Incorrect. When proven, they're established as facts. — Michael Ossipoff


When proven they are no longer "if-then". — Janus

Sure they are My Slitheytoves & Jaberwockeys if-then proposition is obviously a fact. But, though it's true, it's still an if-then fact.

That's because, though the Slitheytoves & Jaberwockeys if-then proposition is a fact, its "if" premise isn't an established fact. It hasn't been proven that all Jaberwockeys are Slitheytoves and that all Slitheytoves are brillig. Therefore, its "then" conclusion (that all Jaberwockeys are brillig) likewise isn't established as a fact.

But the Slitheytoves & Jaberwockeys if-then remains an obvious timeless if-then fact.

You are just playing with words as usual, as I see it. "Pouring from the empty into the void".

You're welcome to express your opinions on these matters (limiting those opinions to the topic itself) or ask for clarification. But you need to refrain from expressing opinions about who's right or wrong,

As I said, that's a matter for others to judge.

Michael Ossipoff

"Timeless if-then facts are routinely spoken of in logic and mathematics". — Michael Ossipoff

They are propositions, not facts. — Janus

Incorrect. When proven, they're established as facts.

If there is an "if' then it is a proposition; there can be no "if" about a fact.

Yes the "if" premise is a proposition, not necessarily a fact. Likewise the "then" conclusion, which isn't a fact unless the "if" premise is fact.

But when an if-then proposition, itself, has been proven to be a fact, and then it's not just a proposition. It's then known to be a fact.

I'd said:

If all Slitheytoves are brillig, and all Jaberwockeys are Slitheyitoves, then all Jaberwockeys are brillig.

My Jaberwockeys and Slitheytoves if-then proposition is obviously a (timeless) fact, even if none of the Slitheytoves are brillig, and/or none of the Jaberwockeys are Slitheytoves. ...and even if there are no Slitheytoves and no Jaberwockeys.

The proposition "If the associative axiom is true for addition of integers, then 2+2=4 (given the definitions I stated)" is provably a fact, A provable timeless abstract if-then fact.

I have no criticism of, or impatience with you when you ask questions, ask for clarification, or express your opinion.
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Michael Ossipoff

None of this addresses my central criticism of your position, which is that "if-then" conditionals are relevant only to the future; and that the notion of "if-then abstract facts" is incoherent. — Janus

That's nonsense.

Timeless if-then facts are routinely spoken of in logic and mathematics.

The relation between ifs and thens needn't have anything to do with the future, this physical world, or its time..

It isn't possible to talk to you, and the pointlessness of answering you couldn't be more obvious than it is now.

Bulk is not a substitute for quality of response.

I wanted to show others that I wasn't evading answering your claims.

As for "quality of response" or the matter of who has supported what they've said, that's a matter for others to judge for themselves. What you, I, or any other participant or advocate on the matter say about that is irrelevant.

We've both had our say about this, and I suggest that there would be no point in continuing this conversation.

Michael Ossipoff

It's true that there could be fairly nearby civilizations,within robotic traveling-distance, that just aren't interested in it.

But, for a spacefaring civilization to not care, or having a prime-directive against intervention--I feel that any technically-advanced civilization would also be morally-advanced, and would want to help us. ...because it would be grossly obvious to anyone, even aliens, that we're badly in need of help here.

If I find an insect drowning in water, I rescue it, fish it out. Likewise, any advanced civilization that knew about us would help us--bring us the help, the babysitting, that we obviously so badly need.

So I'd rather that you be right about there being nearby life.

Our society very badly needs babysitting, interstellar intervention.

So it would be better if you were right.

Michael Ossipoff

"An infinite size is simpler and un-arbitrary." — Michael Ossipoff


As I said, I can provide no evidence that the universe is finite. — T Clark

I'm just speaking from intuition too.

I'd said:

Maybe one reason why the universe is very large or infinite is because the initiation of life is so vanishingly rare, that a universe that leads to us living things is much more likely to be a super-large or infinite one, instead of a smaller one. But, for any particular large size, why that particular large size? — Michael Ossipoff

This is the same as the strong anthropic principle, isn't it?

Yes, it fits with the metaphysics that I propose.

I am not a fan. Why do you assume life is rare.

Some biologists have said that life is vanishingly unlikely, and, so, most likely vanishingly rare.

There is no direct evidence yet. My bet is on life being abundant.

Then as Enrico Fermi asked, "Where are they?"

Though this galaxy has had life-capable stars for long enough that, if life were abundant, someone could have thoroughly explored and cataloged every star and planet in the galaxy, we've never heard from anyone.

hat's based on my understanding that we are starting to understand how life might develop out of non-living conditions. As I say - "might."

Yes, but they don't know how that happened. Of course it did happen. But it isn't biologically established (though some biologists have an opiniion on that) how rare it can be expected to be. But the Fermi paradox suggests that life is quite rare. The nearest space-faring civilization is probably so far away that, for practical purposes, they aren't there.

By the way, another reason why the anthropic principle might favor a very large, or infinite, universe is that there might be some reason why life is more lilkely (or possible at all) if space is at least nearly flat, Euclidean.

Michael Ossipoff

I’d said:
.

How could it be false, even in principle, in a context in which it is true? — Michael Ossipoff

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You replied:
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"If that is so, then why the need to state a conditional as you did earlier.

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If you know that the additive associative axiom is true for the real numbers, the rational numbers, the integers, the positive integers, and the non-negative numbers; and if you know that if that’s so, then 2+2=4, then that tells you that 2+2=4.
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As I’ve already explained, mathematical theorems are proved by showing that if an axiom is true (and maybe if other propositions are true as well), then a certain desired conclusion is true.
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I’d said:
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"The abstract fact that If the additive associative axiom is true, then 2+2=4 (by an obvious definition of 1, 2, 3 & 4 in terms of the multiplicative identity and addition), is a timeless abstract if-then fact."
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You replied:
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…if the "additive associative axiom" could not be false even in principle.

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An axiom can be false with respect to some systems of elements and operations on the elements. The multiplicative inverse axiom is false for the integers. The commutative axiom is false for many groups, though there’s a class of groups for which it’s true.
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In case you want to say that it isn’t the same associative axiom or commutative axiom, when applied to different systems, then let me clarify a bit.
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It’s true that a group is only defined with respect to one operation. And that operation isn’t usually addition or multiplication. But a group’s operation is often similar to addition, where the elements are things that are done, and the binary operation on those elements consists of doing one thing, and then doing a different thing. ..which could be regarded as adding one thing to another.
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Anyway, the “+” sign is often used to stand for a group’s operation.
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Suppose, just for the moment, we let “+” stand in for addition or multiplication (for numbers), or for whatever operation a group is defined with respect to.
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So, the associative axiom, (a+b) + c = a + (b+c) is true for groups, just as it’s true for the integers with respect to addition and multiplication.
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And likewise, the commutative axiom, a+b = b+a, is false for many groups, while true for Abellian groups, and for the integers with respect to addition and multiplication.
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The fact is that you want to make 2+2=4 seem to be a "timeless if-then abstract fact" rather than merely a timeless abstract fact

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No, I don’t.
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2+2=4 isn’t an if-then fact.

