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Today's era is Post Modern. This means that a frame of refernce is not necessarily required or if one is employed it can be changed mid argument. IOW, today it appears valid to move your goal posts to kick a goal removing falsifiability from most arguments, even within the sciences. Mathematically this means that a defined constant to which all the variables within a theory must remain dependent is no longer required reducing Post Modern science to nothing more than reversible (tautological) mathematics. It was Galileo who proposed that only comparing variables without a constant to act as a falsifiable frame of reference prohibits any meaningful concept of cause and effect. We cannot tell if the sun goes around the earth or vice versa without a valid, i.e. constant frame of reference which of course, cannot change except via falsification allowing the evolution of a new theory contradictory to the old one. For example, Einstein's c, which Newton thought was just a variable was shown to be a constant reducing M and T (mass and time) to just variables within Special Relativity. Likewise, Darwin reduced species to evolving variables allowing a combination of survival and reproduction to be maximized providing a new falsifiable frame of reference for the biological sciences in contradiction to religious dogma.

In a world overburdened by massive debt, a science of climate change entirely dependent on mathematical modeling, theory within the physical sciences dominated by non falsifiable infinities and a Neo Darwinism that cannot be empirically falsified only non verified, I ask: what is your FALSIFIABLE frame of reference?


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  • Jun 7 2012: In your first example, you have not separated the difference between living and non living "existence". While it is true that all the non living are connected this remains untrue for living systems. Darwinism works via separate individuals competing and cooperating within evolving populations. Natural selection absolutely requires this separation. Nothingness within reality does not mean that reality is only nothingness because if it did this axiom only represents a tautology ( any circular argument) which cannot be used as a valid, falsifiable frame of reference.
    A reality within a reality without end is also circular so it cannot present a valid frame of reference. Randomness, like all the other axioms you offered, has no possible cause and effect so it is only mathematical not scientific. My point is that mathematics, which is all you appear to be employing here, is not a science. This is because everything within mathematics is logically revresible. To provide a theory of science you must provide at least one non reversible (non tautological) proposition such as " all swans are white". This immediately plugs into the "square of opposition" allowing the falsiying contradiction "some swans are not white". The contrary proposition "no swan is white" does not falsify it only non verifies. This is because nobody can validly claim to have observed every swan (the problem of induction). Because "all swans are white prohibits " all white (things) are swans" the falsifying frame of reference in this instance is the predicate "white". The problem of induction is removed because the falsifying contradiction " some swans are not white" is allowed. IOW, only if a proposition completes a square of opposition can it be said to be reasonable. Mathematics is logical but it isn't reasonable because the axioms of mathematics cannot complete a square.


    John Edser
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      Jun 7 2012: Hi

      "therefore there is only reality within other reality", it isn't a circular or infinite. What i mean is, that "inside reality there is only reality" (in line with "there is no nothingness within reality").

      There is scenario:

      - There is proposition (should be tested whether it's true or not) = "all swans are white"
      - Just one fact to prove (falsify) "that not all swans are white, but there are several swans are black"

      What i mean is, whether scientific or not, or any other way to find another knowledge (induction or deduction), in essence, is the way to get a consistent knowledge.

      And falsifying is a part of a way to find out whether a proposition is consistent (universally) or not. It's the essence. And we shouldn't limit falsifying by targeting through frame of reference.

      Axiom is another way to falsify whether a knowledge is consistent or not. And in my opinion it's enough to be a tool to falsify. It just that i don't want to be trapped on limited falsifying.

      Somehow, we could use falsify to justify: "he was good", but when he did mistake, then he is bad, and similar to this. It's debatable, & we just stop there, and we couldn't understand the essence of something.

      The point is (about falsifiability): that we should understand falsifying and see the essence of it and if possible try to move to a higher capability that give better capability to expand the area of ​​certainty. That's why i choose axiom as another way to falsify. It leads us to a better understanding, the essence, so we can do a proper act within our life. And it could be considered (in my opinion) falsifying but much better.

      Sorry, for having conversation on a different line, but that's falsifiability on my side (since, known and formal falsifiability could lead to chaotic as i mentioned). Hopefully we have the same purpose, having the essence.

      • Jun 7 2012: The main falsifiable point that Darinism makes is that the fitness of individuals that are competing and cooperating within the same population, must differ to allow any natural selection. This absolutely requires a complete separation of all biological individuals, e.g. I can't eat or breath for you. Life is very unlike non life because all living individuals remain biologically separate. This is why physics alone cannot explain life. Allowing a reality within another is tautological if the proposed realities are proposed equal. If they are different then you must say how exactly.

