The Contradiction of the Three Laws of Logic

[Eodnhoj7]

You can't trust intuition. Never. Intuition is a GUI (Graphical User Interface) for the brain to work with, but as with other software, if you really want to understand stuff, you go behind the GUI and read the source code itself.

I don't think you can go behind intuition, let alone read the "source code". All we have is our intuition and rational methods of inquiry. But dismissing intuition is really insane. Unfortunately, it has become the dogma of our time: don't trust intuition. I wonder how humans managed to survive at all, apparently for more than 400,000 years, in a world without formal methods.
EB

Agreed, both are needed.

[Logik]

I don't think you can go behind intuition, let alone read the "source code". All we have is our intuition and rational methods of inquiry. But dismissing intuition is really insane. Unfortunately, it has become the dogma of our time: don't trust intuition. I wonder how humans managed to survive at all, apparently for more than 400,000 years, in a world without formal methods.
EB

Such irony.

https://en.wikipedia.org/wiki/Construct ... thematics)

Much constructive mathematics uses intuitionistic logic, which is essentially classical logic without the law of the excluded middle.

https://en.wikipedia.org/wiki/Ultrafinitism

In the philosophy of mathematics, ultrafinitism (also known as ultraintuitionism

That you should trust your intuition is a given. That you can become even more in touch with your intuition and develop better judgment through practice and experience is not.
Observe the pattern that as you develop a better intuition through practice - you abandon more and more axioms.

Would I have trusted my intuition in my early 20s? Yeah. And it was wrong a lot.

In my 30s I am an ultrafinitist. I rely on intuition more than I rely on anything else. And it's far less wrong now that I have developed the mental self-discipline and put the systems in place to check myself.

[philosopher]

You can't trust intuition. Never. Intuition is a GUI (Graphical User Interface) for the brain to work with, but as with other software, if you really want to understand stuff, you go behind the GUI and read the source code itself.

I don't think you can go behind intuition, let alone read the "source code". All we have is our intuition and rational methods of inquiry. But dismissing intuition is really insane. Unfortunately, it has become the dogma of our time: don't trust intuition. I wonder how humans managed to survive at all, apparently for more than 400,000 years, in a world without formal methods.
EB

Intuition is good for survival, but you cannot understand the workings of the universe for instance, using intuition. You cannot grasp advanced science with intuition. You have to have abstract thought of a very high quality of course using purely logical reasoning - complex logic.

Intuition is only simple logic, it cannot be used for advanced mathematics, unless you are a math genius.

[Eodnhoj7]

I don't think you can go behind intuition, let alone read the "source code". All we have is our intuition and rational methods of inquiry. But dismissing intuition is really insane. Unfortunately, it has become the dogma of our time: don't trust intuition. I wonder how humans managed to survive at all, apparently for more than 400,000 years, in a world without formal methods.
EB

Such irony.

https://en.wikipedia.org/wiki/Construct ... thematics)

Much constructive mathematics uses intuitionistic logic, which is essentially classical logic without the law of the excluded middle.

https://en.wikipedia.org/wiki/Ultrafinitism

In the philosophy of mathematics, ultrafinitism (also known as ultraintuitionism

That you should trust your intuition is a given. That you can become even more in touch with your intuition and develop better judgment through practice and experience is not.
Observe the pattern that as you develop a better intuition through practice - you abandon more and more axioms.

Would I have trusted my intuition in my early 20s? Yeah. And it was wrong a lot.

In my 30s I am an ultrafinitist. I rely on intuition more than I rely on anything else. And it's far less wrong now that I have developed the mental self-discipline and put the systems in place to check myself.

Good for you....you pull stuff apart again and again...that is what point space does. It continually reduces itself to further points. You can call this "atomism" as well.

It appears you are just unifying everything under one axiom in which all axioms are an extension of it. Already covered this.

[commonsense]

There is a common criticism to the 'Law of Excluded Middle.' I'm not able to find a source right now, but it goes something along the line of "Either penguins can fly, or they can't - but what if only some penguins could fly?" And the reason why that doesn't hold water as an argument against the Law of Excluded Middle, is because the law only applies to bivalent logic - when it's applied to a true dichotomy, like "Nothing can both be and not be." It does not apply to propositions that literally do give way to a middle answer.