If the additive associative axiom is true for the real numbers, the rational numbers, the integers, the positive integers, and the non-negative integers, then 2+2=4 (by an obvious definition of 1, 2, 3, & 4, based on the multiplicative identity and addition).

That's an inevitable abstract if-then fact.
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As you said, 2+2= 4 is a timeless abstract fact.

You can experimentally show yourself that 2+2=4, by sitting on the floor with four apples, and experimenting. But the proof in terms of the number-definitions and axioms shows that 2+2=4 is indeed a timeless abstract fact. …given the associative axiom, which we all know to be true for the real numbers, the rational numbers, the integers, the positive integers, the non-negative integers (under the addition and multiplication operations), and for all groups.
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…, because the former fudge enables you to develop your whole purportedly "non-speculative" metaphysics.

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See above.
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This shows clearly the way in which your thinking is based on a superfluous conditional.

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???
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See above.
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Michael Ossipoff

I’d said:
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Abstract facts are timelessly true.

— Michael Ossipoff
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You replied:
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I don't agree with this principle. That's Platonic Realism and I do not agree with it.

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Yes, I’ve discussed this before, but let me say it again here:
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Absolute Anti-Realism is out of the question. I’ll get back to that later, below.
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For now:
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Fine, that needn’t be an issue for my metaphysical proposal, because my proposal is stated in terms of our individual experience, described as a life-experience possibility-story.
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So, if you want to say that facts are only meaningful with respect to an experiencer, that doesn’t contradict my metaphysical proposal.
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Instead of saying that the abstract facts are independently true, you want to say that the facts and their experiencer are true together, as part of the experience, which is more fundamental. Fine, because my metaphysical proposal is an Anti-Realism, stated in terms or our experience.
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But yes, I did say what you quoted above:
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Abstract facts are timelessly true.

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Does that seem to contradict the Anti-Realist character of my proposal?
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It doesn’t, because I don’t advocate absolute Anti-Realism.
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As I said, I propose that, for you, the world around you is just the setting for your (more fundamental) life-experience possibility-story. You, the experiencer, are primary and central to that story, as its protagonist.
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The complex system of inevitable abstract if-then facts that is your life-experience possibility-story is just as valid as any other abstract fact, or system of them. And it and its validity are self-contained, and quite independent of anything outside it, such as other abstract facts or systems of them. The only reality that it has or needs is in its own inter-referring context.
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Like any system of inter-referring abstract if-then facts, your life-experience possibility-story doesn’t and needn’t have objective reality or existence in some global context, or in any outside context or medium.
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But obviously, on the other hand, the abstract if-then facts that constitute your life-experience possibility-story aren’t really different from all the other abstract facts.
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That’s why I say that it would be animal-chauvinist to say that the only abstract facts that are valid are the ones that are in someone’s experience. That would only be so if you define validity as “experienced by someone”. That would be distinctly un-objective, It would also be something made true only by a special definition that says that it’s true.
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I’ve previously said that that would be reminiscent of the following (only roughly quoted) passage from Kenneth Patchen:
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“Alright”, said the Giraffe, “then let’s just say that the one with the longest neck gets all the jellybeans.”
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That’s why I say that absolute Anti-Realism is out of the question.
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Another thing:
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I’ve given a few examples of inevitable abstract if then facts. One was about Slitheytoves and Jaberwockeys. Another was about “if the additive associative axiom is true for the real numbers, the rational numbers, the integers, the positive integers, and the non-negative integers, then 2+2=4.”
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The point is that these inevitable abstracts are absolutely, timelessly, true for anyone anywhere. …true now or in ancient Greece, true for someone on a different planet, or in a different galaxy, or in a different sub-universe of a physically-inter-related multiverse of which our Big-Bang Universe (BBU) is a part….or even in an entirely different self-consistent possibility-world
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(All possibility-worlds are self-consistent, or they’d be impossibility-worlds. Possibility-worlds and possibility-stories are built on inevitable abstract if-then facts. Mutually-contradictory propositions aren’t facts.)
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So, since the inevitable abstract if-then facts are true for anyone, anywhere or anywhen, even in an entirely different possibility-world, they’re universally, timelessly true. …not just locally true in some particular person’s experience.
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That’s another reason why I say that absolute Anti-Realism is out of the question, and that abstract if-then facts are inevitably timelessly true.
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You said:
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I believe in an ever changing world where human beings have free will, and if there is anything which is outside of time (timeless), it is not abstract facts.

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We needn’t get into the free-will issue here.
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As I mentioned above, my metaphysical proposal doesn’t need for abstract facts to be true independent of an experiencer.
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But I told, above, why inevitable abstract facts have independent validity, and why absolute Anti-Realism has problems.
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I’d said:
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Your confusion is linguistic. — Michael Ossipoff

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You replied:
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That's right. You and I use the same words in completely different ways

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Yes indeed. You use “is” and “are” to refer exclusively to the present, meaning that you disagree with their timeless meaning frequent used in mathematics and logic.
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, so I haven't the capacity to really comprehend what you are saying.

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…then at least comprehend that your meaning for “is” and “are” contradicts a meaning for them that is routine and standard in mathematics and logic.
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If you don’t speak the language that I and others speak, then we can’t talk.
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I understand enough to get a gist of what you are saying, and I disagree with it.

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…and I’ve been answering your disagreements.
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Whether they’ve been adequately answered isn’t for you, me, or any advocate of a position on the matter, to judge. It’s for outside observers of the discussion to judge.
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Michael Ossipoff

A proposition is a statement. There is no such thing as a proposition which is not a statement.

[...]

Sorry, but a proposition is an actual statement, not a potential statement, and a fact is an actual thing known, not a potential thing known. You are using words in an unacceptable way, and that's why I disagree with your metaphysics. — Metaphysician Undercover

From Cambridge Philosophy Notes:

A statement usually means that which is said when a sentence is uttered or inscribed. Not all sentences makestatements, for instance imperative or interrogative sentences, or sentences uttered in,
say, reciting a play. A proposition is the hardest to define, but can be taken to mean
that which is common to a set of synonymous declarative sentences. Propositions,
even the false ones, are usually taken to exist timelessly and independently of
anything that expresses them, and even independently of whether they are ever
expressed.

Michael Ossipoff

Well, a definite name-able size for everything in our physical world leads to this question: Say it's eventually determined that the universe is a 4D sphere with a diameter of about 5.87 trillion trillion lightiyears. But why that particular large size instead of some other? Why about 5.87 instead of about 5.88?

