Creationists: How do you test for "truth"?

[sandy whitelinger]

There *is* no first fraction greater than 0. And that is as true in Robinson arithmetic as it is in the standard model. If x>0, then 0<x/2 <x. That's all that is required for the proof.



Two issues here:

1. If you pick any specific infinitesimal, say x. Then x/2 will be a smaller infinitesimal. So the trick doesn't work.

2. Why do Cantorian infinities irritate you? It is simply a relationship between sets (the existence of a bijection) and the realization that there are infinite sets (for example, the set of natural numbers). If you then allow the construction of the power set of any set (the set of all subsets), you inevitably get the Cantor hierarchy, although perhaps not with an identification with the ordinals.

Is there a situation where you know one set is inside another set but you can't define the other set?

 

[Polymath257]

Is there a situation where you know one set is inside another set but you can't define the other set?

There are alwsy many sets that a given set is contained in. It is even fairly easy to define one: If A is a set, then the union of A with {A} will be a set larger than A and not equal to it.

 

[blü 2]

There *is* no first fraction greater than 0. And that is as true in Robinson arithmetic as it is in the standard model. If x>0, then 0<x/2 <x. That's all that is required for the proof.

So what is 1 ∞th / 2?

1. If you pick any specific infinitesimal, say x. Then x/2 will be a smaller infinitesimal. So the trick doesn't work.

That doesn't work for ∞ : ∞/2=∞.

So why would it work for fractions? (1/∞) /2 = 1/∞, surely?

2. Why do Cantorian infinities irritate you? It is simply a relationship between sets (the existence of a bijection) and the realization that there are infinite sets (for example, the set of natural numbers).

My argument is not with infinite sets of the natural numbers when 'infinite' has its etymological meaning, 'without boundary, without limit'. But once we come to Cantor's lowest infinite ordinal ω, it strikes me as meaningless nonsense. There isn't even conceptually a point on the number line that has a meaningful 'infinite' gap in it. (I accept that a workable maths results.) Nonetheless, that's the very idea I'm invoking in my reply to sandy, of course.

 

[sandy whitelinger]

There are alwsy many sets that a given set is contained in. It is even fairly easy to define one: If A is a set, then the union of A with {A} will be a set larger than A and not equal to it.

Is {A} ever indefinable in value in that situation?

 

[Polymath257]

Is {A} ever indefinable in value in that situation?

Nope. It is a set with the single element A.

 

[sandy whitelinger]

Nope. It is a set with the single element A.

Thanks again.

 

[sandy whitelinger]

But is that an unknowable? Certainly not. It is simply unknown.

True. I thought it an amusing antidote though.

 

[Polymath257]

So what is 1 ∞th / 2?
That doesn't work for ∞ : ∞/2=∞.

Not in Robinson arithmetic. For any particular infinitely large Robinson real, ∞, 2∞ is a larger and ∞/2 is a smaller infinitely large Robinson real..

So why would it work for fractions? (1/∞) /2 = 1/∞, surely?

Well, the issue is that in Robinson arithmetic, there are several 'infinities' and the usual axioms for the real numbers still apply. For any given ∞, (1/∞)/2 is a smaller infinitesimal and is NOT the same as 1/∞.

Robinson arithmetic is different than limits and it is also different than cardinal arithmetic.

My argument is not with infinite sets of the natural numbers when 'infinite' has its etymological meaning, 'without boundary, without limit'. But once we come to Cantor's lowest infinite ordinal ω, it strikes me as meaningless nonsense. There isn't even conceptually a point on the number line that has a meaningful 'infinite' gap in it. (I accept that a workable maths results.) Nonetheless, that's the very idea I'm invoking in my reply to sandy, of course.

Well, the old definition of 'infinite' as 'without boundary or limit' runs into many severe issues. For example, the open interval (0,1) does not have a 'boundary'. A sphere has neither boundary nor a 'limit' (it *is* a boundary, but has none itself).