No, the Excluded Middle stands.

“Either some penguins can fly or some cannot,”

Which yields:

P^ = some penguins that can fly

P* = some other penguins that cannot

So, in a universe where only some penguins can fly

and no penguins can fly and not fly:

P^ /= P*

P^ & P*

None of the above contradicts the Excluded Middle.

[Logik]

There is a common criticism to the 'Law of Excluded Middle.' I'm not able to find a source right now, but it goes something along the line of "Either penguins can fly, or they can't - but what if only some penguins could fly?" And the reason why that doesn't hold water as an argument against the Law of Excluded Middle, is because the law only applies to bivalent logic - when it's applied to a true dichotomy, like "Nothing can both be and not be." It does not apply to propositions that literally do give way to a middle answer.

No, the Excluded Middle stands.

“Either some penguins can fly or some cannot,”

P^ = some penguins that can fly

P* = some other penguins that cannot

So, in a universe where only some penguins can fly

and no penguins can fly and not fly:

P^ /= P*

P^ & P*

Equivocation. Violates identity and obscures modality.
If your claim is to be believed then the negation of the pronoun "some" is still "some". Then SOME = ¬SOME

This assigns equal truth-value to all three of these propositions:
1 flying and 99 non-flying penguins.
50 flying and 50 non-flying penguins.
99 flying and 1 non-flying penguin.

Basically - you have a standard distribution. If you have maximum entropy you have zero knowledge: https://en.wikipedia.org/wiki/Principle ... um_entropy

TL;DR: Some penguins can fly and some cannot translates to "for any given penguin there is 50% chance that it can fly and 50% chance that it can't"

[commonsense]

There is a common criticism to the 'Law of Excluded Middle.' I'm not able to find a source right now, but it goes something along the line of "Either penguins can fly, or they can't - but what if only some penguins could fly?" And the reason why that doesn't hold water as an argument against the Law of Excluded Middle, is because the law only applies to bivalent logic - when it's applied to a true dichotomy, like "Nothing can both be and not be." It does not apply to propositions that literally do give way to a middle answer.

No, the Excluded Middle stands.

“Either some penguins can fly or some cannot,”

P^ = some penguins that can fly

P* = some other penguins that cannot

So, in a universe where only some penguins can fly

and no penguins can fly and not fly:

P^ /= P*

P^ & P*

Equivocation. Violates identity and obscures modality.
If your claim is to be believed then the negation of the pronoun "some" is still "some". Then SOME = ¬SOME

This assigns equal truth-value to all three of these propositions:
1 flying and 99 non-flying penguins.
50 flying and 50 non-flying penguins.
99 flying and 1 non-flying penguin.

Basically - you have a standard distribution. If you have maximum entropy you have zero knowledge: https://en.wikipedia.org/wiki/Principle ... um_entropy

TL;DR: Some penguins can fly and some cannot translates to "for any given penguin there is 50% chance that it can fly and 50% chance that it can't"

Touche

[Eodnhoj7]

There is a common criticism to the 'Law of Excluded Middle.' I'm not able to find a source right now, but it goes something along the line of "Either penguins can fly, or they can't - but what if only some penguins could fly?" And the reason why that doesn't hold water as an argument against the Law of Excluded Middle, is because the law only applies to bivalent logic - when it's applied to a true dichotomy, like "Nothing can both be and not be." It does not apply to propositions that literally do give way to a middle answer.

No, the Excluded Middle stands.

“Either some penguins can fly or some cannot,”

P^ = some penguins that can fly

P* = some other penguins that cannot

So, in a universe where only some penguins can fly

and no penguins can fly and not fly:

P^ /= P*

P^ & P*

Equivocation. Violates identity and obscures modality.
If your claim is to be believed then the negation of the pronoun "some" is still "some". Then SOME = ¬SOME

This assigns equal truth-value to all three of these propositions:
1 flying and 99 non-flying penguins.
50 flying and 50 non-flying penguins.
99 flying and 1 non-flying penguin.

