@layman,
I have been working, reading the responses, and considering clarifications (the other question of time was merely a passing thought: as I stated, physics isn't my strong suit.) I am unsure why you included quote marks.
To your initial question: I am unsure whether logical positivism is actually necessary for the success of the argument: though in answer of [some] of the questions: perhaps this will help:
The human brain interprets the world as patterns. Mathematics is the understanding of that perception of patterns. Physics is the application of that understanding of the perception of patterns. And our picture of the world is the experience of those perceptions of patterns.
1.[The meaning of a statement relies on the possibility that it can be known to be true or false.] 1.1. Meaningful statements cannot exist without the possibility of meaningless statements. 1.2. The structure of meaning exists, not in one statement, but in all statements. 1.3. As the meaning of one statement is reliant on another. 1.4. Therefore: it is impossible to know whether a statement is meaningful or meaningless without prior knowledge of all possible statements.
2. It is possible for a structure of meaningless statements to exist, which is similar to that of meaningful structure in every aspect but meaning. 2.1. The distinction between the former and the latter is that one can be known and the other cannot. 2.2 Though for each there must be an actual distinction between the two, and so for one to exist, both must exist.
3. We assume that meaning exists because we assume that patterns of truth exist. 3.1. The difference between one thing and another is not meaningful unless there is a pattern which describes why one thing is and the other is not. 3.2. Therefore, meaning is reliant on an accurate perception of patterns.
4. The human brain perceives physical states as patterns because it has evolved to structure the states in to the form of patterns. 4.1. Therefore our brains are predisposed to witness meaning and meaningless states prior to any possible knowledge that such states exist outside of our perception.
5. Since the brain can only perceive in patterns, we cannot know whether a structure expresses an actual pattern, or, that we simply perceive the structure in that way. 5.1 Therefore we cannot know whether a structure has meaning or not. 5.2. Though we can ask ourselves which is more probable. 5.3 That we perceive reality in a structure of patterns that exist. 5.4 And which also happen to be the best tools for survival. 5.4. Or that we perceive reality in a structure of patterns because they are the best tools for survival.
6. Outside of our perception of patterns, it is possible that true propositions lay at the end of false statements, or false propositions lay at the end of true statements.
7. It is intrinsically impossible to know which structures are meaningful and which are meaningless, when we perceive reality in patterns, and therefore, within a mechanism of meaning. 7.1. We cannot say which is an actual pattern and which is a constructed pattern from a perspective that can only perceive patterns.
8. Therefore, it is just as possible that truth, if it exists, is random, and that no set of statements can make a proposition meaningful. 8.1.That some truths appear to work together (are logically coherent) and that some do not (are paradoxes) offers some slight support to this claim.
9. To say meaning exists, or indeed that it does not, is to presuppose the existence of patterns outside of the pattern seeking neural network, which is impossible to verify. 9.1. That which is impossible to verify is meaningless in itself. 9.2. It is impossible for us to perceive anything outside of the boundaries of patterns: absolute nothing, infinity etc, etc. 9.3. Though these abstracts may exist outside of the forms of all possible patterns.
10. It is wrong to assume that states contain meaning intrinsically, as such states are reliant on the knowledge of the existence of patterns. And since the perception of patterns is the starting point for all we can know, and is, therefore, the lever with which we separate one thing from another. 10.1. It is impossible to withdraw from this perspective and verify whether patterns exist actually or not.
11. The human brain cannot perceive anything which lays outside of the parameters of the evolved perception of patterns. 11.1. Therefore, it is impossible to know whether patterns truly exist or not. 11.2. Therefore, it is impossible to know whether meaning truly exists or not.
12. There are phenomena within the natural world which we can now perceive for the first time. 12.1. Such phenomena contradict the current structure of meaning. 12.2. As we could not perceive the phenomena during the process of natural selection which formed the current structure. 12.3. And so, such new perceptions lay outside of the current structure of meaning. 12.4. Though, it is possible to include new perceptions within the current structure. 12.5. Which may initially seem counter-intuitive.
13. Though, as we transpose through time our understanding builds. 13.1. As each thing which is not part of the structure may or may not be included within the structure itself. 13.2. Though such inclusion requires the support of a network of reliant patterns. 13.3. And may require the construction of another set of patterns all together. 13.4. Such a subset of patterns is a part of the set of all sets*. 13.5. Which is to say, the structure of meaning itself. 13.6. Which is to say, inexpressible from within itself.
14. Though, there is an important difference between that which we do not understand and that which we cannot understand. 14.1. As that which we cannot understand may be understandable in different circumstances. 14.2. And that we do not understand may never be known. 14.3. And each problem of metaphysics may be one or the other. 14.4. As each proposition is intrinsically meaningless. 14.5. And each perception intrinsically unreliable.
15. Though each of these propositions, if they are true, are not. 15.1. In that they mean nothing. 15.2. Though, equally, any reductio which is applied to them also means nothing. 15.3. The conclusion is that meaning itself is rejected. 15.4. As is the meaning of that meaning of rejection. 15.5. And the success or failure of the proposition. 15.6 Which can be expressed in action alone. 15.8. Is the final solution to the problem.