The lowest infinite ordinal is just the same as the set of natural numbers. I'm not sure why you think there would need to be an 'infinite gap' in it for the set itself to be infinite.

 

[blü 2]

Not in Robinson arithmetic. For any particular infinitely large Robinson real, ∞, 2∞ is a larger and ∞/2 is a smaller infinitely large Robinson real.

I missed that point. I was still with Cantor.

Well, the issue is that in Robinson arithmetic, there are several 'infinities' and the usual axioms for the real numbers still apply. For any given ∞, (1/∞)/2 is a smaller infinitesimal and is NOT the same as 1/∞.

Then the answer to sandy would be ─ um ─ 0+(1/∞ (cardinal ∞)) ─ or something along those lines.

The lowest infinite ordinal is just the same as the set of natural numbers. I'm not sure why you think there would need to be an 'infinite gap' in it for the set itself to be infinite.

No, the lowest infinite ordinal is a notionally fixed point, the first point you come to on the far side of infinity. Which is terms of the number line is meaningless ─ there is no last point before infinity, no first point after it, no little door in the number line which you step through into wonderland.

An enjoyable conversation.

 

[Polymath257]

I missed that point. I was still with Cantor.

Then the answer to sandy would be ─ um ─ 0+(1/∞ (cardinal ∞)) ─ or something along those lines.

And care is required here. Division of cardinals cannot be consistently defined.

No, the lowest infinite ordinal is a notionally fixed point,

Yes, and that ordinal is the set of natural numbers.

the first point you come to on the far side of infinity.

Yes, it is the smallest infinite ordinal.

Which is terms of the number line is meaningless ─ there is no last point before infinity, no first point after it, no little door in the number line which you step through into wonderland.

An enjoyable conversation.

That's right, there is no immediate predecessor of the first infinite ordinal. It is what is known as a limit ordinal (as opposed to a successor ordinal).

And you are also right. The first infinite ordinal is not a point in the number line. It is a different type of object.

 

[Polymath257]

I should also point out that there a number of subtleties when doing cardinal and ordinal arithmetic. As a reminder, cardinality has to do with size of a set and ordinality has to do with order properties (and so is only defined for sets with an order on them).

So, for example, if x is any infinite cardinal, and we use cardinal addition or multiplication, we have 1+x=x=x+x and 1*x=x=x*x. Because of this, division by cardinals is not a well-defined operation. But both addition and multiplication of cardinals is commutative (order doesn't matter).

For ordinals, things are stranger. If x is any infinite ordinal, we have 1+x=x. But x+1 ≠ x. Essentially, if you put one point before an infinite, ordered set, you get the same order type back. But if you put that point *after* the same infinite set, you get a different order type (one that does have a last element).

Similarly, for ordinals, if x is the first infinite ordinal, 2*x=x, but x*2 ≠ x. This happens for similar reasons.

So addition and multiplication of ordinals fails to be commutative.

Finally, for Robinson arithmetic, addition and multiplication are commutative and any non-zero Robinson real has an inverse. But in this context, if x is an infinitely large Robinson real, x*2 ≠ x ≠ x/2 and
all three are infinitely large. It then happens that y=1/x is an infinitesimal, But then, y/2 is a smaller infinitesimal.

One must be *very* careful about context when dealing with infinities. They do not act like finite quantities. They have their own rules, which are consistent (as far as we know), but different.

 

[sandy whitelinger]

And care is required here. Division of cardinals cannot be consistently defined.


Yes, and that ordinal is the set of natural numbers.


Yes, it is the smallest infinite ordinal.



That's right, there is no immediate predecessor of the first infinite ordinal. It is what is known as a limit ordinal (as opposed to a successor ordinal).

ah, so this is one of the boundaries that I asked about before.

 

[Polymath257]

ah, so this is one of the boundaries that I asked about before.

What, precisely, do you see as the 'boundary' here?

 

[sandy whitelinger]

What, precisely, do you see as the 'boundary' here?

The limit ordinal?

 

[Polymath257]

The limit ordinal?