Maybe one reason why the universe is very large or infinite is because the initiation of life is so vanishingly rare, that a universe that leads to us living things is much more likely to be a super-large or infinite one, instead of a smaller one. But, for any particular large size, why that particular large size?

An infinite size is simpler and un-arbitrary.

Michael Ossipoff

Alright, that's enough for this evening. I'm calling it a day. I'll resume replies tomorrow.

Michael Ossipoff

You are just playing with words and clutching at straws. The challenge for you is to show how an axiom could be false in a context where it is applicable. — Janus

Alright, the multiplicative inverse axiom is applicable to the integers, in the (perfectly meaningful) sense that we can apply it to them by evaluating them by it, and asking "Do the Integers meet the multiplicative inverse axiom? Is that axiom true for the Integers?"

So the multiplicative inverse axiom is applicable to the integers, and is false in their context.

Michael Ossipoff

An axiom typically isn't defined only for a particular set of elements and operations, Various axioms are true for, various sets of elements and operations. So it's meaningful to speak of an axiom's truth or falsity over various sets of elements and operations.

Michael Ossipoff

You are just playing with words and clutching at straws. The challenge for you is to show how an axiom could be false in a context where it is applicable. — Janus

Oh, ok, all you're asking is that i show how an axiom could be false in a context in which it is true :D

The salient point is, that it makes no sense to say that something is true in some context, if it could not be, even in principle, false in that context.

How could it be false, even in principle, in a context in which it is true?

I'd say that you're asking a lot :D

But I'm not saying that the multiplicative inverse axiom is or could be false for the real numbers or the rational numbers. I'm just saying that it's false for the integers.

Maybe this is the kind of answer you're asking for:

How would the rational numbers have to change in order for the multiplicative inverse axiom to become false for them? Delete every rational number that isn't also an integer, The multiplicative inverse axiom will then be false for the (thus modified) rational numbers.

In fact, don't do that much. Just delete one well-chosen rational number such as 1/37.

Then the multiplicative inverse axiom will be false for the (thus slightly modified) rational numbers.

Michael Ossipoff

The fact that axioms might be limited in their applicability does not speak to their truth or falsity, but to their relationship with context. — Janus

Yes, in some contexts they're false.

Michael Ossipoff

I refer you to my most recent post.

Various axioms of mathematics are false for various sets of elements with respect to various operations.

In the example i gave, the multiplicative inverse axiom is false with respect to the Integers.

Michael Ossipoff

If you want to say that something could be true or false, then you must be able to give an account of what difference that would make in either case.

You want to say that the axioms of mathematics could be either true or false, so you need to give an account of what differences we would find in either case.

Or, put it another way, you need to give an account of how we might be able to discover that the axioms of mathematics are true or false. I don't believe you will be able to give any such accounts; and if I am right, and you can't give any such accounts, your claim that the axioms of mathematics could be either true or false is an empty one. — Janus

When you prove a theorem, you show that, if the relevant axioms are true (and maybe of certain other propositions are true too), then the conclusion that you want to prove is true.

In other words, you prove an if-then fact.

You said:

The point is that within a system it is redundant to specify "if the axioms are true, then..." . The system. and any truth within it, does not exist without the axioms which are simply taken to be self-evident and fundamental. — Janus

...and it's because the axioms are taken to be self-evident and fundamental (for a certain set of elements, under certain operations*), that the if-then statement that you prove establishes the truth of the conclusion that you want to prove.

*The multiplicative inverse axiom isn't true with the Integers, for example, and so,, unlike the real numbers and the rational numbers, the integers aren't a field (They're a ring). So, you see, there's an instance in which the multiplicative inverse axiom is false.

Of course there are numerous other examples in which an axiom, or several axioms, are false with respect to some set of elements, under certain operations.

But it's well-understood, and often said, that what you're proving is that your desired conclusion is true if the axioms (and whatever other propositions) are true.

The alternatives of truth and falsity cannot be applied to the axioms.

Yes they can be an are. See above*.

Michael Ossipoff

The idea of an "abstract if-then fact" is redundant.

??? :D

Well yes, you could say that, because all abstract facts are timeless.

But you were the one who wanted to say that "is" and "are" can only refer to the present.
— Janus

'2+2=4' is true by definition; there is no "if-then" about it.

Incorrect. 4 isn't defined as 2+2.

4 is defined (most obviously at least) as 3+1

As you might guess, 3 is defined as 2+1.

2 is defined as 1+1

1 is the symbol for the multiplicative identity referred to in the multiplicative identity axiom.

It is unnecessary to define every counting number from 2 to 9, multiple times, as every sum of lower counting-numbers that it's equal to.--when one obvious sum would do.

But, given those definitions that I stated:

If the additive associative axiom is true, then 2+2=4.

That's a timeless abstract if-then fact.

All abstract facts are timeless.

In general, a proved and correct mathematical theorem is an if-then fact whose "if " premise includes (but isn't necessarily limited to) a set of mathematical axioms (algebraic or geometric).

Michael Ossipoff

Whether or not you’re the same person you were at an earlier time depends on how you mean the question. As I mention below, I think most would agree with me that you’re the same person as you were yesterday or last week, but not the same person you were a long time ago, in a much earlier distinctly-different part of your life.
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I would prefer not to rely on faith in the existence of a physical "soul" like described in many religions

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There’s no “Soul”, “Mind” or “Consciousness” separate from the body. The animal (including humans) is unitary. We’re the person, the animal, full-stop.
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, and I would also like to believe that the world around me is to some extent real.

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It’s real in the context of your life, and that’s real enough.
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Firstly, I understand that there is no argument or relevance for continuation of brain matter/brain atoms as the atoms in a brain are constantly being replaced all the time, and I don't see much significance in whether they are or not anyway.

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Yes, and an animal, including humans, is a system. There’s a story about a ship, in which one piece of the ship at a time is replaced, until eventually, years later, every part of the ship has been replaced, and the question is, is it the same ship as it was before the replacement process started? Sure, if the ship is regarded as a system.
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“This hatchet belonged to George Washington. Oh sure, it’s had a few new heads, and a few new handles.”
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But whether you’re the same person that you were at an earlier time depends on how you mean that question.
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There’s also a meaningful sense in which you aren’t the same person you were a long time ago. It’s plain to me that I’m not the same person that I was as a child, or even as a teenager. Of course I remember some of my concerns and priorities in those days, but I don’t know or understand how I justified those, though I suspect where I might have gotten some of them. It’s as if I know a few things about that person, as one might know about another person. I don’t even know the person that I was then.
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So I wouldn’t expect a definite, all-applicable, answer to that question. It depends on how you mean it.
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I’d say that (as I mentioned above) most would probably agree that you’re the same person as you were yesterday or last week, but not the same person that you were in a much earlier and distinctly different period of your life.
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I do accept that memory is important, but I have forgotten 99.9% of my memories and even the things that I do remember, I am not remembering in this very moment, if that makes sense.

