foundations of reality from six logical tautologies

Philosophy Forums Philosophy
41

Escape velocity is only important for aggregate masses. Obviously individual water molecules in the thermosphere would not have the same vector (direction, and velocity).

Also, as the earth spins the suns radiation would force any gas back into the earths thermosphere (vector towards the earth)… If the molecules get too far they will definitely turn into plasma and will be held by the earths magnetic field (ions follow magnetic lines of force… and cannot escape).

There currently is gaseous atoms in the thermosphere as well as plasma ions in the ionosphere with high velocities!

That’s what.

42

Hahahahaha, whoa boy, I’ve made my point.

This from the guy that doesn’t know basic physics.

Of course there are some atoms in the thermosphere.

Escape velocity isn’t important for gasses indeed.

Hahahahaha. Goodbye for now.

43

“distinction between four different meanings of ‘is’ — the ‘is’ of existence, of identity, of predication, and of generic implication (inclusion),”
plato.stanford.edu/entries/existence/
* ‘Socrates is’, rendered in regimented language as ‘(∃x)(Socrates = x)’.
* ‘Cicero is Tully’, rendered as ‘Cicero = Tully’.
* ‘Socrates is wise’, rendered as ‘Wise(Socrates)’.
* ‘Man is an animal’, rendered as ‘(x)(Man(x) → Animal(x))’.

existence; (∃x)(A = x)… (not sure how to express this, obviously it is not just “nothing is” but rather “nothing is nothing”)
identity; A = A
predication; A(A)
implication; (x)(A(x) → A(x) or simply A → A

I know for certain that A = A and A → A are logical tautologies.

Lets use the words “exists as” ((∃x)(A = x)…), “equals” (A = A), “has” (A(A)), and “implies” (A → A), instead of “is” and see if it means what we wanted to express.

  1. “no thing” is “nonexistence”
    1a) “no thing” exists as “nonexistence”
    1b) “no thing” equals “nonexistence”
    1c) “no thing” implies “nonexistence”
    1d) “no thing” has “nonexistence”

It seems every one of these makes sense.

  1. “nonexistence” is “no thing”
    2a) “nonexistence” exists as “no thing”
    2b) “nonexistence” equals “no thing”
    2c) “nonexistence” implies “no thing”
    2d) “nonexistence” has “no thing”

Everyone of them seems to work except maybe 2a.

  1. “no thing” is “no thing”
    3a) “no thing” exists as “no thing”
    3b) “no thing” equals “no thing”
    3c) “no thing” implies “no thing”
    3d) “no thing” has “no thing”

At first difficult to comprehend. But each one has a unique and rich meaning.

  1. “nonexistence” is “nonexistent”
    4a) “nonexistence” exists as “nonexistent”
    4b) “nonexistence” equals “nonexistent”
    4c) “nonexistence” implies “nonexistent”
    4d) “nonexistence” has “nonexistent”

It seems 4b and 4c work but 4a and 4d don’t.

Ok, so here are the ones that do not cognitively work;

2a) “nonexistence” exists as “no thing”
4a) “nonexistence” exists as “nonexistent”
4d) “nonexistence” has “nonexistent”

44

If escape velocity is such an issue why don’t the atoms in the thermosphere and ionosphere escape the effect of the earth?

You didn’t even know that water would be a gas in the thermosphere and only block a particular radiation spectrum so don’t tell me I know nothing of basic physics.

45

“distinction between four different meanings of ‘is’ — the ‘is’ of existence, of identity, of predication, and of generic implication (inclusion),”
plato.stanford.edu/entries/existence/

* ‘Socrates is’, rendered in regimented language as ‘(∃x)(Socrates = x)’.
* ‘Cicero is Tully’, rendered as ‘Cicero = Tully’.
* ‘Socrates is wise’, rendered as ‘Wise(Socrates)’.
* ‘Man is an animal’, rendered as ‘(x)(Man(x) → Animal(x))’.

existence; (∃x)(A = x)… (not sure how to express this, obviously it is not just “nothing is” but rather “nothing is nothing”)
identity; A = A
predication; A(A)
implication; (x)(A(x) → A(x) or simply A → A

I know for certain that A = A and A → A are logical tautologies.

