Lorraine, you are making assumptions there that may not be valid. Barad for example takes as foundational the fact that various 'agencies' work together to create phenomena, some of the agencies involving language. In a mysterious way, the combination of assertions in a language, and processes possessed by people who are familiar with that language, gives rise to appropriate responses to such assertions. This is something known to anyone who has encountered foreigners (and babies) who don't understand their own language. You may want to postulate that this can all be explained in terms of algorithmic logic, etc. but it is unclear that this is enough. Indeed, it is unclear even whether mathematical proofs can be understood thus (see Penrose, and arXiv:1307.6707 ("we think that we think clearly, but that's only because we don't think clearly: Mathematics, Mind and the Human World')).

I think therefore that it is better to take Barad's 'entanglement of matter and meaning' as foundational, and see where we can go from there.

Brian,

1) Re "You may want to postulate that this can all be explained in terms of algorithmic logic, etc. but it is unclear that this is enough. Indeed, it is unclear even whether mathematical proofs can be understood thus" i.e. Re creative leaps:

I never meant to imply that all aspects of outcomes can be logically explained in terms of algorithmic logic or mathematics. What I'm getting at is that all outcomes involve some aspects that are "creative leaps"; and that these creative leaps can't be represented as logical consequences of a complex mathematical/algorithmic system.

I would argue that it is these creative leaps that are driving the system forward to new outcomes, where the outcome is thought of as being representable by a set of numbers associated with fundamental variables, and where at least one of these numbers is due to a creative leap (i.e. not due to logical consequence). The creative leap itself can't be represented, but the outcome can be represented, and a "creative leap" outcome can be thought of as the assignment of a new number to a variable.

2) Re "language"/ perception:

One can never avoid using symbolic representations when trying to characterise something about the (e.g. fundamental) nature of the universe; and when forming conclusions about the (e.g. fundamental) nature of the universe from these symbolic representations.

The representations are usually mathematical, not "language". One can look at complex dynamic systems that might seem to evolve in time from the mathematical representations; or one can look at the mathematical representations themselves, and say that underlying every such representation there are categories, and relationships between such categories; and that therefore there is something fundamental about categories and relationships. I would argue that the fundamentals of perception are categories and relationships.

I think we're largely in agreement at this point, though there remains that question of what you mean by 'number'. If it's sufficiently general I probably agree with you.

This is maybe a point to bring up Yardley's cryptic ideas. She makes 'circles' basic, being both things and actions, but they can also be thought of as triads, e.g. lines, circles and the 'mandatory relationships' between the two. But the two related entities can manifest in a range of forms, e.g. zero and one (nothing and something) or a unit and a pair, or yin and yang, night and day. In other words, there is a concept that is the ultimate abstraction, or the basic contrast one would want to make, the 'difference that makes a difference'. This may fit in well with what you are saying (and of course there is again this business of thesis-antithesis-synthesis).

One point, however: isn't language as such about properties and relationships? What makes things mathematical is I believe the idea of truth. We do of course have the idea of truth in ordinary speech, but there is as it were a degree of commitment to it in maths that we don't necessarily have in ordinary speech (a bit like a court of law).

The point now is that there can be useful speech even without truth, e.g. talking in terms of what is likely. Yardley incidentally talks truth and proof being opposite pairs, and she has a section 'Mathematics: More and Less, Possible and Probable, Proof and Deduction', including for example this:

Counting and numbers give us a way to articulate and interact with the more basic ideas of more and less. They also give us a way to articulate and interact with the more basic ideas of possibility and probability. Counting and numbers also give us a way to prove, and deduce, reality.

But as always her exposition is minimal and it is hard to figure out precisely what the argument is.

I've been looking at your own essay, and have added a comment on it, which is at http://fqxi.org/community/forum/topic/3081#post_146752.

Brian, Re "things and actions" and "'... relationships' between the two" (Mar. 22, 2018 @ 09:43 GMT): I don't know what you or Yardley mean by "things and actions" or "'... relationships' between the two", but I doubt that there is a relationship if it is not representable as a mathematical relationship. Close to 100 years of experiment has shown that there are "quantum" aspects of the universe (like "creative leaps", the fact that matter "knows", and "coherence") that are not representable as mathematical relationships, because clearly they are not due to relationships.

Re numbers:

As you have seen in my essay, I contend that "laws of nature" are constructed out of relationships between categories, and that (initial value) numbers must seemingly also be constructed out of relationships between categories, relationships where the numerator and denominator categories cancel out, leaving a thing that has no category (the categories are in effect hidden). What physics represents as algebraic and non-algebraic numbers must seemingly all ultimately derive from simple relationships between categories.