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Yes, that’s like I was saying above.
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I know I do feel like I'm the same person, but say that the many worlds interpretation of quantum mechanics is true, there will be an unimaginably huge amount of people who also think that they are me, does that mean all of them actually are?

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Depends on how you mean it. They’re all the person with your name, but after a while they might differ significantly from you. You feel what you feel, not what they feel, and, in that meaningful sense, they aren’t you.
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Does that mean that the woman who thinks she is a reincarnation of Marilyn Monroe actually is Marilyn Monroe?

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No. I disagree with the notion that someone can remember a past life. In fact, I claim that the matter of whether or not a person has lived a past life is completely indeterminate.
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Maybe the way I perceive the world is fundamentally different to the way other people see the world - as in maybe the way I see/interpret colours is different from the way other people see them, but I do not have evidence for this and even if it is true, would it really be sufficient?

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I think a lot of people would agree with your impression of not being the same person you were a long time ago. I think you’re right.
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Michael Ossipoff

Or not? I can't square those two statements.[...that I intuitively reject infinite density, but intuitively expect that the universe is infinite]. — fishfry

It just doesn't seem like the universe, the whole of all that is, in our physical world, would be a piece of space of a name-able size.

But, as I said, that's just intuition.

I'm going to look into this question. What the physicists really think about the singularities where the equations break down.

Your suggestion that the physics just isn't valid in the region in question seems to make more sense than saying that the density there is infinite.

Michael Ossipoff

"Sure there were, before there were humans on the Earth. There were facts, but there were no utterances made about facts, because there were no animals with speech". — Michael Ossipoff
— Metaphysician Undercover

A "fact" is a thing known to have occurred

No. A fact needn't be about a past event.

, and this implies a knower.

There's no consensus to that effect. it's a contentious issue. But it needn't be an issue here, because my metaphysics is about individual subjective experience. If you say that a fact is only meaningful with respect to an experiencer, that isn't an objection to my metaphysical proposal.

What makes you think that there was a knower before there was animals with speech?

The fact that nonhuman animals aren't language-speakers doesn't mean that they aren't knowers.

A proposition is a statement. There is no such thing as a proposition which is not a statement.

I've told the definitions that explain what i meant when I used those words.

As I said, I'll check on the listed definitions of the terms that you dispute.

I'd said:

Again, you could truly say that, for any proposition, there's a potential statement. I don't deny that.

I agree that, for any fact, there's a potential statement of that fact. But I'm talking about facts instead of statements. — Michael Ossipoff

Sorry, but a proposition is an actual statement, not a potential statement

So you're saying that a proposition is an utterance, and requires a speaker. If that's how it's defined, then maybe there's another word for what might or might not be a fact, but which hasn't been uttered.

I'll check the published definitions.

, and a fact is an actual thing known, not a potential thing known.

So then, if there's a wiring short-circuit in a building, but no one knows about it, until later, when the fire-inspectors examine the scene, it can be truly be said that was no fact of a wiring short-circuit before the building burned down?

...and a building owner can assure his employees that there isn't a wiring-fault in his old dilapidated building, because no one knows of one (and no one has looked for one).

You are using words in an unacceptable way, and that's why I disagree with your metaphysics.

You're grasping at straws.

You're confusing the metaphysics with the definitions that you dispute. I've stated the metaphysics in terms of a set of definitions that I've specified. I have nothing against the use of standard definitions, when I find out what they are.

I'd said:

The physical world consists of facts, and I agree that, for every fact, there's a potential utterance about that fact.

But the facts are what the world consists of. — Michael Ossipoff

You replied:

As far as I know, there are two principle ways that "fact" is used. One is to refer to a thing known, and this requires a knower. The other is to refer to a truth, and a truth is something which is true. True means to correspond with reality. If you are using "fact" to refer to something which corresponds with reality, rather than to refer to something which is known to have occurred, then how is this not a statement?

It's a state of affairs, which may or may not be the subject of an utterance. A statement is an utterance that claims a fact.

By the definitions that I've been using. But,as I said, I'll check many sources, for the standard definitions of those terms.

Michael Ossipoff

"A fact is a state of affairs, an aspect of the way things are." — Michael Ossipoff


There is a big problem with this definition. "The way things are", refers to a moment of time at the present. But time is passing, and things are changing. So there is really no such thing as "the way things are", because this would require a stoppage of time, and that would create an unreal situation. — Metaphysician Undercover

Incorrect.

Your confusion is linguistic.

Abstract facts are timelessly true. An abstract fact can be defined as an aspect of the way things (timelessly) are.

Likewise "A state of affairs" needn't mean a state of affairs at one particular time. It can refer to a timeless state of affairs, which is what an abstract fact is.

You're insisting that the "is" and "are" refer to the present, but abstract facts are timeless facts. They're timelessly true.

The abstract fact that If the additive associative axiom is true, then 2+2=4 (by an obvious definition of 1, 2, 3 & 4 in terms of the multiplicative identity and addition), is a timeless abstract if-then fact.

Likewise, my abstract if-then fact about Slitheytoves & Jabberwockeys is a timeless abstract fact.

It isn't only true today, for example. One could insert the word "timelessly" in front of "is" and "are" where needed, and I sometimes do. But often its understood.

In logical discussions and articles, in mathematical theorems and proofs, "are" and "is" are often understood to have timeless meaning.

Your definition of "fact" is not only wrong in the sense that it is inconsistent with the standard definitions, that I gave in my last post, but it is also wrong in the sense that it describes something which appears to be physically impossible,

Only if you think that "is" and "are" must always only refer to the present, or that a state of affairs can only mean a state of affairs at one particular time.

See above.

And if the definition of a fact as a state of affairs is wrong, then you'd better inform SEP that they're wrong too.

Anyway, as I said, after replying to your latest message of yesterday, I'll check on the definitions of the terms that you dispute, at a lot of sources., and will post what I find.

Michael Ossipoff

Because birth, the beginning of a life, is so astonishing and miraculous, it's difficult to believe that we were born in a pocket of space that has a state-able size like we do.

Michael Ossipoff

For a long time, I didn't believe about the infinite density in a black-hole. Then, eventually, I'd heard it so much, and it seemed so unanimous, that I decided that it must be true. But more recently, it occurs to me that there's really something ridiculous about the notion of places of infinite matter-density scattered here and there around us. Infinite density in our physical world is nonsensical.

I realize that the astrophysicists know their subject a lot better than I do, but I don't care who says it. If physics says that there are places with infinitely dense matter, then it seems to me that physics must need some more work.

Anyway, isn't it widely agreed that general relativity still needs more work? So, if the prediction of infinite mass-density in a black-hole has general relativity as part of how that prediction was arrived at, then doesn't that suggest that the prediction isn't so reliable?

But intuitively I expect that the universe is infinite.