Lets use the words “exists as” ((∃x)(A = x)…), “equals” (A = A), “has” (A(A)), and “implies” (A → A), instead of “is” and see if it means what we wanted to express.

  1. “no thing” is “nonexistence”
    1a) “no thing” exists as “nonexistence”
    1b) “no thing” equals “nonexistence”
    1c) “no thing” has “nonexistence”
    1d) “no thing” implies “nonexistence”

It seems every one of these makes sense.

  1. “nonexistence” is “no thing”
    2a) “nonexistence” exists as “no thing”
    2b) “nonexistence” equals “no thing”
    2c) “nonexistence” has “no thing”
    2d) “nonexistence” implies “no thing”

Everyone of them seems to work except maybe 2a.

  1. “no thing” is “no thing”
    3a) “no thing” exists as “no thing”
    3b) “no thing” equals “no thing”
    3c) “no thing” has “no thing”
    3d) “no thing” implies “no thing”

At first difficult to comprehend. But each one has a unique meaning. 3c seems a little weird though.

  1. “nonexistence” is “nonexistent”
    4a) “nonexistence” exists as “nonexistent”
    4b) “nonexistence” equals “nonexistent”
    4c) “nonexistence” has “nonexistent”
    4d) “nonexistence” implies “nonexistent”

It seems 4b and 4d work but 4a and 4c don’t.

Ok, so here are the ones that do not seem to cognitively work;

2a) “nonexistence” exists as “no thing”
3c) “no thing” has “no thing”
4a) “nonexistence” exists as “nonexistent”
4c) “nonexistence” has “nonexistent”

Since some of the existence and predication uses of “is” in “nothing is nothing” have problems we can safely interpret “is” as identity and implication;

1b) “no thing” equals “nonexistence”
1d) “no thing” implies “nonexistence”
2b) “nonexistence” equals “no thing”
2d) “nonexistence” implies “no thing”
3b) “no thing” equals “no thing”
3d) “no thing” implies “no thing”
4b) “nonexistence” equals “nonexistent”
4d) “nonexistence” implies “nonexistent”

There is plenty meaning in here to infer the corollary; “nothing is nonexistence” from “nothing is nothing” either as identity or implication.

These cognitively work;

1a) “no thing” exists as “nonexistence”
1c) “no thing” has “nonexistence”
2c) “nonexistence” has “no thing”
3a) “no thing” exists as “no thing”

46

Ok, I have updated the first two logical tautologies to remove potential interpretation of “is” in “nothing is nothing” as predication or existence;

(T1) Nothing equals or implies nothing. - Nothing equals or implies nonexistence. (Mars Turner)
This is a law of identity and reflexivity of implication truth of the form (A = A)∨(A → A).
(T2) Nothing equals or implies nonexistence. - Something equals or implies existence. (Parmenides)
This is a definitional synonym truth as well as [T1] corollary.

Thank you for your help.

47

I am switching back the first logical tautology;

Talking to you guys about “is” in “nothing is nothing” has forced me to update my first logical tautology because “is” can be interpreted in four different ways; of existence, of identity, of predication, and of generic implication (inclusion). I am certain identity and implication represent logical tautologies. But still working on predication and existence…

plato.stanford.edu/entries/existence/

(T1) Nothing is nothing. - Nothing is nonexistence. (Mars Turner)
There are four senses of “is” meant here; of existence, of implication, of identity, and of predication;
b(A = x)[/b] “nothing exists as nothing”
(A → A) “nothing embodies nothing” Reflexivity of Implication
(A = A) “nothing equals nothing” Law of Identity
A(A) “nothing has the property of nothing”

48

Mysidd - regarding A → A:

This is not an identity, or a tautology of any kind. You have misunderstood the Stanford Encyclopedia entry here. The example in the Stanford is this:

‘Man is an animal’, rendered as ‘(x)(Man(x) → Animal(x))’.