That's the terminology used for an ordinal without an immediate predecessor. There will still be a successor, though, so a limit ordinal isn't a largest ordinal.

 

[Zosimus]

What is truth? said jesting Pilate, and would not stay for an answer.

─ Francis Bacon, 'On Truth'​

Dear Creationists

My own view is that truth is conformity with reality. This, often called the 'correspondence' view, means that if you want to know whether a particular statement is true or not, you check how accurately its report corresponds to objective reality. Thus truth can in principle be objectively verified ─ a wholly admirable quality, surely you agree, for any claim of truth to have.

You must use this definition of truth at least part of the time, even if just to know that it's true it's daytime, you're in Kamloops, those are Bikkios on the supermarket shelf, and so on.

But then you add a wholly different concept of 'truth' ─ that the bible is inerrant and therefore all its factual statements are necessarily 'true'.

What truth test did you carry out on the bible to determine that it's inerrant?

Oh this looks like an interesting thread! It doesn't talk about evolution though. Still, I think I'll chime in.

I positively laughed out loud at the long string of nonsensical logical fallacies that you put forward with (I assume) a straight face! It's hard to know where to begin, but let's start with the most egregious error, shall we?

To paraphrase, you claimed that the truth can be objectively verified. If that is so and if that statement is true, please indicate how you objectively verified the statement "The truth can be objectively verified." That ought to be good for a start!

Second, your ridiculous 'correspondence' view is logically fallacious too. In short, your 'correspondence' test goes something like this:

If theory (T) is true, then it will make verifiable predictions (P).
We observe P.
Therefore T is true.

However, this is a prime example of the affirming the consequent logical fallacy. To illustrate why this is absurd, let's test the 'correspondence' of the claim: Richard Dawkins is the prime minister of England.

If that is true, then Richard Dawkins will be:
1) British
2) Controversial
3) Well known.

Richard Dawkins is British, controversial, and well known, so I have just 'proved' that he is the prime minister of England! Ha!

Seriously, friend -- you need help. As you can see in my avatar, there is a Bible for you. It's called the Critical Reasoning Bible. I suggest you stop worrying about the Christian one and try that one on for size!!

 

[blü 2]

If that is so and if that statement is true, please indicate how you objectively verified the statement "The truth can be objectively verified."

The statement is, 'truth' means correspondence with reality, and it's a definition, a proposition or opinion, about what 'truth' means. The 'true' statement relating to it is, Many people think truth is correspondence with reality.

This thread is about definitions of truth and asks which one creationists use, but to this point, none of them has addressed the question.

Second, your ridiculous 'correspondence' view is logically fallacious too. In short, your 'correspondence' test goes something like this:

If theory (T) is true, then it will make verifiable predictions (P).
We observe P.
Therefore T is true.

No.

IF we use my definition, THEN for statement S to be true, when we look at (external) reality we need to find a satisfactory correspondence between S and real state of affairs S', that which makes S true. (In metaphysics S' is accordingly called a 'truthmaker'.)

That's all. The only prediction involved in the statement S is true is, "If we look, we will find that S corresponds to S'."

For example, let S be the statement "You have already posted the post I'm replying to." Using my definition of 'truth', can you find S'? (If you can't, one of several available S' is the relative positions in this thread of #336 above, and #337 here.)

It's clear that very many statements in the bible have never had a corresponding S'. Since creationists assert that the bible contains only true statements, they're clearly using some other definition of, some other test for, 'truth'.

But as I said, none of them seems to know what that is.

As a matter of interest, how do you define truth? What test do you use?

 

[Zosimus]

The statement is, 'truth' means correspondence with reality, and it's a definition, a proposition or opinion, about what 'truth' means. The 'true' statement relating to it is, Many people think truth is correspondence with reality.

Oh, I see. You have your own definition of truth, and you ask us to embrace it with blind faith.

This thread is about definitions of truth and asks which one creationists use, but to this point, none of them has addressed the question.

John 14:6 -- I found that within 10 seconds on Google.