The universe is the whole of all that there is in our physical world. How could that whole universe be finite like us? Sure, the things in the universe, like us, our planet, etc., are finite. But wouldn't the universe be a whole grand order-of-magnitude bigger than we are? If we're finite, must it not be infinite?

I emphasize that that's just intuition, not logic or physics.

Michael Ossipoff

I’ll again look up “fact”, “proposition”, “statement” and “utterance”. This time I’ll check many sources.
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For now, I’ll just tell you how I use those words:
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A fact is a state of affairs, an aspect of the way things are.
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A proposition is a maybe-fact. It’s like a fact, except that it might not be a fact. A hypothetical “fact” that might not really be a fact. My definition of a proposition doesn’t require that it be uttered. For example, an if-then fact relates two hypothetical propositions, one of which is true if the other is true. …none of which need be uttered.
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A statement is an utterance that claims a fact. A statement is an (not necessarily true) utterance about a fact. A statement expresses a proposition, which may or may not be a fact. A statement can be a true statement or a false statement. A proposition could be called a potential statement.
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An utterance is something that’s actually said.
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Things are what can be referred to. Things are what facts are about.
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[end of definitions]
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Definitions need only to be reasonable, clearly-specified, and consistently-used.
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But if any of the above-stated definitions are wrong, in the sense of being strongly-contradicted by standard philosophical usage, then of course I’ll use the standard definitions instead.
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Of course we should all use the standard definitions, for clarity of meaning.
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I didn’t intentionally violate standard philosophical usage. As I said, if some of my definitions are definitely wrong, then I’ll change them.
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But, in the meantime, all that’s needed is that they be reasonable, clearly-specified, and consistently-used (by the person who uses them).
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As long as they’re well-specified and consistently-used, they certainly don’t invalidate a metaphysics that’s stated in terms of them.
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Now, I’ll post these definitions, to clarify what I’ve meant by what I’ve said.
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Then (maybe today, maybe tomorrow morning) I’ll reply to the rest of your message.
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Then I’ll check on the philosophical definitions of those terms (fact, proposition, statement, utterance), at many sources, and then post what I find.
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Michael Ossipoff

I don't know about the set-theory consideration that leads you to doubt that there could be infinity in the world.

But most physicists must not either, because they're nearly unanimous about there being black-holes in which there's matter with infinite density.

As I was saying, I'm not interested in cosmic matters, and I don't claim to be qualified to say whether the universe is likely to be infinite. As I mentioned, Tegmark says that the evidence is tending toward support for an infinite universe, but of course physicists are divided about that.

Just speaking for myself, without claiming any qualification to judge the matter, the universe being infinite is, to me, the more plausible and believable possibility. ...that everything in our physical world isn't spatially limited.

But, again, I don't claim any qualification for judging that matter.

Michael Ossipoff

It seems to me that that conflates what is: 'the green car out front' with a possibility: 'that I will look at it'.

You're using the meaning of "conflate" that means "confuse".

You're saying that I'm confusing what is, with a possibility. ...the green car out in front, with the possibility that I'll look at it.

Well, I only said "If you look out the front window."

"If you look out the front window" is the "if " premise of the if-then fact.

I'm saying that "There's a green car out in the parking space out in front" implies and corresponds with "If you look out the window, a green car will be visible to you in your parking space out in front."

But no,I'm not confusing "There's a green car out in front" with "You'll look at it". Yes, I'm relating "There's a green car out in front" with an if-then fact whose "if " premise is "If you look out the front window."

— Janus

An example you didn't give 'if there is a green car out front, then someone must have parked it there" might seem to be a counterexample that addresses the past; but this is merely apparent. On analysis we can see that this is merely an inductive inference. The car could have gotten there any number of ways, no matter how unlikely.

Yes, and so I didn't say, "If there's a green car out in front then someone must have parked it there." Maybe it just accidentally rolled out of the steep driveway across the street, when someone didn't set the parking-brake.

So yes, that proposition wouldn't be true, and I didn't state it..

Also it reflects that fact that, for us epistemologically speaking, it actually invokes a possible future in which we come to discover how the car got there.

As you said, it wouldn't be a true proposition, and I didn't state it. As for how the car got there, that's a matter that my comments didn't address. I did say that if it's there then your parking-space won't be available to you, and that if someone parks it there, it will be there (well, for a while at least).

Michael Ossipoff

I don't see how there could be a fact without a statement as to what that fact is. — Metaphysician Undercover

Sure there were, before there were humans on the Earth. There were facts, but there were no utterances made about facts, because there were no animals with speech.

Sure, you can say that, for any fact, there's a potential statement of that fact. I don't deny that.

What is an "if-then fact" without the "if" and the "then".

Nothing, of course. It wouldn't be an if-then fact.

It doesn't make sense that there could be an if-then fact without the "if-then"

Agreed. An if-then fact relates two hypothetical propositions The if-then fact is a fact that one hypothetical proposition is true if the other is. An if-then statement must have those two parts, consisting of those two hypothetical propositions.

, and these are utterances.

No, they're just propositions. Of course any proposition is something that there could be a statement about, if there's someone to make that statement, and if s/he chooses to make it.

Again, you could truly say that, for any proposition, there's a potential statement. I don't deny that.

Since I conceive of a statement of the fact as necessary for the existence of any fact

I agree that, for any fact, there's a potential statement of that fact. But I'm talking about facts instead of statements.

A fact is a state-of-affairs, or an aspect of the way things are.

A statement is an utterance about a fact.

, then what you say, to me, necessarily implies that the world consists of utterances.

The physical world consists of facts, and I agree that, for every fact, there's a potential utterance about that fact.

But the facts are what the world consists of.

Michael Ossipoff

I won't engage further if you are going to respond with (deliberately?) stupid, uncharitable interpretations. — Janus

Yes, sorry about the answer to an obvious misinterpretation of what you were saying.

It was deliberate in the sense that I knew that I was replying to something that you didn't mean. But it wasn't intentional in the sense of trying to be evasive, or not wanting to give a straight answer to what you said. I wasn't pretending to not know what you meant. I didn't know what you meant.

I honestly didn't understand the objection. I didn't understand what you meant.

Of course you didn't mean what I implied and answered about, so maybe it would have been better to just express that I didn't understand the objection.

You said:

We could even say the same of the valley; 'if it rains the valley will be eroded'. This addresses only possibilty though and says nothing about what is or what has been.

On this account it is not conceptually adequate to underpin a comprehensive metaphysics. — Janus

You're saying that if-thens can't be the basis of a metaphysics, because they aren't about what is or has been.

I claim that some of them are.

How does the fact that there's a green car out in front relate to an if-then fact. Well,if you look out the front window, then you'll experience that a green car is visible to you..

Maybe that sounds contrived, because we don't always say things that way, but it's a genuine implication and correspondence between facts.