“Man” and “animal” are different logical types, one being a greater degree of abstraction, or generalisation, than the other. In other words, “man” is a member of the class “animal”. But so is “penguin”. But “man” does not equal “penguin”.

Material implication is not a reflexive relation. Implications that state “if and only if” are reflexive. But those are, in the end, material equivalences. If the statement in question cannot be translated into A = A, then the implication is not reflexive.

A different problem occurs in A(A). This is a nonsense statement, or a nonsense statement form (take your pick). If it states that A (nothing) has the property of “nothing”, it also states that A has no properties. It is not a statement form at all. It can make no claim or assertion, except perhaps to say that the word “nothing” has no meaning, which is false.

Your overall problem here is that you are claiming that “nothing” is an object of some kind. But an empty set (which is what “nothing” or “zero” is defined as) has no properties - it states the absense of properties, because it states that there are no objects in the class.

49

Good morning. Had to update your perfect, all-knowing god geometric, I see.

Escape velocity is exactly why Mercury has almost no atmosphere:

The sun heats the gasses, increasing the average velocity of the gas particles past the escape velocity. As long as the gas particles aren’t ‘aimed’ at the surface of the planet and don’t bump into anything, they’ll escape into space.

Particles in the thermosphere and ionosphere do escape the gravitational effects of earth. That’s why there is almost no gas there. There are a very few amount of particles, mostly hydrogen and helium, I would imagine, and I’m sure they do escape into space on occassion. New particles can enter the thermosphere from the lower regions of the atmosphere and probably back from space as well.

As far as water gas vapor only blocking a certain spectrum of radiation…do you know what clouds are? I admittedly know less about the properties of ionized water vapor than the regular kind, but I would think you would have to spread the water vapor so thinly through the thermosphere to avoid a big cloud, and even then I don’t believe the only effect would be that it blocks just one spectrum of radiation. But as I pointed out, maintaining that much water vapor in the thermosphere is impossible.

50

There are several things about Mercury besides it’s lower gravitational density that causes it to lose it’s atomosphere;

It’s magnetic moment is 2,500 times weaker than Earth’s.
The solar wind pressure at Mercury is seven times that of at Earth.
Mercury has a slower rotation than Earth’s moon.

Clouds ARE NOT gaseous water. They are micron liquid water droplets which cannot exist in the thermosphere!

You would need to cite a source that says particles in the thermosphere and ionosphere escape the Earth’s effect. I have already corrected your physics several times now… and have no inclination to take your uninformed word on it. I have explained to you that any particle trying to escape the thermosphere will become an ion and therefore cannot escape the effect of Earth’s magnetic field!

51

I realize (A → A) is not identity.

Are you saying that if the statement in question cannot be translated as identity (A = A), then it cannot have reflexive implication (A → A)???

“The statement in terms of the material conditional holds only in logics that have the semantic equivalent of the deduction theorem.”
en.wikipedia.org/wiki/Logical_implication

Is that what you are saying?

Scroll down on that link and you will see (A → A) called a tautology.

Here is one way (A → A) reflexivity of implication is proven as a tautology;

  • To be shown that A → A.
  • One possible proof of this (which, though valid, happens to contain more steps than are necessary) may be arranged as follows:

Example of a Proof

  1. A
    premise
  2. A ∨ A
    From (1) by disjunction introduction
  3. (A ∨ A) ∧ A
    From (1) and (2) by conjunction introduction
  4. A
    From (3) by conjunction elimination
  5. A ├ A
    Summary of (1) through (4)
  6. ├ A → A
    From (5) by conditional proof

Interpret A ├ A as “Assuming A, infer A”. Read ├ A → A as “Assuming nothing, infer that A implies A,” or “It is a tautology that A implies A,” or “It is always true that A implies A.”

