moving finger
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Hi Paul
The first words at the start of this thread were :
Calling “the receptive principle” a mathematical primitive is thus (it seems to me) simply a convenience in this case, so that one may avoid giving any further explication of what one means by “the receptive principle”. I have no idea what you mean by the term “receptive principle”, and when asked to explain what it is supposed to mean you then seem to hide behind your “mathematical primitive” excuse in order to avoid further explication, hence your argument is totally unintelligible to me.
Are you now saying that your definition is incorrect?
Best Regards
The first words at the start of this thread were :
I agree 100% with this statement. What I have been trying to do since then is to understand your own definitions of these very terms. “Knowledge” for example you define in terms of something you call the Receptive Principle, but you refuse to define what you mean by the Receptive Principle. This seems to me simply to be replacing one undefined term (“Knowledge”) with another (“the Receptive Principle”), thus I cannot see how it is supposed to be a step forward.Paul Martin said:It seems to me that we too frequently use the terms 'truth', 'knowledge', 'belief', 'faith', 'reality', 'existence', and 'consciousness' without first defining them.
It may indeed be the case that I don’t understand enough mathematics, since I am not a mathematician like yourself. However I do not believe there is much in the way of mathematics in your proposal, and I see your response here (with the greatest respect) as simply a possible attempt at evading the real issue, which is the meaning of the term “knowledge”.Paul Martin said:it seems to me that you don't understand enough mathematics to understand my proposal.
Forgive me, but I simply don’t see what relevance this has to understanding the meaning of English language terms such as “Knowledge” and “Consciousness”.Paul Martin said:I doubt that one can grasp the significance of the power of abstract mathematics to solve, in this example, problems of squaring the circle and trisecting an angle with ruler and compass, unless one has done the hard work of studying and understanding enough Galois Theory.
It seems to me that you are adopting mathematical conventions to suit your philosophical argument (and then accusing anyone who does not understand enough maths as being unable to understand your argument). The assertion that knowledge is to be defined in terms of the receptive principle (which is your assertion) is not a definition in terms of a mathematical primitive (no matter how much you would like it to be), it is a definition of one concept in terms of another concept. If you wish to present a true mathematical argument then I would probably not attempt to enter into any discussion with you because I freely admit that my maths is appalling, but you have not presented a mathematical argument.moving finger said:Are you saying that you cannot offer any definition or meaningful interpretation of this thing you call the Receptive Principle?
Paul Martin said:Of course I could offer a definition or interpretation. But if I did I would be violating a fundamental rule of mathematics. It is strictly forbidden in mathematics to define or describe or interpret any primitive. That's the whole idea. Primitives are undefined.
Calling “the receptive principle” a mathematical primitive is thus (it seems to me) simply a convenience in this case, so that one may avoid giving any further explication of what one means by “the receptive principle”. I have no idea what you mean by the term “receptive principle”, and when asked to explain what it is supposed to mean you then seem to hide behind your “mathematical primitive” excuse in order to avoid further explication, hence your argument is totally unintelligible to me.
Understanding math has nothing to do with understanding what the term “receptive principle” is supposed to mean.Paul Martin said:I thought you understood more math.
My question was in response to your definition in post #26 :moving finger said:Any “set of bits” (including a random set) qualifies as “information”?
Paul Martin said:No. In a mathematical development you must remain consistent with all previously taken definitions, axioms, and primitives. It is not permitted to simplify the definition of a defined term later on.
I was simply asking a question regarding your claimed definition.Paul Martin said:First, I would define 'information' as sets of bits.
Are you now saying that your definition is incorrect?
As AKG has also pointed out, this leads to the absurd notion that X can know something which is false, such as for example “Paul knows that Hitler won the 2nd World War”. You may believe this statement makes sense, but most users of the English language would agree that in this case Paul does not in fact possesses knowledge, instead he is simply mistaken in believing that Hitler won the 2nd World war.moving finger said:According to your definition, X can correctly claim to possesses knowledge that Y, even if ~Y? (ie Y is false).
Paul Martin said:Yes.
It is most certainly not consistent with ordinary usage. You seem to have adopted a private meaning for the word “knowledge”. I might claim (based on my belief that Y) that I know that Y, but if Y is in fact false (ie if ~Y) then I do not in fact know that Y (I simply believe that I do). Just as you claim that I am ignorant of mathematics and therefore cannot understand your argument based on mathematical primitives, I respectfully suggest that you need to study a little more epistemology so that you can understand your mistake regarding the meaning of knowledge.Paul Martin said:That is consistent with ordinary usage. Think of the generations of scientists and technologists prior to Einstein who did exactly that with respect to Newton's "Laws". Take 'Y' to be 'F = ma'. Y is extremely useful knowledge in spite of its being false.
Then I must conclude that you and I have fundamentally different understandings of the word “knowledge” – which gets right back to the first sentence of your first post in this thread - that we too frequently use the terms 'truth', 'knowledge', 'belief', 'faith', 'reality', 'existence', and 'consciousness' without first defining them. Your suggested definition of “knowledge” in terms of “apprehending bits” (with respect) is not a definition that makes sense on its own, and it is only when we try to understand just what it is you are trying to say (via the discourse we have just had) that we realize that you have a very peculiar and personal interpretation of just what you think “knowledge” means.moving finger said:Your definition seems to imply that one can know things which one does not believe, and even worse that one can know things which are false. Would you agree?
Paul Martin said:Yes, I agree, except that I would get rid of the word 'worse'. I don't think it is bad at all.
Best Regards
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