To use my usual example, the fact that there's a traffic-roundabout at the intersection of 34th & Vine, implies and corresponds to the if-then fact that, if you go to 34th & Vine, then you'll encounter a traffic-roundabout.

As I've been saying, any fact about our physical world implies and corresponds to an if-then fact.

In my reply, I said:

A set of hypothetical physical quantity-values, and a hypothetical relation among them (called a "physical law"), are parts of the "if" premise of an if-then fact.

...except that one of those quantity-values can be taken as the "then" conclusion of that if-then fact.

Of course the world of your experience, when closely investigated and examined (by the physicists whose discoveries come into our experience via articles, but also in your direct physical experience), consists of a complex and intricate system of such facts. Of course time is one of the hypothetical quantities that many physical laws relate.

I'm suggesting that there's no reason to believe that the world of your experience consists of other than that.

Also, any fact about what is, can be rightly regarded as the "if" premise or the "then" conclusion of an if-then fact. ...or of course both, with respect to different if-then facts.

An if-then fact relates two hypothetical propositions. One is true if the other is true.

So, in addition to the fact that any fact about the physical world implies and corresponds to an if-then fact, it's also true that any fact about the physical world is one of the two hypothetical propositions that some if-then fact relates.

A fact that something is, isn't, of itself, an if-then fact, but it's one of the two hypothetical propositions that an if-then fact relates...the "if" premise or the "then" conclusion. It's part of an if-then fact.

"There's a green car out in front, parked in your parking-space.".

If someone parks their Green car in front of your house, then there will be a green car out in front.

If there's a green car parked in your parking-space out in front, then your parking space that it occupies won't be available for you to park your own car.

So, 1)Any fact about our physical world implies and corresponds to an if-then fact, and 2) That fact is also part of an if-then fact (one of the two hypothetical propositions that an if-then fact relates). In fact, it's the "if" premise of various if-then facts, and it's the "then" conclusion of other if-then facts.

We don't ordinarily speak in terms of if-thens,but all of the facts about our world imply some if-then facts, and are parts of other if-then facts..

...whether in physics, or the everyday experienced facts.

There's no reason to believe that your experience is other than a complex system of inter-referring abstract if-then facts about hypothetical propositions...your life-experience possibiity-story.

Of course the basic requirement for your experience-story is that it be self-consistent, non-contradictory. Your own direct experience, and the discoveries of physicists, coming into our experience via articles and books, are of things that are consistent with your life having started.

Sometimes there have been seeming inconsistencies, physical findings that contradicted known physics: The Michaelson-Morely experiment result. The black-body radiation energy-wavelength curve, The seemingly anomalous rotation of apsides of the orbit of the planet Mercury. Those things were later found consistent with an improved system of physical laws

Now there's the unexplained acceleration of the recession-rates of the more distant galaxies.

Because any seeming inconsistency might later be reconciled with new physics, maybe it's impossible to prove that a physical world is self-inconsistent.

No one doubts that the unexplained acceleration of the recession-rates of the more distant galaxies will be explained by new physics--or could in principle, if physicists can advance far enough.

As for the past, what is found out about the past, too, must be consistent with the current state of affairs that you experience. For instance, when physicists study the history of the Earth, the solar-system, the galaxy, and the universe, what they find is of course consistent with the fact of your own existence.

Have I answered your objection?

Michael Ossipoff



















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"There are abstract if-then facts. There couldn't have not been abstract if-then facts. And, just as inevitably, there are complex inter-referring systems of inevitable abstract if-then facts about hypotheticals.

In fact, there are infinitely-many such complex logical systems." — Michael Ossipoff


...but then no idea what this could mean.

Is this saying that an assumption of intelligibility - as in the laws of thought - are a precondition to cognition — apokrisis

No, I didn't mean anything other than what I said.

I don't think anyone denies that there are abstract facts. Even if you say that they're inextricably bound up with us experiencers, you don't say that there aren't abstract facts. So that seems a completely uncontroversial statement.

But likewise there are abstract facts that refer to eachother, and there are complex systems of them. Since you don't deny that there are abstract facts, you aren't likely to deny that there are complex systems of inter-referring abstract facts.

For example, there's a complex system of hypothetical physical quantity-values, and hypothetical relations (physical laws) among them, For any particular such hypothetical relation, a hypothetical proposition, and the set of hypothetical quantity-values that it relates, that hypothetical proposition and those hypothetical quantity values are parts of the "if " premise of an abstract if-then fact.

Obviously there's an intricate and complex system of such physical laws and quantities, and if-then facts about them.

I'm saying that there's one such complex system of abstract if-thens that has the events and relations of your experience. And that there's no reason to believe that the world of your experience consists of other than that.

Of course facts about this physical system are what physicists find when they investigate and examine the physical world. It enters your experience when they report it and you read it. But also, in various ways, in your direct physical experience.

But, in general, any fact about our physical world implies and corresponds to an if-then fact. If you examine some particular thing, then you'll find a certain thing about it.

What your life-experience possibility-story requires is self-consistency, non-contradiction, because it's a story consisting of facts. Mutually contradictory propositions can't all be facts.

Michael Ossipoff


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Whatever it is that we formulate in terms of "if-then" may be thought to be in a certain restricted sense "true for and known by animals".

We could even say the same of the valley; 'if it rains the valley will be eroded'. — Janus

Not if it only rains once, with a few seconds of drizzle.

This addresses only possibility though and says nothing about what is or what has been. On this account it is not conceptually adequate to underpin a comprehensive metaphysics.

Of course not. I wouldn't consider basing a metaphysics on just one fact, least of all a questionable fact like that.

I spoke of a complex system of inter-referring abstract if-then facts about hypotheticals.

I'll say this again in case you didn't see the other posts where I said it:

A set of hypothetical physical quantity-values, and a hypothetical relation among them (called a "physical law"), are parts of the "if" premise of an if-then fact.

...except that one of those quantity-values can be taken as the "then" conclusion of that if-then fact.

I gave an everyday example of how any fact about this physical world implies and corresponds to an if-then fact.

The world can be completely described in conditional grammar. We tend to believe our convenient declarative indicative grammar too much.

Instead of a world of "Is", infinitely-many worlds of "If".

Michael Ossipoff

Out of curiosity, what metaphysical proposal? There doesn't seem to be one in this thread from you. So a link would be helpful. — apokrisis

Sorry, it was in other threads that I posted it. Here, below, I've pasted an account of it that I recently posted in a different thread, to answer a question. I've quoted the question, but not the name of the person who asked the question:

This question was asked:

When I was born, how did 'nature' conjure up my perspective into this body? Why and how did it decide that my perspective is the right one? These were questions that I asked myself since I was 9 years old. Why am I me? Why am I not my brother? How did 'I' happen to be?

Anyway, this is the thought I never had the chance to discuss with anyone. I tried raising it with my friends but none of them had any good answers. Would really like to gain some insight from someone who has delved very deep into this subject matter

My reply:

Sometimes a seemingly difficult question like that is just the result of metaphysical assumptions that aren't valid. For example, the metaphysics of Materialism has been hammered into us from elementary-school on.