Besides this proof there is also another using two axioms to prove (A → A) reflexivity of implication in this link;

en.wikipedia.org/wiki/Propositional_calculus

There seems to be two ways the “A” is viewed in A(A);

A(x) set function
x(A) set element

Maybe I am seeking to say a idempotent unary operation;

A(A) = A

f(f(x)) = f(x)

en.wikipedia.org/wiki/Idempotency

“Since the identity element of a monoid is unique, one can alternately define the identity function on A to be this identity element. Such a definition generalizes to the concept of an identity morphism in category theory, where the endomorphisms of A need not be functions.”

en.wikipedia.org/wiki/Identity_function

f : A → A is an endomorphism of A

en.wikipedia.org/wiki/Identity_morphism

52

Here is our updated first logical tautology;

(T1) Nothing is nothing. - Nothing is nonexistence. (Mars Turner)
Four senses of “is” are meant here; of existence, of predication, of implication, and of identity;
b(A = x)[/b] “nothing exists as nothing”
id_{A}: A → A “nothing has the property of nothing” Identity Morphism
A → A “nothing involves nothing” Reflexivity of Implication
A = A “nothing equals nothing” Law of Identity

53

Mysidd - all I can say is “What?”

That first Wiki citation basically is what I am talking about, yes.

I am confused about your notation, only because I don’t use the very common symbols that you are using. Is the little box “or”? I am guessing because after the first instance of it you say “disjunction introduction”. But then you use the same symbol in (3) and call it a conjunction introduction.

Sorry, but I’m old, and still use the symbols I learned as a lad.

54

Oh, I see. it’s just a line break, right?

Hmmm. Maybe not.

55

Maybe your computer is unable to read logic symbols “or” and “and”.

en.wikipedia.org/wiki/Propositio … of_a_proof

I will put it in English for you;

  • To be shown that A → A.

Example of a Proof

  1. A
    premise
  2. A or A
    From (1) by disjunction introduction
  3. (A or A) and A
    From (1) and (2) by conjunction introduction
  4. A
    From (3) by conjunction elimination
  5. A ├ A
    Summary of (1) through (4)
  6. ├ A → A
    From (5) by conditional proof

Interpret A ├ A as “Assuming A, infer A”. Read ├ A → A as “Assuming nothing, infer that A implies A,” or “It is a tautology that A implies A,” or “It is always true that A implies A.”

56

the link is interesting, may i put this all in laymans terms to make sense of it…

T1) Nothing is nothing. - Nothing is nonexistence. (Mars Turner)
This is a predicative truth from the law of identity.

means; there is no-thing that is a nothing. the problem is in first defining it all as things or non-things, infinity is not a ‘thing’ because it has no limits to define it as such. it exists though or else we have to define the entire space [not ordinary space] of reality in some other way. infinity though is the only way we can define that entire space without giving it limits, hence infinity is a thing that is not a ‘thing’ [defined by its limits].

may i go on to this;
D1) One thing has the essence of existence (Spinoza) [monism]
Proof–The true definition of a thing neither involves nor expresses anything beyond the nature of the thing defined.
&
D3) One thing exists everywhere (Mars) [omnipresent]

we cannot arrive at a true definition of a thing. any definitive and absolute thing cannot be observed or defined. just as everything belongs to something else, so to do the meanings, eventually we arrive at a place of indescription which is married to infinity by default; i.e. they are both unlimited.

hence the ‘one thing’ that binds all things is nothing [as defined above]. 1 = 0.

omnipresence? infinity is its own dimension and cannot include ordinary [any given other] dimensions, in short; infinity has no x,y,z, coodinates to qualify its ‘presence’ amongst things.

I3) (Max Planck & Werner Heisenberg) [infinite, omnipresent, perfect]
Zero-Point Energy; we have a contribution of 1/2 hbar omega from every single point in space resulting in a substantial infinity as well as making energy spatially infinite. Because it is infinite it is unchanging in it’s nature, while embodying the existence of all things, it therefore is perfect.

what is a substantial infinity? what is spatially infinite? how can it be possible to have an infinity that in one instance is unchanging, then in the next that it embodies everything that we would define as changing!?