        My swan example was provided to demonstrate how a falsifiabe frame of reference differs to your axiomatic frames; axioms are not falsifiable only non verifiable. With regards to your argument for consistency I would like to point out that while every tautology is consistent, none of them can be falsified. Reason requires much more than self conintency, i.e. while all reasoning must be consistent not all logically consistent propositions are reasonable. When something is shown inconsistent (proffers a contradiction) this does NOT falsify the proposition simply because there was no proposition. All it can do is prove the proposition invalid. Falsifiability is a term reserved for comparing at least two self consistent propositions via experiment in order to discover which one remains empirically correct. There is no higher capability than falsification simply because all falsifications are verifications of a contradictory proposition. In my swan example the predicate "white" provided the frame of reference. This can be empirically falsified by the obervation of just a single non white swan. As you suggested, this means a black, red or some other colored swan has to be observed as a verification of a contradictory proposition. Unfortunately Karl Popper, the father of falsifiability, failed to understand this leading him to discount the value of verification.

        John Edser
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      Jun 7 2012: Hi,

      Axiom is not always related to mathematics, the fact "that we are aware therefore we are exist", it is an axiom. But when something empirical observation can not be replaced by the axiom through mathematics, while being pulled down to its most basic, we often use the axioms of mathematics.

      There are several things for me:

      - That something that can be falsified, can't be considered empirically falsified if we never found a chance to falsify. Although it is possible according to its proposition.

      The statement "all swans are white" that can be empirically falsified through further observation to find out whether there is just one "swan with black color (or other color), and it will be meaningless if there is someone for the entire life could not see a black swan.

      - As well as for the axiom, as far as we understand the axiom as a representative of a reality, and explore the structure of the axioms is the same as exploring the possibilities of reality, then the axiom can also be falsified if there is a chance for it.

      The points are:

      - I'd rather thinking about falsifiability as: "something regarded as a universal truth and could be considered as axiom, at first", and verify it through empirical observation (or may be represented by other axiom) "

      - As generally known about falsifiability, while i see the meaning of "falsifiability" is not specifically related to a form of reasoning. Axiom can justify and can be justified (falsified). It's similar to empirical observation that can justify and can be justified.

      - Since the term of empirical could be different to others, therefore, consistency could be reasonable or not, scientific could be widen or not, and falsifiability could be different to others. It's relative to people's experience.

      • Jun 8 2012: The test for falsifiability is not difficult: if you state something such that when the subject S and predicate P are reversed this changes the meaning entirely then the proposition is minimally falsifiable via this reversal. For example, you proposed " we are aware therefore we exist" (as a non mathematical axiom ). Does "we exist therefore we are aware" mean the same ? If so, then the axiom is not falsifiable because it is absolutely self referential. If the meaning is not the same then reversing the proposition provides a contradiction such that if it is observed in nature it falsifies your proposition.

        Your point that faslsifiability is entirely subjective is not true. The reason why science can be clearly understood in any culture demonstrates this.


        John Edser
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          Jun 8 2012: Hi

          It's not subjective, but it's subjective within advanced, deepening, or widen. It's like the way we manage ourselves are subjective, but the purpose may be just the same.

          It's the way we use (in practice) that it is different to others, but the structure (in essence) is just the same.

          Please refer to my answer below.

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      Jun 7 2012: Perhaps, this could describe my structure of thinking on this case:

      - all S(wan) -> (therefore, asserts) y (white)
      - If all S(wan) -> y, then there shouldn't be an existence of S(wan) -> -y (black)
      * But there is S(wan) -> -y, therefore it's falsified

      - all (axiom, x) -> asserts (an axiom, y)
      - If all (axiom, x) -> asserts (an axiom, y), then there shouldn't be an existence of (an axiom, x) -> asserts (an axiom, -y)
      * But there is (an axiom - x) -> asserts that (an axiom, -y), therefore it's falsified

      - all ( f(x) = x^n ) -> asserts (a graph is symmetric to the y-axis)
      - If all ( f(x) = x^n ) -> asserts (a graph is symmetric to the y-axis), then there shouldn't be an existence of ( f(x) = x^n ) -> asserts (a graph is not symmetric to the y-axis)
      * But there is ( f(x) = x^n ) (where "n" is an odd number) -> asserts (a graph is not symmetric to the y-axis), therefore it's falsified.

      We shouldn't confuse with axiom & swan, where "S" for any Swan, but for axiom(s) as different animals, but it's incorrect. Actually, "S" for any Swan (typical), and for axiom(s) as (typical) the same animal.