Materialism has several aliases. A currently fashionable one is "Naturalism". Also, the word "Nominalism" is often, currently fashionably, used to refer to what is really another way of wording Materialism.

Sometimes, answering questions such as the ones that you expressed, requires a completely different metaphysics.

I'll answer that in terms of the inevitable and uncontroversial metaphysics that I've been proposing here.

I've posted the whole proposition at so many discussions in these forums, that I shouldn't repeat it all here.

But, to just summarize:

All that you know about the physical world is from your experience, in fact all of it is your experience. That's all there is, for you.

There are abstract if-then facts. There couldn't have not been abstract if-then facts. And, just as inevitably, there are complex inter-referring systems of inevitable abstract if-then facts about hypotheticals.

In fact, there are infinitely-many such complex logical systems.

In fact, there's one whose events and relations are those that you encounter in your experience,

There's no reason to believe that your life-experience is other than that, or that the world you live in is other than the hypothetical setting for that hypothetical life-experience possibility-story consisting of a complex system of inevitable abstract if-then facts about hypotheticals.

That complex system of inter-referring inevitable abstract logical facts about hypotheticals is your life-experience possibility-story,

Let me re-quote your question:

When I was born, how did 'nature' conjure up my perspective into this body? — Susu


Your perspective is prior to this life. Your perspective consists of your inclinations, predispositions, etc.

Those are attributes of the protagonist of one of the infinitely-many life-experience possibility-stories.

So, why are you in a life? Because you, someone with your perspective, is the protagonist of one of the infinitely-many life-experience possibility-stories.

Being in a life is part of the your nature, as the possessor of your perspective, the protagonist of a life-experience possibility-story.

So it's no surprise that you're in a life. That's why this life started.

Why and how did it decide that my perspective is the right one?

Your perspective is what it started from. ...your perspective and the life-experience possibility-story whose protagonist has that perspective.

So there's really no question of why it's the right perspective for you. It is you, and it's the reason why this life started.

Michael Ossipoff

Good point. The fact that we don't remember experience doesn't mean that it wasn't there.

So we should be cautious what we assume.

Anyway, hypothetically, suppose that there really isn't any experience during deep sleep, just as there isn't after complete shutdown at death

Well, just before that complete shutdown and absence of awareness (in deep-sleep or afterdeath-shutdown. ), you, by definition, have awareness. But most likely, when you're that nearly shut-down, you don't know about waking-life. Or identity, events, time. ...that there are or ever were such things. ...or that there even could be such things. At that point, you've reached timelessness.

Sure, shutdown occurs soon, but you don't know that, because you've reached timelessness. So the temporariness of your experience just before that shutdown is meaningless.

But, as you pointed out no one can say that there isn't any experience during deep sleep, just because we don't remember it.

There are things that your survival requires you to know. What it was like in deep sleep isn't one if them, so it isn't surprising that the body doesn't provide you a memory of that time. Aside from that, most likely it's so close to what the "awake" person would call "nothing" that there usually doesn't seem to be anything to remember. Maybe there isn't any of what waking consciousness would call something. But, from your point of view when you were in deep sleep?

Of course, after death, when the body and awareness have completely shut down, there's no experience. So you'll never experience a time without experience. Only your survivors will experience the time after your complete death-shutdown.

Michael Ossipoff

Let me further answer this:

An "if-then fact" is exclusively a linguistically formulated fact. I experience the world as has been, is being and could be; only the last is possibility or "if" rather than "is". Only language enables the apprehension of the future, of possibility. So, I see no reason to think the provenance of "if-then" extends beyond language. — Janus

First, though I've been saying that any fact about our physical world can be stated as an if-then fact. But it isn't necessary to mention statements. I should, instead, say that any fact about our physical world implies and corresponds to an if-then fact.

One objection to my proposal is a claim that abstract facts are created by us, and don't have existence independent from us. ...that abstract facts are inextricably bound-up with us the experiencers.

That's fine, because my metaphysics is an Anti-Realism, about the individual's life-experience possibility-story.

So, saying that abstract facts are in relation to our experience, rather than being independently existent doesn't contradict my metaphysical proposal.

I said that there are abstract if-then facts. You can't say that there aren't abstract if-then facts.

But, aside from that, for another thing:

The fact that the abstract facts are the same for everyone, and would be the same for someone living on another planet, or in another galaxy, or in a very distant part of our universe, or in a different sub-universe of a physically-inter-related multiverse that we're in, or even in different, physically-unrelated possibility-worlds--that makes it difficult to say that the abstract facts are created by us, and that otherwise, without us, they "aren't".

No, the fact that all these observers, in all these worlds, would agree with my Slitheytoves & Jaberwockeys abstract if-then fact, and likewise the abstract if-then fact that, if the additive associative axiom is true, then 2+2=4 (based on a reasonable, obvious and natural definition of 1, 2, 3, & 4, in terms of the multiplicative identity and addition)...Because of those, and all the other abstract facts that are obviously true for anyone anywhere--then those facts obviously "are". They're true everywhere, in every world, for everyone.

As I've said, the if-then facts that comprise your life-experience possibility-story aren't really different from all the other abstract if-then facts. So, objectively, calling a fact meaningful or valid only if's part of someone's experience is animal-chauvinistic.

So that's why I say that absolute Anti-Realism is out of the question.

But it's also true that your life-experience possibility-story is completely independent of anything else, facts or systems of them, outside it, and that story is about your experience. ...justifying a subjective-based, individual-experienced-based metaphysics. ...which could, in terms of already-used language, be described as Eliminative Ontic Structural Anti-Realism..

That subjective story isn't everything, but it's completely independent of anything else, self-contained.. ...even though its system of inter-referring abstract if-then facts are only a subset of all of the abstract if-then facts that are.

Michael Ossipoff

What we don't know is whether this means that reality consists of abstract facts. — Janus

Reality doesn't consist of abstract facts.

Neither metaphysics, nor anything described by metaphysics covers, explains or describes Reality.

However, uncontroversially, there's a complex system of inter-referring abstract if-then facts about hypotheticals (the hypothetical propositions that are their "if " premise and "then" conclusion, and the hypothetical things that those propositions are about), whose events and relations are those in your experience.

You can say that we don't know if that's all that our world is. What can be said, however, is that there's no reason to believe that our world is other than that. And it can be said that any other metaphysical system, as a brute fact, unverifiably and unfalsifiably duplicating that logical system's events and relations, is superflous.

Michael Ossipoff

For a long time it didn't seem to make sense, when we're told about infinite density in a black-hole. And I've had some doubts about whether our Big-Bang Universe (BBU) could be infinite. (...or could even be part of an infinite physically-inter-related multiverse?).