Basically - you have a standard distribution. If you have maximum entropy you have zero knowledge: https://en.wikipedia.org/wiki/Principle ... um_entropy

TL;DR: Some penguins can fly and some cannot translates to "for any given penguin there is 50% chance that it can fly and 50% chance that it can't"

False; identity is grounded in both equivication and non-equivocation where "identity" itself is grounded in "relations" in which one axiom exists as fundamentally a ratio.

A exists as B and C; hence b and c are a ratio.

For example "horse" exists as the ratio of the axioms "mammal", "herbivore" and "x" (with "x" observing other definitions).

Horse = mammal, herbivore, "x"

observes equivocation where the horse is the connection of axioms as a static unchanging role.
It also observe equivocation where the horse is a boundary of change where it progresses from one axiom to another.


Equivocation as undefined takes on a dynamic role in "P=P"

Equivocation as defined takes on a static role in =P=.

Equivocation, as well as the variable, in which both exist through eachother observe function as form (or "proof" as "function" where the "proof" effectively is a "form"): "P=".


The axiom of "excluded middle" observes divergent properties.

The axiom "inherent middle" (as an oppositve of "excluded middle" where the "excluded" middle either exists or does not exist" observes convergent properties.

"Excluded Middle" and "Inherent Middle" as both divergence and convergence observes all axioms as synthetic in nature.

[Logik]

No, the Excluded Middle stands.

“Either some penguins can fly or some cannot,”

P^ = some penguins that can fly

P* = some other penguins that cannot

So, in a universe where only some penguins can fly

and no penguins can fly and not fly:

P^ /= P*

P^ & P*

Equivocation. Violates identity and obscures modality.
If your claim is to be believed then the negation of the pronoun "some" is still "some". Then SOME = ¬SOME

This assigns equal truth-value to all three of these propositions:
1 flying and 99 non-flying penguins.
50 flying and 50 non-flying penguins.
99 flying and 1 non-flying penguin.

Basically - you have a standard distribution. If you have maximum entropy you have zero knowledge: https://en.wikipedia.org/wiki/Principle ... um_entropy

TL;DR: Some penguins can fly and some cannot translates to "for any given penguin there is 50% chance that it can fly and 50% chance that it can't"

False; identity is grounded in both equivication and non-equivocation where "identity" itself is grounded in "relations" in which one axiom exists as fundamentally a ratio.

A exists as B and C; hence b and c are a ratio.

For example "horse" exists as the ratio of the axioms "mammal", "herbivore" and "x" (with "x" observing other definitions).

Horse = mammal, herbivore, "x"

observes equivocation where the horse is the connection of axioms as a static unchanging role.
It also observe equivocation where the horse is a boundary of change where it progresses from one axiom to another.


Equivocation as undefined takes on a dynamic role in "P=P"

Equivocation as defined takes on a static role in =P=.

Equivocation, as well as the variable, in which both exist through eachother observe function as form (or "proof" as "function" where the "proof" effectively is a "form"): "P=".


The axiom of "excluded middle" observes divergent properties.

The axiom "inherent middle" (as an oppositve of "excluded middle" where the "excluded" middle either exists or does not exist" observes convergent properties.

"Excluded Middle" and "Inherent Middle" as both divergence and convergence observes all axioms as synthetic in nature.

The sentence "some penguins fly and some do not" contains zero bits of information. It's meaningless.

Because you can't use to make any inferences or deductions about penguins from it.

[commonsense]

The sentence "some penguins fly and some do not" contains zero bits of information. It's meaningless.

Because you can't use to make any inferences or deductions about penguins from it.

From the above you have this piece of information, although I leave it to you to deem it equivocation or useful:

It would be wrong to say that all penguins can fly and it would be wrong to say that all penguins cannot fly.

[Logik]

It would be wrong to say that all penguins can fly and it would be wrong to say that all penguins cannot fly.

Indeed. It would be wrong to say it.

In a universe where 49 penguins can fly and 51 cannot fly it is equally wrong to say "Some penguins can fly and some cannot".

Because you are using the word "some" to mean two different things.

"Some penguins can fly".
some means 49

"some penguing cannot fly"
some means 51

49 != 51 => Contradiction.