IF we use my definition, THEN for statement S to be true, when we look at (external) reality we need to find a satisfactory correspondence between S and real state of affairs S', that which makes S true. (In metaphysics S' is accordingly called a 'truthmaker'.)

All right. For the sake of argument, let's use your definition.

Electrons do not exist.
Dark matter does not exist.
Dark energy does not exist.

Because when we look at (external) reality, we do not find a satisfactory correspondence between these things and reality. Electrons cannot be seen, tasted, felt, smelled, or heard. Why should we believe in them?

That's all. The only prediction involved in the statement S is true is, "If we look, we will find that S corresponds to S'."

And how do you know that this statement is true? How did you test this statement to determine that it really did correspond to reality?

For example, let S be the statement "You have already posted the post I'm replying to." Using my definition of 'truth', can you find S'? (If you can't, one of several available S' is the relative positions in this thread of #336 above, and #337 here.)

Perhaps that's because your definition is self-contradicting?

It's clear that very many statements in the bible have never had a corresponding S'. Since creationists assert that the bible contains only true statements, they're clearly using some other definition of, some other test for, 'truth'.

To you, perhaps. Obviously Christians feel otherwise. At any rate, the claim of Biblical inerrancy applies to the autographs themselves, most of which were written in Greek. It is a simple matter to go online and find dozens of different translations of any given passage of the Bible. This also depends on the copies that have been found and identified to date, and the assumption that they are, to some extent, a good copy of an inerrant autograph.

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As for what I think truth is? Why, that's simple! Truth is any statement that is part of a coherent belief system. For example, if someone says "All elephants are blue. I have a pink elephant in my basement," then we have two statements that do not cohere. These statements are false.

And, although you don't want to admit it, you also subscribe to a coherent definition of truth. To you, truth is anything that coheres to previous statements that you have accepted. If, for example, I were to put together a room of people who all claimed to have seen an angel that came to visit them, you would disbelieve these statements because they do not cohere with what you have previously accepted.

Similarly, your statement that truth must be verifiable is incoherent. Thus, the statement cannot be true.

 

[Zosimus]

Either that, or look in a dictionary, or perhaps go online and check it out in Wikipedia or the Stanford Encyclopedia of Philosophy or whatever. There you'll find that S: Many people think that truth is correspondence with reality has S's aplenty.

Oh you mean, for example, The Coherence Theory of Truth?

So you think that "I swear to tell the Jesus, the whole Jesus and nothing but the Jesus" is a meaningful statement?

If it is part of a coherent belief system then it is not only meaningful but also true.

Electrons exist. The manner in which they exist is described in physics, and you can read up on them if you wish. They're detectable, they're well described, they have known qualities which are harnessed in even simple technologies like a torch, and so on. They have an S'.

I see. So electrons exist because you can detect their effects and, by extension, them. I'm sure Christians will argue that God can be detected through his effects. So what's the difference?

Dark matter and dark energy don't exist. The expressions denote no real thing. Rather they're names for problems (concepts). Neither term has an S'.

I'm sure that a number of physicists would disagree with you.

-------------------------
Well, since you didn't format your answer right, most of the bulk of your post has been lost. However, I can see it, so I'll just rebut it without quoting. You claim that correspondence logically follows from the correspondence theory of truth. Even if that is true, that only means that you have engaged in circular reasoning. Why should I accept your definition of truth?

You said that I did not specify the contradiction in your belief system. That's simple. You claim that the statement "Truth corresponds to reality" is true. Yet you have not demonstrated that this statement corresponds to reality. How, therefore, can you assert that the statement is true?

As for the definition of truth, I have already quoted from the Christian holy text. Jesus is truth, according to Christian theology. Everything he says and does is true.

As for the Tanakh, you don't seem to be able to read it very well. Let me quote for you (KJV):

Genesis 1:9-10

>>And God said, Let the waters under the heaven be gathered together unto one place, and let the dry land appear: and it was so.
>>And God called the dry land Earth; and the gathering together of the waters called he Seas: and God saw that it was good.