Re "What makes things mathematical" and "counting" (Mar. 22, 2018 @ 11:36 GMT):

Mathematics and counting are complicated things: they involve steps that can only be likened to the algorithmic steps in a computer program, which shows that they are complicated things, it doesn't show that people who count or do mathematics are like computers. Counting, for example, involves the identification of objects, to identify whether they should be counted or not - a very complicated process. In other words, it takes an advanced organism to count and do mathematics. Fundamental-level reality cannot count or do mathematics: it can only do "creative leaps" and experience relationship.

Re "the 'difference that makes a difference'" (Mar. 22, 2018 @ 09:43 GMT) (I have also responded differently above, beneath the "show all replies"):

I don't see it as a yin/yang, zero/one issue. I'm tending to see it as a one/many issue.

I don't assume an initial nothing or "zero" (an initial plus-one in relationship with an initial minus-one), which is actually a type of "one" i.e. a type of something. Because this type of "something" seems to assume the pre-existence of (what we would represent as) 1) mathematical relationships 2) balance. As a result of these mathematical relationships, purportedly emerges the superficial appearance of particles, consciousness and creativity. This type of view fails to explain what is going on, hidden in the background: how the mathematical relationships are created; and what "knows about"/responds to the relationships; and why anything would know about/respond to the mathematical relationships in the first place.

Instead, I assume an initial "one", which becomes many, which are the source of what we represent as mathematical relationships (they create them and know about them).

For years, in the back of my mind, there has been the question: "relationships exist between categories like momentum or energy, but shouldn't there be relationships between particles themselves, if the one has become many?" But now I'm tending to the view that this is a coherence/decoherence issue: coherence is not a relationship - its an inherent aspect of reality that pre-exists the appearance of mathematical relationships.

    Initial: becomes. When did this happen? If reality is eternal the term 'initial' has no meaning. I'd prefer reciprocal 'one' and 'many'.

    Initial: "Existing or occurring at the beginning" [https://en.oxforddictionaries.com/definition/initial]. The structure of this universe had a beginning, the structure started more or less from scratch: this seems to be the evidence-based theory of physicists/cosmologists.

    This view seems to be correct because, working backwards in time: more complex life came from simper life, simpler life came from molecules, molecules came from atoms, the atomic elements were formed out of simpler elements in the periodic table, and atoms came from particles. The foundation of all of this is seemingly particles, law of nature relationships and numbers.

    Without the law of nature relationships and the numbers you can't have a universe with a structure, but the structure of the universe is subject to change (time). Also, working backwards, without what creates and knows about the law of nature relationships and numbers, you can't have a universe with a structure, but this aspect of the universe is not subject to change.

    This view is now a bit out of date -- see https://aeon.co/videos/was-there-any-before-before-the-big-bang.

    So, what is this "time" that Tim Maudlin is talking about [1]? E.g. if time is just a variable that is indirectly measured by numeric change of some other variable, then: 1) is time just an indirect measure of change in the universe? (i.e. an algorithmic entity) 2) what causes change i.e. what causes new variables/categories or new numbers? 3) are there aspects of reality that don't change?

    1. Tim Maudlin said: "...that thing we call The Big Bang-- Was there anything before that? ...was there... any physical story we can tell about the origin of the Big Bang. The answer ...is that we don't know and all options are on the table... Modern cosmological theory imagines ...that there was something before this thing we call the Big Bang, there was a another state from which our observable universe evolved and ...continue to evolve. ...there are theories of that character...if time doesn't go any further, to ask what happened before the big bang, it's just logically incoherent. There can't be a before...does that mean that nothingness somehow gave birth to the universe? That sounds very strange...The universe is a kind of totality, it's a whole, it's everything there is, and it's limited in a certain way, it's limited in the time extent that you can go backwards. Now, on the other model there was something before the Big Bang, you can then ask, what came before it? How did the Big Bang come out of that?...All we have to go on is theory. And cosmology switches over from the astronomers to the theoreticians who might say 'Yeah, I have a theory that will tell you what this earlier state was like.' And then you could only ask the theory, can I keep going back? ...Does it go back forever? Now in the case of going backward in time...how could time itself begin? But if you never stop you're going to say well how could an infinite amount of time have elapsed? ...if you're dealing with everything then there are going to be certain kinds of explanations or certain kinds of understandings which automatically by logic, there can't be for everything taken together, but there can be for any little part..." [https://aeon.co/videos/was-there-any-before-before-the-big-bang].

    This is probably the point at which we should close the discussion and pursue our separate paths. Thanks for all your thoughtful comments, anyway.