Nested Propositions: True False Meaningless; A Thought Experiment

[muazjalil]

According to Bertrand Russell (The Open Society and its Enemies: Vol II, Popper, K. ; 1945) there are three types of propositions, namely True, False and Meaningless or pseudo proposition. Now Popper (1945), if I understood him correctly, was against the idea of equating true proposition with proposition of natural science (Wittgenstein’s idea) as such a step would remove false hypothesis from the realm of science. And since we cannot know if a hypothesis is true or not, by definition, it becomes part of metaphysics and as such meaningless. Now let us take popper’s side and assume that there is a class of propositions (Y) which state that certain proposition, X, cannot be tested (i.e. proven or disproven). Now if (Y) is true then falsification theory cannot be applied to X but one can very well apply it to Y itself. Then Y becomes a testable hypothesis, which can be true false or meaningless.

Now we can construct a thought experiment, whereby we can state under what condition we can state Y is true or false. And so we can state if the result is Z1, then Y is true and if it is ‘not Z1’ then Y is false. Based on falsification paradigm, we should be looking for ‘not Z1’ and until we find it we can say Y is provisionally true. If the result is ‘not Z1’ then Y is false and X is indeed testable. If the result is Z1 then Y is provisionally true and X cannot be tested. But this in turn means X cannot be proven or dis-proven and therefore cannot be true or false and therefore is meaningless. Now what characteristic must ‘not Z1’ have is the important question, since upon it depend all outcomes; A proposition can be false in many ways and therefore Not Z1 includes all possible outcome other than Z1.

‘Not Z1’ implies X is testable; therefore if we can construct a hypothetical situation where we can state X is true or false then we have already proven Y is false (which is obvious). It seems the truth value of Y cannot be determined without trying to determine the truth value of X. If X is either true or false then Y is false but if X is meaningless then Y is true. Thus if we fail to construct such a situation whereby we can state under this condition we can test X then Y is provisionally true and X is indeed meaningless.

Let us take the hypothetical proposition “the statement ‘there is a God’ cannot be tested’, where ‘there is a God’ is X. Create a thought experiment which can prove or disprove X or simply take the situation (to help you visualize): Under what condition would a theist believe there is no God or vice versa an Atheist would believe there is a God. I could not find any condition which could satisfy or answer this question. Therefore X is meaningless and Y is true. And since Y is true it is part of the totality of true propositions (Wittgenstein) while X is not. The result does seem a bit trivial, much ado about nothing.

[cafolini]

According to Bertrand Russell (The Open Society and its Enemies: Vol II, Popper, K. ; 1945) there are three types of propositions, namely True, False and Meaningless or pseudo proposition. Now Popper (1945), if I understood him correctly, was against the idea of equating true proposition with proposition of natural science (Wittgenstein’s idea) as such a step would remove false hypothesis from the realm of science. And since we cannot know if a hypothesis is true or not, by definition, it becomes part of metaphysics and as such meaningless. Now let us take popper’s side and assume that there is a class of propositions (Y) which state that certain proposition, X, cannot be tested (i.e. proven or disproven). Now if (Y) is true then falsification theory cannot be applied to X but one can very well apply it to Y itself. Then Y becomes a testable hypothesis, which can be true false or meaningless.

Now we can construct a thought experiment, whereby we can state under what condition we can state Y is true or false. And so we can state if the result is Z1, then Y is true and if it is ‘not Z1’ then Y is false. Based on falsification paradigm, we should be looking for ‘not Z1’ and until we find it we can say Y is provisionally true. If the result is ‘not Z1’ then Y is false and X is indeed testable. If the result is Z1 then Y is provisionally true and X cannot be tested. But this in turn means X cannot be proven or dis-proven and therefore cannot be true or false and therefore is meaningless. Now what characteristic must ‘not Z1’ have is the important question, since upon it depend all outcomes; A proposition can be false in many ways and therefore Not Z1 includes all possible outcome other than Z1.

‘Not Z1’ implies X is testable; therefore if we can construct a hypothetical situation where we can state X is true or false then we have already proven Y is false (which is obvious). It seems the truth value of Y cannot be determined without trying to determine the truth value of X. If X is either true or false then Y is false but if X is meaningless then Y is true. Thus if we fail to construct such a situation whereby we can state under this condition we can test X then Y is provisionally true and X is indeed meaningless.