So now you claim that the Earth was a sphere. Yet the text itself defines Earth as the dry land. By definition, that's what it is.
So you want to hide behind your definition of truth while denying Tanakh's definition of Earth.

That's what we call "special pleading" in the logic business, a discipline you know nothing about.

At this point I need to quote you... let me see whether I can do so...

In the definition I've offered, the question of who's right can be resolved by looking.

Bull. You just said that electrons exist. The question of whether they exist cannot be resolved by looking. No one can look upon an electron. Electrons are a useful fiction that science dabbles in -- nothing more.

 

[blü 2]

Oh, I see. You have your own definition of truth, and you ask us to embrace it with blind faith.

Or you could just look in a dictionary, or check it on Wikipedia, or in the Stanford Encyclopedia of Philosophy, or whatever. S: Many people think truth is correspondence with reality is true, has many S'.

John 14:6 -- I found that within 10 seconds on Google.

That's not a definition. It leads to meaningless sentences like "I swear to tell the Jesus, the whole Jesus and nothing but the Jesus".

All right. For the sake of argument, let's use your definition.

Electrons do not exist.
Dark matter does not exist.
Dark energy does not exist.

Because when we look at (external) reality, we do not find a satisfactory correspondence between these things and reality. Electrons cannot be seen, tasted, felt, smelled, or heard. Why should we believe in them?

Electrons are real is a true statement. They're well described in physics, they're detectable, their properties are known and are used in many technologies, even the simple torch. >Here's< a lab image of an atom with one electron. S has its S'.

Dark matter is real and Dark energy is real are not true statements. Those are names of problems (concepts), not things with objective existence. Neither S has an S'.

And how do you know that this statement is true? How did you test this statement to determine that it really did correspond to reality?

They follow logically from the definition, which as I said is an opinion, so are not 'true'.

Perhaps that's because your definition is self-contradicting?

You've shown no self-contradiction.

To you, perhaps. Obviously Christians feel otherwise. At any rate, the claim of Biblical inerrancy applies to the autographs themselves, most of which were written in Greek.

The Tanakh is written in old Hebrew with some passages in old Aramaic. The NT is written in koine Greek with some Aramaic words.

It is a simple matter to go online and find dozens of different translations of any given passage of the Bible. This also depends on the copies that have been found and identified to date, and the assumption that they are, to some extent, a good copy of an inerrant autograph.

That won't rescue the bible from its bronze age science. It repeatedly says the earth is flat, and fixed, and the sun goes round it, that the sky (firmament) is a solid dome and the stars are affixed to it, and if they come loose they'll fall to earth, and so on. Much errancy just there, without looking at the other examples.

As for what I think truth is? Why, that's simple! Truth is any statement that is part of a coherent belief system. For example, if someone says "All elephants are blue. I have a pink elephant in my basement," then we have two statements that do not cohere. These statements are false.

Here's where we differ. I go down and check the elephants. You cover your eyes with a book. I report what's real. You say it's not true in your terms, keeping your eyes covered. As you use it. 'true' is a meaningless word.

you also subscribe to a coherent definition of truth. To you, truth is anything that coheres to previous statements that you have accepted.

Some I have to accept, not having my own LHC. But otherwise, I accept things I read and hear and see no immediate fault with, and revisit them if doubt arises.

If, for example, I were to put together a room of people who all claimed to have seen an angel that came to visit them, you would disbelieve these statements because they do not cohere with what you have previously accepted.

As you tacitly acknowledge by your choice of example, the claim is inherently incredible. Nonetheless, one could examine it forensically, first by separating all the witnesses and taking their statements separately, second by checking their phones and any CCTV for images and videos, third by searching the premises for artificial means of producing the claimed phenomenon, fourth by seeing who might have a motive to fake it, and so on. If all that stacked up (not least unambiguous images), then we'd have a scientific question, a question about reality, on our hands.

Similarly, your statement that truth must be verifiable is incoherent. Thus, the statement cannot be true.

There you go again! You've shown no incoherence.