“You’re saying all mathematical statements are true or false but the liar parado

—“You’re saying all mathematical statements are true or false but the liar paradox is one example of an ordinary language sentence which hasn’t got a truth-value, right? Well, stated that way, I’d say you’re right about all of that, but are you also saying that the liar sentence expresses a proposition? That might be the part where it starts to get problematic.”—

Good question.

In short, we can ask a question, or we can assert an opinion, conflate the two, or we can speak nonsense. And only humans (so far) can ask, assert, conflate, and fail at all of them. But out of convenience, we subtract from the real to produce the ideal, and speak of the speech as if it can act on its own.

Just to illustrate that the test we are performing (context) limits both what we are saying and what we can say. From the most decidable to the least:

1 – The mathematical category of statements, (tautological) single category. (relative measure)

2 – The ideal category of statements, (logical) multiple categories. (relative meaning)

3 – The operational category of statements (existential possibility)

(sequential possibility )

4 – The correspondent (empirical) category of statements. all categories. ( full correspondence )

5 – The rational category of statements ( an actor making rational choices) (‘praxeological’)

6 – The ‘moral’ category of statements ( test of reciprocity)

7 – The fully accounted category of statements (tests of scope)

8 – The valued (loaded) category of statements. (full correspondence and loaded with subjective value)

9 – The deceptive category of statements (suggestion, obscurantism, fictionalism, and outright lying.

We can speak a statement in any one or more of these (cumulative) contexts.

So for example, statements are not true or false or unknowable, but the people who speak them speak truthfully, falsely, or undecidedly. So performatively (as you have mentioned) only people can make statements.

However, to make our lives easier, we eliminate unnecessary dimensions of existence unused in our scope of inquiry, and we conflate terms across those dimensions of existence, and we very often don’t even understand ourselves what we are saying. (ie; a number consists of a function for producing a positional name, from an ordered series of symbols in some set of dimensions. Or, only people can act and therefore only people can assert, and therefore no assertions are true or false, the person speaking speaks truth or falsehood. etc.)

This matters primarily because no dimensional subset in logic closed without appeal to the consequence dimensional subset. In other words, only reality provides full means of decidability.

Or translated differently, there just as there is little action value in game theory and little action value in more than single regression analysis, there is little value after first order logic, since decidability is provided by appeal to additional information in additional dimensions rather than its own. Which is, as far as I know, the principal lesson of analytic philosophy and the study of logic, of the 20th century.

Or as I might restate it, we regress into deeper idealism through methodological specialization than is empirically demonstrable in value returned. Then we export these ‘ideals’ as pseudosciences to the rest of the population. This leading to wonderful consequences like the copenhagen consensus. Or the many worlds hypothesis, or String Theory. Or keynesian economics. Or the (exceedingly frustrating) nonsense the public seems to fascinate over as a substitute for numerology, astrology, magic, and the rigorous hard work required

FOUNDATIONS OF LOGIC

The foundations of logic like those of mathematics are terribly simple as subsets of reality. But by doubling down in the 19th and 20th centuries all we have found is that we say rather nonsensical terms like ‘the axiom of choice’ or ‘limits’ rather than ‘undecidable without appeal to information provided by existential context’. After all, math is just the discipline of scale independent measurement, and the deduction that is possible given the precision of constant relations using identical unitary measures. Logic is nothing more than than set operations. Algorithms are nothing more than sequential operations restoring time. Operations are nothing more than algorithms restoring physical transformation, time and cost. etc.

As a consequence, I find most of this kind of terminological discourse … silly hermeneutics. As Poincare stated ‘that isn’t math its philosophy’. Or as I would say, ‘with platonism we depart science and join theology. It may be secular theology in that it is ideal rather than supernatural, but it is theology none the less’.

it is one thing to say ‘by convention in math (or logic or whatever dimension we speak of) we use this colloquialism (half truth) as a matter of convenience. It is not ‘true’ as in scientifically true. It is just the best approximation given the brevity we exercise in simplifying our work.

There exists only one possible ‘True’: the most parsimonious and correspondent testimony one can speak in the available language in the given context. Everything else is a convention.

Ergo, if you do not know the operational construction of the terms that you use, you do not know of what you speak. That does not mean you cannot speak truth any more than monkey cannot accidentally type one of the Sonnets.

This is why the operationalist movement in math we call Intuitionism failed.

Anyway. Well formed (grammatically correct) statements in math may or may not be decidable but our intention is to produce decidable statements. In symbolic logic, well formed (grammatically correct) statements may or may not be decidable. in logic (language), well formed (grammatically correct) statements are difficult to construct because of the categorical difference between constant relations (ideals in math), constant categories (ideals in formal logic), and inconstant categories (ordinary language). Furthermore the process of DEDUCTION using premises (or logical summation) limits us to utility of true statements. Ergo for that purpose statements can only evaluate to true or not-true (including false and undecidable). While for the purpose of INDUCTION (transfer of meaning by seeding free association, or the construction of possibility by the same means) seeks only possibility or impossibility not truth or falsehood.

Now. I have written far too much already, so I won’t try to increase the precision of what I’ve written, but hopefully the answer is the same:

How can you claim to make a truth proposition and demand precise language when your premises are mere demonstrably falsehoods used by convention?