This makes zero sense. — Lionino

This makes zero sense to you.

Okay. Fine.

You're not giving me anything to work with.

You provide no clue as to why you perceive my statement regarding meaninglessness to be meaningless.

You've made a statement with no associated context or argument.

Do you agree with everything else I say, but this specific statement is causing you problems?

Those "sets of axioms" are the logical language chosen. — Lionino

And that Logical language has a set of axioms that need a set of axioms that need a set of axioms.

Formal languages are, very specifically, axiomatic systems. They don't just magically exist as handy off-the-shelf starting points.

This is the fundamental problem with the axiomatic approach to knowledge: there is no fixed, known starting point. You have a choice between infinite regression of definitions or Circular definitions.

You are right, that whenever possible, mathematicians prefer a formal language over a natural language to describe new axioms. However, formal languages have axioms that need to be described (just like every other axiomatic system).

In practical terms, the first axiomatic systems were described by natural languages - So this rock solid foundation of formal languages turns out to be built on a foundation that can't be defined.

The only difference between a natural language and a formal language is the degree of obfuscation between the two.

Formal languages cannot and do not define anything with any more precision than natural language (c.f. circular definitions and infinite regression).

You've got a post on metaphysics and mathematics on the front page right now that directly refers to the foundational crisis in mathematics. This is that crisis: axioms cannot be defined.

Also makes zero sense. — Lionino

Again: why make this statement?

Meaning of words

You declare: "This makes no sense" as if a given sentence has a fixed, objective meaning independent of context.

Even axiomatic mathematics recognises that the meaning of a given sentence is relative to the axioms.

A sentence in one axiomatic system can be true while it is false in another axiomatic system.

You appear to be implying that meaning is independent of context. That a sentence always has a fixed meaning (or lack thereof).

This presumption is not unique to you. It is, however, impossible to justify.

Mathematicians have been trying to pin a single fixed meaning to a set of axioms since the first axiom. It can't be done.

Meaning always depends on context. Truth depend on context. Not sometimes. Not when we feel like it. Always.

Axiomatic mathematics wants axioms to have a fixed meaning but knows that meaning of statements within an axiomatic system depend on the axioms of the system.

Pick a lane. Are axiomatic statements context dependent or not?

You can't define statements in a formal language according to their axioms - and then turn around and claim that the statements of the formal language are fixed and independent of context when used to describe the next axiomatic system.

The confusion in your thread on Grundlagenkrise and metaphysics of mathematics is entirely down to an inconsistent approach to language in which sometimes meaning is contextual and sometimes it is inherent.

Recognising that all meaning is context dependent and being consistent with respect to this observation causes everything to neatly slip into place.

The idea that because something doesn't make sense to you - it therefore cannot make sense to anyone else is utterly unsustainable.

Many people cannot make sense of General Relativity. Are we to suppose that their perception is necessarily universal and that General Relativity is nonsense?

Is that really how you think knowledge works?

Is my perception of your statements the only possible way to interpret them?

Roundup

At some level you know that meaning is context dependent. You know that different people interpret the same words differently.

All I'm pointing out is that there are no exceptions.

Axiomatic mathematics is trying to find fixed axioms while defining axiomatic systems contextually. One or the other has some potential to succeed. Mixing the two just leads to confusion.

This makes zero sense to you. — Treatid

No, I am informing you that your string of words makes zero sense. It perhaps "makes sense" to you in the same way that 12+12=22 made to me in my early childhood.

And that Logical language has a set of axioms that need a set of axioms that need a set of axioms. — Treatid

That is not how it works. A language is not a theory. The axioms of language, in this case n-order logic, are not the same as the axioms of a mathematical theory. And the axiom tree/chain does not keep going forever.

If I wanted to release the kraken, I would tag Tones and he would inundate this thread with corrections on your posts. I am using my posts to inform you that you don't really understand what it is that you are saying. It is up to you to insist in mistakes or not.

I thought some might find this interesting. A non-mathematical wander through black holes, white holes, simplified solutions to Einsteins equations, multiverses etc. Rather good I thought - better than the opening graphic suggests at any rate.

If we were to create a universe, what are the simplest possible building blocks that we could use? — Treatid

Ideas. — RogueAI

Probably the bit (or qbit), right? 1 or 0, nothing more complex. Presumably, you can say everything about any of the other candidates (except perhaps ideas) with bits. — Count Timothy von Icarus

I think it’s safe to say, that whatever the fundamental substratum is, it doesn’t consist of things. — Wayfarer

I may be hearing Heraclitus playing the lyre here, but it seems to me that “oppositeness” is the simplest possible building block of the universe. In fact, our entire universe and existence are built upon oppositeness.

