important is wrong.

Quote

No, my argument is not full of assumptions.

The fact that you are not aware of them (even after people have pointed them out) doesn't stop them being there.

Quote

Read what I have written carefully and if you can comprehend the constraints I want to work with let me know. 

I have. I can.

And it is fairly insulting to assume that people who do not instantly accept everything you say are either not reading it or unable to understand. I can read and I can understand what you write. I just happen to disagree with some of it. 

(Of course, you are now claiming that you sometimes mean something other than what you write. That does rather complicate things.) 

Quote

I do this by setting n equal to the largest value required by the largest possible thought.

Why do you assume that n is finite?

[Area54]

@Doctordick

I note that Strange has found, as I did, that your writing is sometimes ambiguous. Ambiguity is not unusual in forum posts; we are not writing papers for Nature. However, you are seeking to present/develop, if I understand you, a fundamental concept relating to language, communication and explanations, amongst other things.

Given that ambitious intent it behoves you to post with more precision and care than the typical forum post. Your have failed to do so. I shall continue to watch this thread, but if you continue to redefine your meaning each time you are questioned I shall rather rapidly abandon the effort.

If this comes across as aggressive I apologise. I think I am partly influenced by your comment in the OP - " It also points out a few minor errors in modern physics not realized by the professionals." This has echoes of the internet trolls who "have a theory" based upon the fact that "science has got it wrong". I hope I am mistaken and this is just another example of you not wrting what you meant.

Edited July 26, 2017 by Area54

[Strange]

1 hour ago, Doctordick said:

These men have played a large roll in my thoughts.

Role. 

[swansont]

1 hour ago, Doctordick said:

These men have played a large roll in my thoughts.

Thank you for this. I kneaded it.

[Area54]

5 minutes ago, swansont said:

Thank you for this. I kneaded it.

Are you suggesting his thoughts may be half-baked?

[Manticore]

Rather than merely converting symbols to numbers, maybe you should look up Gödel Numbers (here's a good simplified explanation http://www.jamesrmeyer.com/ffgit/GodelSimplified3.html).

Basically every possible combination of symbols can be used to create a unique number.

[Strange]

That's a very good point. Any system that the OP comes up must be (by his own definition) sufficiently expressive that it will, by Godel's theorem, be incomplete; i.e. will say things that may be either true or false (undecidable). I wonder if he has taken this fact into account ...

[Doctordick]

I get the definite feeling that you entirely failed to read (or failed to comprehend my post of 7/26/2017

 

On 7/26/2017 at 1:57 PM, Doctordick said:

Yes, it is dammed near "Nothing" --- but not quite!!!

And representing experiences without making any assumptions of any kind is quite a difficult thing to achieve. 

I would rather you comprehend that I used the word "language" to specify the means of communication without specifying exactly how that communication is achieved. My central point is the fact that any communication received from the universe is built from concepts which can be labeled. And using that numeric representation, any thought can be represented via collections of those concepts in a form  (x₁,x₂,⋯,x_i,⋯,x_n).

The existence of such a representation is my only assertion. If you disagree present me with a thought which cannot be so represented.

You are simply not concerned with the issue of "explaining" itself. Explanations are the central issue of most all sciences and my point is the fact that John Cuthber's comment, "What can be deduced without making presumptions!" -- Nothing, (though quite close to right), is not absolutely correct!

I am not concerned with the issue of "coming up with an explanation", I am concerned with "communicating an explanation"! I am looking at that communication as referring to what the receiving individual has to work with: i.e., the universe he (or she) experiences. And most all of our beliefs are built upon presumptions built on presumptions. The only real defense of those beliefs are self consistency with our experiences. The real issue I am concerned with is "do there exist explanations which we have not thought of?"

Have you no interest in "truth"? I suspect "meaningful" is no more than requiring that self consistency I just referred to above.

You are presuming I am talking about those beliefs being "true". I am not, I am concerned with the "receiving individual's" belief that they are true (that the source is not feeding them invalid information), an issue central to whatever conclusions are arrived at.

No, my argument is not full of assumptions. Your reading of it is embedded in assumptions as to what you think I am saying and/or where you think I am going!

Read what I have written carefully and if you can comprehend the constraints I want to work with let me know. 

 

My first step in redefining those indices is to add ignorance to the representation. I do this by setting n equal to the largest value required by the largest possible thought. This makes n the same in all represented thoughts.

Thank you for reading this -- DoctorDick

On 7/27/2017 at 4:49 AM, Strange said:

That's a very good point. Any system that the OP comes up must be (by his own definition) sufficiently expressive that it will, by Godel's theorem, be incomplete; i.e. will say things that may be either true or false (undecidable). I wonder if he has taken this fact into account ...

You should comprehend that adding "ignorance" to the representation (when I set "n" in every expressed thought to be the largest value required by the largest thought representation) adds elements (included concepts which are explicitly (undecidable). That was my first example of changes in the definition of those indices required to make it possible to view P(x₁,x₂,⋯,x_i,⋯,x_n) as a valid mathematics expression. A step designed to remove problem #2 in my opening post!

If that step is incomprehensible to you why don't you just stop worrying about this thread. Just as an aside, can you come up with a change in my definitions which will remove  the first problem? It is not actually a very difficult issue to fix.

Have fun ---- Dick 

Edited July 30, 2017 by Doctordick
latex errors

[Strange]

58 minutes ago, Doctordick said:

why don't you just stop worrying about this threa

I am waiting for you to say something novel and/or interesting. I don't know why you are taking so long to get to the point....

[Doctordick]

 

In my opening post, I pointed out the fact that a numerical representation requires a rather surprising constraint: i.e., 

                                        P(x₁+c,x₂+c,⋯,x_i+c,⋯,x_n+c)−P(x₁,x₂,⋯,x_i,⋯,x_n)=0

is absolutely required under such a representation. It is interesting because absolutely no presumptions were made: i.e., (x₁,x₂,⋯,x_i,⋯,x_n) can represent any thought expressed in any language. And I also assert that it is novel as I have never seen any such assertion made in any scientific article I have read and I have read a great number.

Now, if that assertion can be converted into a mathematical expression (which it certainly is not as originally defined) by redefining those indices without constraining what is expressed, some rather astounding results can be obtained. 

If you do not find that to be both interesting and novel, I suggest you (and all the other mindless readers) cease posting to this thread. I have already pointed out a rather trivial adjustment in the definition of those numerical indices which rids the problem of the fact that "n" varies from expression to expression (which is totally contradictory to the definition of mathematical functions). I have merely added ignorance to the representation!

If this is totally beyond your mental comprehension, I apologize! 

Have fun ---- Dick 

Edited July 31, 2017 by Doctordick
failure of latex expression to hold together!

[John Cuthber]

Re

"   P(x₁+c,x₂+c,⋯,x_i+c,⋯,x_n+c)−P(x₁,x₂,⋯,x_i,⋯,x_n)=0"

you seem to have used some symbols there.

There's a tacit presumption that the symbols mean what you think they do and that the relationships between the symbols in some way mimic relationships between real entities.

 There's also a presumption that some entities exist, in order to be represented by those symbols.

 

That's a whole pile of presumption.

 

 

[Strange]

31 minutes ago, Doctordick said:

If this is totally beyond your mental comprehension, I apologize! 

It is readily comprehensible, unoriginal and apparently worthless. Still waiting for you to get to the point. 

Edited July 31, 2017 by Strange

[John Cuthber]

23 hours ago, Strange said:

I am waiting for you to say something novel and/or interesting. I don't know why you are taking so long to get to the point....

I have to say I agree; the statements are either trivially true, or trivially false, depending on the interpretation.