How do you determine something exists?

@ughaibu,

Ughaibu:
Okay, but my question was an enquiry as to what this means. Do you hold that the number of entities in the world that are false is equal to the number of those which are true? If so, I reject this. The number of truths is countable, the number of non-truths is uncountable, so, under realism about falsity, almost everything is false, the probability of anything being other than false is zero.

Ughaibu: "The number of truths is countable"

How do you know this?
There is no system of logic that contains all truths.

Ughaibu: "the probability of anything being other than false is zero."

Is silly talk also allowed?

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@Owen phil,

Owen phil wrote:

How do you know this?

It's a theorem in ZF.

Owen phil wrote:

There is no system of logic that contains all truths.

Other than, possibly, IF, there is no system of logic (that I know of) which contains any truth. Logics aim to preserve truth, that's all.

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@ughaibu,

ughaibu wrote:

Owen phil wrote:
How do you know this?
It's a theorem in ZF.
Owen phil wrote:
There is no system of logic that contains all truths.
Other than, possibly, IF, there is no system of logic (that I know of) which contains any truth. Logics aim to preserve truth, that's all.

Nonsense and more nonsense.

Can you demonstrate, or refer to a demonstration that ZF set theory asserts that all truths are countable.

Godel's incompleteness theorems deny it!
There is no system of mathematics, strong enough to include elementary arithmetic, that includes all mathematical truths, let alone 'all' truths.

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@Owen phil,

Owen phil wrote:

Can you demonstrate, or refer to a demonstration that ZF set theory asserts that all truths are countable.

Unless you do not differentiate truths from facts, it's obvious, the number of expressable propositions is countable. If a proposition is unexpressable, there is no truth, regardless of facts.

Owen phil wrote:

Godel's incompleteness theorems deny it!

No it doesn't. If we cant express the truth which is unprovable, then there is no such truth.

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This is a bit like asking if transcendence cannot be transcendent...Transcendence to be transcendent aims nothing...Something to not exist, it not in relation to what does...what does, accounts numerically in its nature to be always the opposite to what does not...if a cat, therefore also, a not bird, a not dog, a not sheep...but a cat ! We are each one equal in size with the fullness of the Universe, precisely why we are able to see it and interact with it...what is not is in relation to what is... a shadow ! beyond that nothing matters...

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@Fil Albuquerque,

Fil Albuquerque wrote:

This is a bit like asking if transcendence cannot be transcendent...Transcendence to be transcendent aims nothing...Something to not exist, it not in relation to what does...what does, accounts numerically in its nature to be always the opposite to what does not...if a cat, therefore also, a not bird, a not dog, a not sheep...but a cat ! We are each one equal in size with the hole of the Universe, precisely why we are able to see it and interact with it...what is not is in relation to what is... a shadow ! beyond that nothing matters...

Quite, I think. But the realists about abstract objects maintain that there exist causally inert objects with no location in time or space.

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but then you see, I believe we are all necessary...awkwardly we are in all time and all space, even if to manifest in one point !
I am all the not I´s there is in order to my identity to be complete...

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...its like saying that for a given number to know its rightful place must know all other numbers place to not confuse its identity with any other...they match in size...I mean ONE and the TOTAL !

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@ughaibu,

ughaibu wrote:

Owen phil wrote:
Can you demonstrate, or refer to a demonstration that ZF set theory asserts that all truths are countable.
Unless you do not differentiate truths from facts, it's obvious, the number of expressable propositions is countable. If a proposition is unexpressable, there is no truth, regardless of facts.
Owen phil wrote:
Godel's incompleteness theorems deny it!
No it doesn't. If we cant express the truth which is unprovable, then there is no such truth.

Facts are situations not propositions.
Factual propositions, propositions about states of affairs, are true or false.
'Truths' include factual propositions and tautologous propositions.

"The number of expressible propositions, is countable." need justification.

Owen phil wrote:

Godel's incompleteness theorems deny it!

"No it doesn't. If we cant express the truth which is unprovable, then there is no such truth."

Wrong again.
If there is an undecidable proposition in system A, then we can extend system A, so that the truth of the undecidable- in A, is showable.
But, of course, there are then undecidable proposition within this new system ..etc, etc.
All such systems are incomplete, which means that there are some 'truths' that are not included in all such systems.

That is to say, there is no system such as ZF which contain all truths.

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@Owen phil,

Owen phil wrote:

"The number of expressible propositions, is countable." need justification.

Fine, if you reject this, then explicate what it is about set theory that you are objecting to. And elucidate your theory of abstract object realism consistent with this rejection.

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@Mindlapse,

The fact that you use algebra freely shows you are using the Cartesian system. Algebra and the Cartesian axes was what provided the foundation of science which in those days was called Natural Philosophy. Your extensive use of Boolean and Symbolic logic is an outgrowth of the Cartesian System. Otherwise you would still be mired in Geomtetry.

This is where your intepretation is wrong. He meant consciouness. Since a rock is inanimate it is an absurdity. However, Dwayne Johnson was also the Rock. Since this Rock thinks, he is conscious and a man. In those simpler days they used simple terms which today would be better to interpret the words correctly.

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@jeeprs,

jeeprs wrote:

Quote:
The same is true of words. I dont think you've presented a difficulty, in either case.