With oppositeness, there are electrons and protons; negative integers and positive integers; matter and energy; photons and waves; infinity and infinitesimal; vacuum and pressure; apoptosis and paligenosis; black and white; life and death; poetry and prose; work and play; sleep and wakefulness; mountains and beaches; art and commerce; music and cacophony; notes and rests; sterility and fertility; heat and cold; real and imaginary; laughter and tears; fact and fiction; good and evil. (And even “agreement and disagreement,” which is the hallmark of this forum!)

Oppositeness is patently a simple building block. It is easy-to-understand and readily applicable. Objects, processes, states of affairs, feelings – whatever – can all be paired with other objects, processes, states of affairs and feelings of opposing qualities. (See the above list for examples.)

And yet, as simple as oppositeness is, an entire, rich, diverse and wondrous universe can be constructed from it. Life itself is an expression of opposites and even develops from it – e.g., the sperm fertilizes the egg.

So I stake my claim with Heraclitus, who argued that the world could not exist without opposing qualities – like the tension that is created from the opposite ends of the strings on a lyre. It’s as “simple” as that.

Argumentation from authority is a fallacy.

I get that you think you are right.

For my part, I'm pretty sure I know what I'm talking about.

You reiterating your assumptions, claiming you are right by fiat - isn't an argument.

Saying your dad can beat up my dad isn't an argument.

The very fact that you think someone else can put me in my place tells me you don't actually understand the position you are trying to defend. If you understood it - you'd be able to present the evidence to me yourself.

As it stands - you are telling me I'm wrong but providing no justification for that position.

It is almost as if you aren't trying to persuade me you are right. It looks somewhat as if you are trying to defend your own beliefs without understanding where those beliefs are coming from.

If I really wanted, I would tag Tones and he would inundate this thread with corrections on your post. — Lionino

I would be delighted to engage with someone who knows the difference between a dialogue and a sermon.

Your claim that a given sentence has a fixed (nonsensical) meaning in all possible languages across the entirety of time and space is simply absurd.

Your claim that formal languages are not axiomatic systems is straightforwardly counterfactual. ZFC set Theory is the axiomatic system for which the axiom of choice was invented. This is an easy lookup. No-one who has the slightest knowledge of axiomatic mathematics thinks otherwise. This suggests to me that you a regurgitating something you heard - not talking about things you understand.

If you can find a single instance of a non-circular definition - you can rub that in my face.

I thought your post on the metaphysics of mathematics was interesting - but when you claim that a sentence has a fixed meaning (albeit nonsensical) you demonstrate beyond reasonable doubt that you don't understand the questions you are asking.

"Context matters" is basic English comprehension.

TL;DR

I don't mind that you think I'm wrong. The feeling is mutual.

I'm bothered that you aren't trying to show me exactly how I'm wrong.

You appear to be going out of your way to avoid presenting an actual argument. On a Philosophy Forum.

It looks to me like you aren't trying to persuade me. It looks to me like you are trying to preserve your own unfounded beliefs.

Care to demonstrate that you know what you are talking about rather than merely declaring it?

And please do sick any tame lapdogs on me. (no typo - bring it).



I think General Relativity is physics done right.

The significant difference between Quantum Mechanics (QM) and General Relativity (GR) is that QM tries to describe an objective universe that can't be directly experienced, while GR describes what an individual observer sees.

In my estimation, most people struggle with GR because they are trying to interpret it from a Newtonian/Eucildean framework.

So the twin paradox is paradoxical given the assumptions of a fixed, objective universe in which The Law of Identity holds - but is just a description of what we would see in GR.

cannot imagine a framework without his implicit assumptions about the world. In his perception, a paradox is always a paradox. But the "twin paradox" is only a paradox within Newtonian/Euclidean space. In GR - the "twin paradox" isn't a paradox of any kind. It is simply what is observed.

GR is such a fundamentally different approach to knowledge that there is no path from Newtonian Mechanics (NM) to GR. GR cannot be constructed using NM. There is no iterative set of steps from one to the other.

Albert Einstein had to go back to first principles. The theories of relativity are built from the single observation that the speed-of-light-in-vacuum is constant for all observers. His theories then take this observation to its ultimate conclusion.

Trying to comprehend GR while holding onto the assumptions of "objective reality" is impossible. Each observer experiences a different reality. Changing the relationships (relative velocity) in GR changes the perception of what reality is. Talking about a singular objective reality isn't meaningful within GR. No observer is "the correct observer" and every observer perceives a different universe - similar, connected, but unique for each observer.

Relational universe

Context Matters.

Meaning is defined by context. Einstein was referring to physics - but the universe is relational in every aspect.

The world you experience is genuinely different from the world everyone else (individually) experiences.

Not chaotically different. There are many similarities - but no two people's experiences are identical.

Everyone knows that experience is subjective. But most are still trying to understand a relational universe in objective terms.