Let us take the hypothetical proposition “the statement ‘there is a God’ cannot be tested’, where ‘there is a God’ is X. Create a thought experiment which can prove or disprove X or simply take the situation (to help you visualize): Under what condition would a theist believe there is no God or vice versa an Atheist would believe there is a God. I could not find any condition which could satisfy or answer this question. Therefore X is meaningless and Y is true. And since Y is true it is part of the totality of true propositions (Wittgenstein) while X is not. The result does seem a bit trivial, much ado about nothing.

I think Popper contributed a bit to logic. But I think we have a fundamental problem that doesn't get resolved that easily by trying to prove something true or false, because indeed some propositions are meaningless under that perspective. Not so if we look for a science of lies, i.e., trying to prove that a lie is a true lie. That's easier and more beneficial. That technique is used a lot in postmodernist thought. But it is not well-defined, and perhaps it will seldom be because it is subject of entanglement. Have fun.

[Ecurb]

I got a bit lost in your z1s, Xs, and Ys, muaz jalil (doubtless if I concentrated more I could figure it out). However, I can easily think up conditions under which an atheist would believe in God. Who can't? It's easy: some sort of personal revelation persuades the athiest that God exists. It's basically the same evidence that would persuade a non-believer that Sasquatch exists -- he sees one, up close and personal.

[Jack of Hearts]

Why call propositions bivalent or meaningless? Some propositions are indeterminate.














J

[cafolini]

I got a bit lost in your z1s, Xs, and Ys, muaz jalil (doubtless if I concentrated more I could figure it out). However, I can easily think up conditions under which an atheist would believe in God. Who can't? It's easy: some sort of personal revelation persuades the athiest that God exists. It's basically the same evidence that would persuade a non-believer that Sasquatch exists -- he sees one, up close and personal.


Well, the entanglement occurs in considering old logics valid. The only valid logic of today and the future is symbolic logic. All the others are obsolete in a museum. Believe or disbelieve anything you wish, but do not confuse it with what you know.
Atheism is just as insane as theism. Agnosticism is just as insane and useless as the other two.

[Ecurb]

Well, the entanglement occurs in considering old logics valid. The only valid logic of today and the future is symbolic logic. All the others are obsolete in a museum. Believe or disbelieve anything you wish, but do not confuse it with what you know.
Atheism is just as insane as theism. Agnosticism is just as insane and useless as the other two.

"Briefly, you can only find truth with logic if you have already found truth without it." -- GK Chesterton.

Logic is inevitably circular (the conclusions are merely a restatement of the postulates). We "know" things through our experience of them. Logic only helps us "know" that if A is true, then B is true. It doesn't help us know if A is true.

[cafolini]

"Briefly, you can only find truth with logic if you have already found truth without it." -- GK Chesterton.

Logic is inevitably circular (the conclusions are merely a restatement of the postulates). We "know" things through our experience of them. Logic only helps us "know" that if A is true, then B is true. It doesn't help us know if A is true.

HA! The most important statement of symbolic logic is one which is often disregarded a-priory. That is that A = A. Don't believe it or disbelieve it.

[Ecurb]

HA! The most important statement of symbolic logic is one which is often disregarded a-priory. That is that A = A. Don't believe it or disbelieve it.

I'll grant that A=A. In other words, "If A, then A." I'm not sure how that affects my comments though.

[Serena03]

If we assume Z1 could equal that God is nothing more than a product of the mind, this may result to Y if we are referring to an external god. However it also may be equal to X if we want to refer to the concept of God as a whole. In this case, X=Y because Z1 is true, everything is true. Y can only be false if Z1 is false, but X can only be testable if Z1 can potentially falsify it, otherwise the statement 'there is a God' will thus be meaningless given that we have a factor than can never completely be proven or disproven without a third refutation. Logistically this fails if there is not enough information to work with to be able to completely prove or disprove. Nevertheless Z1 must also be testable where another factor such as 'Z2" may have to be used for refutation in order to reach an ultimate answer of either X or Y being true. To say that A=A could be just as meaningless if we don't understand why B=B and A could not equal B. This is generally why the scientific method does not often care to interfere with the possibilities of an external god and faith is an island unto itself without a logistical map. Pure evidence is usually the common factor that persuades a believer or non-believer into either state.