(I5)(Mars Turner) [all-power-full]
Power Integral; power involves the transformation of energy, therefore the infinite, omnipresent, and eternal energy is all-power-full.

is energy infinite ~ if so then being stateless we may only define it as essentially zero. any given value would be to define it and hence give it limits, perhaps we can say that energy is infinite until it is given a value or a state, then it becomes quantum. however once given state it will interact with the relative other states creating a third party causal field - if you will. in other words it is not all-powerful as it is limited by second generation interactions which don’t directly belong to it.

57

updating my logical tautologies;

(T1) Nothing is nothing. (Victor Hugo)
(A = A)∧(A → A)∧(idA: A → A)∧(∃Ax)(A = x) (Mars Turner)
Four senses of “is” are meant here; of identity, of implication, of predication, and of existence;
A = A “nothing equals nothing” Law of Identity
A → A “nothing involves nothing” Reflexivity of Implication
idA: A → A “nothing has the property of nothing” Identity Morphism
b(A = x)[/b] “nothing exists as nothing” Reflexivity of Existence

(T2) Nothing is made of nothing. - Everything is made of something. (Parmenides)
(A → A)∧(idA: A → A)

(T3) Nothing is the cause of nothing. - Something is the cause of all things. (Mars Turner)
(A → A)∧(∃Ax)(A = x)

(T4) Nothing is nonexistence. - Something is existence. (Parmenides)
(A = A)∧(∃Ax)(A = x)

(T5) Nowhere does nothing exist. - Something exists everywhere. (Mars Turner)
Predicative truth of (A = A)∧(∃Ax)(A = x)

(T6) At no time has nothing existed. - Something has always existed. (Mars Turner)
Predicative truth of (A = A)∧(∃Ax)(A = x)

58

Yeah, mysidd. that clears it all up for me.

59

Hi quetzal, your picture reminds me of Stephane Hemon.

Even if that is true, it does not negate the fact that a true definition would not involve anything beyond the nature of the thing defined.

If substance is spacetime substantial infinity would be an infinite spatiotemporal manifold. Spatially infinite means everywhere present. Well, everything is created in polarities of the particle and anti-particle pair… so the sum of the energy in form will aways equal zero and yet the formless energy is infinite.

Except that every state (energy form) is continually being created and refreshed from the infinite… as energy is flowing from every energy form in all direction forever (or until that state is destroyed creating a new one). So, if you want to think of energy forms as a state, think of them as a dynamic state not a static state.

So where is all this energy coming from such that every formed energy emits energy in all directions forever (such as charge, and gravity emitting a field at the speed of light in all directions)… it obviously comes from the infinite formless energy. So, this energy is inherently all powerful… as all transformations of energy (including dynamic states) are integral to it.

…

60

mysiddhi, hi ~ interesting stuff here.

true, yet i would think that the very nature of a thing cannot be fully described? one thing is attached to another so you end up having to define everything in order to define any one thing to the absolute. unless we are talking about holistic objects, but they are vague in description and entity.

i would think that ‘presence’ is localised, like i said infinity is not omnipresent because there is nothing in its entity to be present, and it cannot be localised [exist within any x,y,z, coodinates].

i agree, although i would question the meaning of; ‘formless’. perhaps emptiness is better?

there is a relationship between the infinite and the finite, i would think that as soon as energy becomes more than zero, then the laws of infinity no longer apply. its funny how they cannot be defined together yet work together in real terms. energy forms though are localised to the universe and don’t stretch to infinity.

true yes.

whilst i agree that energy is conserved by having an infinite base [not sure if science agrees with that though!], that doesn’t make it ‘all-powerfull’ in the context of a unified all controlling factor, as what it makes kinda goes its own way ~ creates its own causal links with its environment.

i cannot imagine a scenario where we have a beginning nor end, so within that can’t we say there is no primary factors e.g. like a prime mover a creator or an ‘all-powerful’ oneness.