The fixed, objective knowledge that craves doesn't exist. A relational (subjective) universe cannot be understood from the perspective of an objective worldview within which objects are static (The Law of Identity).

I may be hearing Heraclitus playing the lyre here, but it seems to me that “oppositeness” is the simplest possible building block of the universe. — Thales

Yes, yes, yes, yes, yes.

So much yes.

You win all the prizes. This is the right answer.

Some more agreement

I call them relationships or connections or differences - Opposites/oppositeness is just as good a name.

A rose by any other name...

So - yes - there is some fundamental quality of oppositeness and this quality is the building block of the universe.

Way back in the OP - I stated that the minimum possible oppositeness (relationship, connection, difference) is a directed edge in a graph.

Does this make sense to you as a minimum oppositeness. How do you picture/imagine a universe made out of pure oppositeness.

To be clear: I'm impressed with your description of oppositeness and I want to listen to you develop the idea more. Stepping away from the conventional "particle" centric models seems to me to be a huge step.

I think that recognising this oppositeness nature of the universe is the lynch pin. That it is impossible to describe a particle based universe - and (relatively) trivial to describe an oppositeness universe.

You don't have to ... anything. I'm not expecting immediate agreement. I am already sincerely impressed by your insight. I would be honoured to agree, or disagree, with any further thoughts on the matter you have.

Your claim that formal languages are not axiomatic systems is straightforwardly counterfactual. — Treatid

That is not what I said and that is not what counterfactual means.

But the "twin paradox" is only a paradox within Newtonian/Euclidean space. — Treatid

There is no twin paradox in Newtonian physics. The twin paradox is a paradox in Einstenian physics, paradox is not synonym with "contradiction".

You have no clue what you are talking about. I will not bother with the rest of the uninformed ramble.

For my part, I'm pretty sure I know what I'm talking about. — Treatid

So do flat earthers. But alas you are both clueless.

A mathematical point is a definition of nothing. We can't use 'nothing' as a building block. — Treatid

In point-set topology, a point of space can be any set. The simplest set is the empty set, which is not nothing but something that has no parts.

I may be hearing Heraclitus playing the lyre here, but it seems to me that “oppositeness” is the simplest possible building block of the universe.
— Thales

Yes, yes, yes, yes, yes.

So much yes.

You win all the prizes. This is the right answer. — Treatid

I’m humbled and honored to be named discussion winner. But what is my prize? (I hope it’s the poker Ludwig Wittgenstein brandished at Karl Popper!) :cool:

Yet again you respond with assertions but no justification for your position.

Why?

You aren't even trying to show me that I'm wrong.

If you want to win trolling points; reddit has upvotes and downvotes to keep score.

You have no clue what you are talking about. — Lionino

I assure you, the feeling remains mutual.

The simplest set is the empty set, which is not nothing but something that has no parts. — litewave

That seems a lot like a definition of nothing to me.

One of the sub-threads here is that all definitions are circular.

An empty set is defined by set theory. Set theory is defined by the axioms of set theory. The axioms of set theory are defined by something else which is defined by something else which is defined by something else...

This results in infinite regression or circular definitions.

As a result axiomatic mathematics cannot define the meaning of anything. Hence "The Foundational Crisis in Mathematics" among other things.

The good news is that I can't definitively prove that a mathematical point and an empty set are equivalent to "nothing".

The bad news is no-one can demonstrate they are not equivalent, either.

And this brings us to the age old questions: What can we know with certainty? What can we describe?

For example, all definitions related to Quantum Mechanics are circular (this isn't just a mathematics problem). Our perception of what fields and waves are - derives from the universe we are trying to describe.

Quantum Mechanics says that electrons look like (other) bits of universe. This bit of the universe looks similar to that bit of the universe.

It isn't wrong. But it doesn't explain anything.

The reason 's answer is so good is because we can describe the relationships (oppositeness) of things. Indeed - we can only describe relationships.



I believe the standard prize is "a sense of pride and accomplishment". I'm told it nourishes the soul.

I'll certainly consider your suggestion of a physical prize. But I have been assured that "Exposure" is superior to mere material possessions.

That seems a lot like a definition of nothing to me. — Treatid

Empty set? Emptiness is a property, which is something. And so is that which has it.

One of the sub-threads here is that all definitions are circular. — Treatid

Is that a problem? As long as all things are consistently defined, in all relations to each other, it seems fine to me. Of course, we can never prove the consistency of all things, due to Godel's second incompleteness theorem. But that's an epistemical problem, not ontological. Consistency doesn't care whether it can be proven.

As a result axiomatic mathematics cannot define the meaning of anything. — Treatid

What do you mean by "meaning"?

What can we know with certainty? What can we describe? — Treatid

We know our own consciousness with certainty. From that we form, in our consciousness, a representation of an external reality -- not with certainty but with various degrees of certainty.