It would seem to me that all of the major scientific advances since Newton's have relied on insights that are only available by way of mathematics. Obviously relativity and QM are cases in point. Please explain to me how these could have been obtained without mathematics, or, alternatively, any scientific breakthroughs of similar magnitude which were articulated in ordinary language (your choice as to which one, of course).

Darwin.

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@Huxley,

Jeeprs has a point in distinguishing mathematics as a prominent tool for more recent scientific advances, because unlike language per se it is a metalanguage which is relatively culture free. Indeed it has come to the point in physics where "discoveries" are directed by the quest for mathematical symmetry and elegance. It could even be argued that Darwin was engaged in essentially "mathematical thinking" which he ostensibly hated, and advanced the development of statistical analysis.
http://www.sciencenews.org/view/generic/id/40740/title/Math_Trek__Darwin_The_reluctant_mathematician_

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Did I say that "Math really isn't that great of a tool in science"?

I gave a well known example where a more advanced mathematical model wasn't part of a major scientific advance. Therefore, not all major scientific advances need a more advanced mathematical model.

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@fresco,

Quote:

Jeeprs has a point in distinguishing mathematics as a prominent tool for more recent scientific advances

Thanks. And besides, I believe that in the fullness of time, history will judge that Darwin was not to biology what Einstein was to physics. (Although I do concede that yours is a very strong counter-argument to mine, no question.)

But that is a topic for another thread.

(A footnote: I rather like the scholastic notion that what is real is the intelligible form of things, and what exists is only the manifestation of those forms in material substance. In other words, what is real and what exists are separate but overlapping domains. Of course, this re-introduces universals , which are long abandoned and strictly taboo. However I believe it shows up in physics (as mathematical formalism) and biology (for example in protein folding). This is a work in progress.)

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@Owen phil,

Owen phil wrote:

Mindlapse:
"The same is applied to numbers. '62' does not exist, whereas 62 apples do because '62' is only a symbol we use to reference a group of multiple existing objects."

If we define 'x exists' as: (some F)(x has the property F) then....

That which does not exist, does not have properies.

You have affirmed that (62 > 30). That is, you have granted that 62 has the property of being 'greater than 30'.

If (62 > 30) then there is a property that (62) has.
That is: (some F)(62 has the property F), is true.
Therefore, 62 exists.

Why do you believe that it makes sense to say:
(62) does not exist and (62 apples) does exist.
It is a contradiction, imo.

How can we apply the number 62, if it does not exist.
If 62 does not exist then it is false to say: 62 apples exist.
eg. do red apples exist if there are no red things?

Empirical truths, factual propositions, establish the existence of empirical objects.
Logical truths, tautological propositions, establish the existence of abstract (non-empirical) objects.
Because (62 > 30) is a tautology, we can assert that: 62 exists and 30 exists.

So you would say that there are different kinds of truths -- at a minimum, Empirical and logical truths. Are there more than that?

Further, do you agree with kennethamy in that the way to determine the existence of something is dependent upon what it is you want to determine the existence of? (As he said, to see if the square root of 9 exists, you take the square root (a logical object) or to see if an apple exists, you use your senses (an empirical object))

Quote:

(root(-1))^2=-1) implies that root(-1) exists, even if there is no application to the empirical world.

Sure it does: Electrical engineering. QM. Differential equations that model the movement of a weight on a spring.

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@jeeprs,

(Your footnote mentions domains. In contrast, it is interesting that the biologist-philosopher Maturana speaks of the "domain of the organism" and "the observer domain" which need not overlap. The "organism" is merely adapting to "perturbations" and has no requirement to distinguish their origin as internal or external. The "observer" is always involved with linguistic descriptions...a social activity (even of self with self) transcendent of the domain of the adaptations of the organism. "Reality" is a concept in the second domain rather than the first)

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@fresco,

Yes, very interesting indeed. I haven't familiarized myself with Maturana although I have noticed him previously in connection with Francisco Varela, who I am trying to find time to study, and have downloaded that article you referred to yesterday.

Incidentally, thank you for that article on Darwin and statistics, it is directly germane to the point I was trying to make, and I note the closing statement, to which I would very much like to draw Ughiabu's attention

Quote:

Darwin himself came around eventually in his attitude toward mathematics. While he wrote in his autobiography of his youthful distaste for math, he also wrote that he wished he had learned the basic principles of math, “for men thus endowed seem to have an extra sense.”

Indeed they do. I find it both ironic and amusing that the mathematicians often seem those most at pains to downplay the uncanny abilities it has afforded us. It seems the commitment to empiricism must always trump anything felt to be too rationalist in origin.

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@jeeprs,

jeeprs wrote:

I note the closing statement, to which I would very much like to draw Ughiabu's attention

The remark about Darwin doesn't change the fact that evolution isn't a mathematical theory, neither was the discovery and production of antibiotics, or filament lighting, probably the two most revolutionary scientific developments. And the question of maths in physics is something we discussed just a few weeks ago, you are referred to Fields nominalisation program.
In any case, I still dont see how you infer mathematical realism.

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@ughaibu,

simply in that it presents us with a purely logical mode of apprehension which is not at all given in so-called empirical experience. I know many have proposed empiricist philosophies of mathematics but I don't understand how they can be credible. For one reason or another math is innate to the human intelligence, and mathematical structure is also innate to the universe itself.

1 Reply

How do you determine something exists?

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