So the ONLY time it is correct to say "Some penguins can fly and some penguins cannot" is when 'some' represent equal quantities for both the flying and non-flying cohorts.

Which is the same as saying "50% of penguins can fly and 50% cannot"

So you have given me exactly as much information as any coin can give me.

[commonsense]

It would be wrong to say that all penguins can fly and it would be wrong to say that all penguins cannot fly.

Indeed. It would be wrong to say it.

In a universe where 49 penguins can fly and 51 cannot fly it is equally wrong to say "Some penguins can fly and some cannot".

Because you are using the word "some" to mean two different things.

"Some penguins can fly".
some means 49

"some penguing cannot fly"
some means 51

49 != 51 => Contradiction.

So the ONLY time it is correct to say "Some penguins can fly and some penguins cannot" is when 'some' represent equal quantities for both the flying and non-flying cohorts.

Which is the same as saying "50% of penguins can fly and 50% cannot"

So you have given me exactly as much information as any coin can give me.

For me, “some” means > or = 1.

As for the amount of information, you are correct. Yet I still wonder if knowing something can be different than knowing its obverse or is it only equivocation.

[Eodnhoj7]

Equivocation. Violates identity and obscures modality.
If your claim is to be believed then the negation of the pronoun "some" is still "some". Then SOME = ¬SOME

This assigns equal truth-value to all three of these propositions:
1 flying and 99 non-flying penguins.
50 flying and 50 non-flying penguins.
99 flying and 1 non-flying penguin.

Basically - you have a standard distribution. If you have maximum entropy you have zero knowledge: https://en.wikipedia.org/wiki/Principle ... um_entropy

TL;DR: Some penguins can fly and some cannot translates to "for any given penguin there is 50% chance that it can fly and 50% chance that it can't"

False; identity is grounded in both equivication and non-equivocation where "identity" itself is grounded in "relations" in which one axiom exists as fundamentally a ratio.

A exists as B and C; hence b and c are a ratio.

For example "horse" exists as the ratio of the axioms "mammal", "herbivore" and "x" (with "x" observing other definitions).

Horse = mammal, herbivore, "x"

observes equivocation where the horse is the connection of axioms as a static unchanging role.
It also observe equivocation where the horse is a boundary of change where it progresses from one axiom to another.


Equivocation as undefined takes on a dynamic role in "P=P"

Equivocation as defined takes on a static role in =P=.

Equivocation, as well as the variable, in which both exist through eachother observe function as form (or "proof" as "function" where the "proof" effectively is a "form"): "P=".


The axiom of "excluded middle" observes divergent properties.

The axiom "inherent middle" (as an oppositve of "excluded middle" where the "excluded" middle either exists or does not exist" observes convergent properties.

"Excluded Middle" and "Inherent Middle" as both divergence and convergence observes all axioms as synthetic in nature.

The sentence "some penguins fly and some do not" contains zero bits of information. It's meaningless.

Because you can't use to make any inferences or deductions about penguins from it.

Actually the penguin is defined relative to the nature of flying, in these respects it maintains a neutral nature. An inference is made. From this it may be deduced the penguin in neutral in regards to flying.

"No penguin eats mammals" is a negative inference. From this it may be deduced what the penguin is not.

Inference and deduction result in positive, negative and neutral terms.

[Logik]

Actually the penguin is defined relative to the nature of flying, in these respects it maintains a neutral nature. An inference is made. From this it may be deduced the penguin in neutral in regards to flying.

"No penguin eats mammals" is a negative inference. From this it may be deduced what the penguin is not.

Inference and deduction result in positive, negative and neutral terms.

Sure. Negative statements are good grounding for epistemology.

It's what epistemology is.

[Eodnhoj7]

Actually the penguin is defined relative to the nature of flying, in these respects it maintains a neutral nature. An inference is made. From this it may be deduced the penguin in neutral in regards to flying.

"No penguin eats mammals" is a negative inference. From this it may be deduced what the penguin is not.

Inference and deduction result in positive, negative and neutral terms.

Sure. Negative statements are good grounding for epistemology.

It's what epistemology is.

That is a positive statement then; hence we are left with all "meaning" as simultaneous positive/negative/neutral values as observed in the prime directives.