      Where "S" and "the function" is typical as the swan, where the swan is the same animal but it could be conditional (different) at the specific situation. Just the same as this axiom, that it has differences ("^n") to others but still within typical of a function ("x^n").

      • Jun 8 2012: You are employing mathematical notation to make your point. This is not a mathematical discussion group. Please rewrite what you mean in words so that all of us can understand your argument

        I do not understand your last sentence which summed up your main point. Are you saying that it is not necessary to provide another axiom that contradicts in order to falsify a proposed axiom?


        John Edser
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          Jun 8 2012: Hi

          If necessary, we can use an axiom to verify a possible contradiction at the final node of form of axiom as a falsifying (if we agree that such this way could be considered valid as we do empirical observation). Or, if we disagree, we could contradict an axiom at the final node of form of axiom with reality (if we have a chance for it).

          I will try to explain form of axiom using examples:

          //If we touch something then we touch an existence, but axiom asserts there is only zero distance or there is a distance, therefore we never touch existence//

          - all (we touch something, x) -> asserts (we touch an existence, y)
          - if all (that we touch, x) -> asserts (we touch an existence, y),
          --- then there shouldn't be an event of (that we touch, x) -> asserts (we don't touch an existence, -y)

          -- but there is (we have no distance to what we touch - x) -> asserts that (we never touch an existence, -y), Therefore form of axiom COMPLETELY falsified
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          Jun 8 2012: Another example:

          //Every dream is unrealistic, but axiom asserts that there is no nothingness within reality (inside reality there is only reality), and a dream is just another reality, unless we accept our awareness of being accused as something that is not real//

          - all (someone is dreaming about someone's self, x) -> asserts (in someone's dream, someone is not real, y)
          - if all (someone is dreaming about someone's self, x) -> asserts (in someone's dream, someone is not real, y),
          --- then there shouldn't be an even of (someone is dreaming about someone's self, x) -> asserts (in someone's dream, someone is real, -y)

          --- but there is (someone is dreaming about someone's self, - x) -> asserts that (in someone's dream, someone is real, since someone considered within real world, -y), or

          --- but there is (someone is dreaming about someone's self - x) -> asserts that (in someone's dream, someone is ENTIRELY real, since someone's awareness and someone's body inside dream is considered just another "me" and those are real in someone's sense, -y),

          * Therefore it's falsified. In this case, our assertion is an axiom itself. People might argue that "myself entirely while dreaming was real in my own perception"


          --- but there is (someone is dreaming about someone's self - x) -> asserts that (in someone's dream, NOT ENTIRELY someone is not real, since someone's awareness is the only real one that someone believe, -y)

          * Therefore it's falsified, where, one of someone's self (someone's awareness) is the real one. In this case, our assertion is an axiom itself. People might argue that our awareness while dreaming was real, but it wasn't for our hand (nose, etc).
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          Jun 8 2012: Further example:

          //Randomness is everywhere, but axiom asserts its consistency (certainty)//

          - (event is coincident, x) -> asserts (there is inconsistency, y)

          - all (event is coincident, x) -> asserts (there is no consistency, y)
          - if all (event is coincident, x) -> asserts (there is no consistency, y),
          --- then there shouldn't be an existence of (event is random, x) -> asserts (there is a pattern, -y)

          --- but there is (randomness in an event of computer programming - x) -> asserts that (randomness in computer programming was produced based on pattern - since this pattern could be produced using complicated function, it's lack of predictability, -y), therefore falsified.

      • Jun 8 2012: Bernard,

        For some reason no facility is displayed on my computer for me to be able to reply to any of your recent posts. I repeat, I cannot understand your notation. For example I do not know what -> -y means.
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          Jun 9 2012: Hi

          Forgive me. Thank you for being patience.

          "x" -> "y" = "x" then "y"
          all "x" -> "y" = all "x" then "y"
          swan is white = if swan then white = if "x" -> "y" or if "s" -> "w"
          there is black swan = if swan then not white = if "x" -> -"y" or if "s" -> - "w" or if "s" -> "b"

          To be more specific:

          - if (there was someone looking at a swan) then -> (it caused) (there was someone told us that there was white color of something on a swan) = why did he/she say there was white color of something on a swan? yes, because he/she already saw white of something on a swan

          - one day (there was someone looking at a swan) but then -> (it caused) (there was someone told us that there wasn't white color but black color of something on a swan) = why did he/she say there wasn't white color but black color of something on a swan? yes, because he/she already saw another black color of something on another swan

          - therefore, we conclude there were black and white of something on swans = there were black color of something on a swan, or there might be a white color of something on different swan.


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