Though there are infinitely-many possibility-worlds and life-experience possibility-stories, maybe things have to be finite in a universe (by which word I'd also refer to a physically inter-related multiverse).

Tegmark says that the evidence is, more and more, suggesting that the universe is infinite. Is he wrong about those considerations that you spoke of? Is it that he doesn't know about them? ....hasn't heard about them?

I've read that it's being said that evidently the universe is either infinite, or very large. If so, then maybe it's just very large. Maybe large enough to require the g(N) notation to describe its size, or one of the even bigger iteratively-recursive extensions of it?

But, if most physicists accept infinite density in a black hole, then, if that's acceptable to them, then would they have any reason to not accept an infinite size for the universe?

Michael Ossipoff

Yes, the googology hobby includes efforts to propose more compact and elegant notations for super-large numbers, and, if someday a theorem mentions an even larger number, maybe one of their notations could be useful for describing it.

Also, if the universe turns out to be infinite, then maybe physics or astronomy will someday be able to say things that involve the super-huge numbers. Or maybe the size of the universe, even if it's finite, might require one of those super-numbers, in a super-number-notation, to express it.

But the googologists have so many notations, some quite elaborate, and so many named numbers, that I don't recommend wading into it. Sometimes the names of their websites contain the word "Pointless"

What I quoted about the size of SCG(13) (whether it's true or not) is an extension of g(N) and TREE(N), in which they're recursively iterated. Maybe that sort of recursion could be extended to higher levels of recurrent iteration in some elegant way, in which the number of recurrence-levels itself is equal to the number resulting from the previous level of recursive iteration.

Really, the sky's the limit for how far that level-recursion could go.

Anyway, I haven't found anything, outside of the googology-hobbyists' discussion, about how big SCG(13) really is, in terms of Graham's number.

Michael Ossipoff

I was just checking. A Planck Length may be, but is not definitely, the smallest possible length. — T Clark

Yes, they say that it's likely the smallest distance that's physically meaningful to speak of.

It's about a hundredth of a millionth of a trillionth of the diameter of a proton.

If it is, then a cubic Planck Length is the smallest possible volume that can be packed completely in a 3 dimensional space. I guess a sphere with a diameter of the Planck Length would be the smallest possible volume. Then, that would mean that the volume of the universe expressed in cubic Planck Lengths is the largest meaningful number. Yes? No?

Yes, it would be the largest straight physical or spatial object-count that could be made. But the size of the universe isn't known, and it isn't even known whether the universe is finite or infinite.

So I spoke of the number of Planck volumes in the observable universe.

But we can still talk about numbers larger than that. The fact that something might be meaningless has never stopped us from discussing it before.

Yes, no one seems to want to get to the point. There seems to be a tacit understanding that metaphysics is a speculative, relativist sort of topic, in which no progress can be made, no definite statements can be made, and discussion can and must be interminable.

But that notion probably comes from academic philosophy, where it profitably serves as an academic philosopher's perpetual gravy-train and meal-ticket..

But, by bringing up metaphysics, I'm getting off the topic of this big-numbers thread.

As for meaningless and pointless numbers, yes the googology hobbyists make a hobby of competition naming the largest numbers, even though they don't enumerate anything.

Obviously, as we all know, for any number, there's a larger one. A number that doesn't enumerate anything isn't meaningful.

But SCG(13) enumerates something. It enumerates a lower bound on the number of successive graphs that can be drawn, in accordance with the rules that I described, when up to 13 extra points are permitted in each successive graph.

...and it's humungously, incomprehensibly, incomparably, larger than (World Population)!!.

(Note the period at the end of that sentence--The "!!" are factorial signs, not punctuation-marks. It's a disadvantage of the factorial notation that it can easily be mistaken as the emphasis-expressing punctuation-mark.)

A cat knows that if it waits patiently by a gopher hole, then it might get a chance to catch the gopher. A cat doesn't have language.

If-then facts are true for, and known by, animals that don't have language.

Michael Ossipoff

You've described the world as consisting of statements of fact (if-then facts). — Metaphysician Undercover

No. I didn't describe the world as statements of if-then facts.

I described the world as if-then facts.

An if-then fact's "if " premise and its "then" conclusion are hypothetical propositions which may or may not be facts.

What I said about statements was that any fact about our world can be stated as an if-then fact.

I didn't say that every fact about our world is a statement. A statement is an utterance about a fact, and I never said that the world consists of utterances.

Michael Ossipoff

Where does SCG(13) come from?

The name "SGC" stands for "Sub-Cubic Graph". That name might have something to do with the fact that each vertex of a cube has edges connecting it to 3 other vertices.

A graph is a set of dots, at least some of which might be connected by lines. A planar graph is a graph on a flat surface.

Say you're asked to draw a sequence of planar graphs.

These graphs that you're asked to draw are relatively unrestricted, as regards their connectivity. You can draw a graph with no lines connecting its dots. You can draw one with lines connecting all of its dots. You can even have a looped line with both ends connected to the same dot. And you can have several lines connecting the same pair of dots.

In other words, as regards line connections between dots, you can pretty much do what you want.

The only limitation in that regard is that no dot can have more than three line-ends connected to it.
Of course a looped line connected to a dot counts as two line-ends connected to that dot.

Now, you start out allowed to draw one dot. Then, for your 2nd graph, you're allowed up to 2 dots. And for your 3rd graph, you're allowed up to 3 dots...and so on.

But each next graph that you draw must be a completely new graph, in the sense that it couldn't have been made from one of your previous ones by adding dots &/or lines, or by expanding a dot into 2 dots connected by a line, and sharing, between them, the line-end connections that the original dot had.

Those are the only rules.

The question is, how long a sequence of graphs can you draw, by those rules?

Not very many.

But, if you increase the dots-limit for every graph in the sequence by the same number N, then you can draw more graphs before you run out of completely new graphs to draw.

It's proven that, for any N, there's still only a finite number of graphs that you can draw before you run out of completely new graphs to draw..

But, though, with N = 0, you can only draw perhaps 5 graphs in the sequence (It might have been 5, I'm not sure.), and though the number of possible graphs in the sequence remains finite, even as you increase N, that finite number increases tremendously as N increases.

SGC(N) is the number of graphs that you can draw in that sequence before you run out of completely new graphs to draw, if you allow every graph in the sequence to have up to N extra dots.

SGC(0) = 5 (That's probably what they said.)

SGC(13) is a huge number that's tremendously more than TREE(3), which, in turn, is tremendously more than Graham's number, g(64).

Each of those 3 numbers is so great that, dividing it by (World Population)!! gives a result not noticeably different from what you get by dividing it by 1.

...and so great that the power of (World Population)!! that it is, isn't noticeably different from the power of 10 that it is.

Anything that you could do with (World Population)!! to get SCG(13), you could also get a number not noticeably different from SCG(13) by doing that with 10.

Michael Ossipoff