Logic is the realisation of the laws which govern phenomena...Quote source.

Also those phenomena, as logical, require logic to circle back on itself, leading to its own problems under its fallacy of circularity along with ad-hominum, authority, bandwagon relative to its self-referential nature through the observer as a phenomena.

You still have not given me what I ask for, I am getting the impression you are just make all of this up and pretending to be an authority.

Logic is the realisation of the laws which govern phenomena...Quote source. — eodnhoj7

This is my interpretation. However merriam-webster says, the formal principles of a branch of knowledge. I've given that explanation because I've deduced that we perceive phenomena, hence, our knowledge is that of phenomena and its relations.

Also those phenomena, as logical, require logic to circle back on itself — eodnhoj7

You seem to not understand what logic is. Logic is the realisation (or expression) of the laws which govern phenomena. The laws are intrinsic to phenomena and are not phenomena themselves.

You still have not given me what I ask for, I am getting the impression you are just make all of this up and pretending to be an authority. — eodnhoj7

What haven't I answered?

Logic:

Logic (from the Ancient Greek: λογική, translit. logikḗ[1]), originally meaning "the word" or "what is spoken", but coming to mean "thought" or "reason" is a subject concerned with the most general laws of truth,[2] and is now generally held to consist of the systematic study of the form of valid inference. A valid inference is one where there is a specific relation of logical support between the assumptions of the inference and its conclusion.

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

Logic is dependent upon axioms as:

Point of Origin as unification of all axioms and all axioms as inversive, as an axiom.

Linear Definition as connection and seperation of axioms, as an axiom.

Circularity as maintenance and dissolution of axioms, as an axiom.


What haven't I answered? To give me a source for all your arguments which is not subject to circularity or equivocation.

The law of identity states that a thing is the same as itself. It gives each thing its own identity, so P, as a particular thing, is the same as P, itself, that particular thing. This is quite clear, unambiguous, and not open to equivocation. Your examples of multiple interpretations, ambiguity, and equivocation simply reflects your misunderstanding of the law of identity.

Actually no, the law can be expressed in multiple ways.

How can something be equal to itself unless it is seperate from itself? If "I" am equal to "I" it necessitates some form of seperation of "I" which may be observed relative to localizations in time where "I" existing in space/time locality x is equivolent to "I" existing in space/time locality "y".

Unless "P=" where "P=" is a function of equivocation, which is possible "P=P" observes a seperation between P and P.

The evidence indicates that you either completely misunderstand the law of identity, or that you state it in an ambiguous way in order to deceive. I am beginning to think that perhaps your intent is deception.

And what evidence is that? What is evidence but a framework of interpretation? A framework has been presented and it maintains itself while being open to further progression without contradiction.


That's right, each of these fundamental laws has its own definition, what it means. One does not define the other. if that were the case, then it would be only one law. But there are three.

Pi is a relationship. It is not a line. — BrianW

A line is a relation between points, and all axioms are relations of other axioms. A length is a relationship between points as well, under these terms Pi as a relation is Pi as a length.

Each law defines the other through collaboration according to Brian.

How can something be equal to itself unless it is seperate from itself? — eodnhoj7

Gee eodnnoj7, can't you read? The law of identity doesn't say that a thing is equal to itself, it says that a thing is the same as itself. So it's not expressing the equality of two distinct things, it is expressing the identity of one thing. That's why it's called the law of "identity". It implies that a thing has an identity, to itself, and that the thing cannot be other than its identity. Leibniz carries this further with the "identity of indiscernibles", stating the converse, if it has the same identity, it is necessarily the same thing, meaning that two distinct things cannot have the same identity.

There is no issue here of two things being equal, the issue is identity. I went through this already, "2+2" is not the same as "4". They are distinct, having a different identity, despite the fact that they are equal. One line is equal to an infinity of lines, but these two are distinct, having different identities, ergo not the same thing.

And what evidence is that? — eodnhoj7

Try the above for example.

A line is a relation between points, and all axioms are relations of other axioms. A length is a relationship between points as well, under these terms Pi as a relation is Pi as a length. — eodnhoj7

If a length is a relationship, this does not imply that all relationships are lengths. Give it up eodnhoj7, it's a lost cause.

P = P... it means that P is equal to itself...facepalm...

That is the point...equality observes a form of seperation, hence the law of identity observes (P,P) as 2 P's with the P being determined by it position in space/time or the argument itself.

The argument observes a form of repitition, where P is repeated and "=" acts as not just a connector between P and P but as a connector observes a seperation in the respect what is connected necessites a prior or future seperation.

Actually it does considering a length observes a connection between specific localized points, I may walk 30 feet from Point A to Point B, where that 30 feet is the connection in space and time with Point A and Point B.

Metaphysician, I would tell you to give it up...but you have no argument to give up.

P = P... it means that P is equal to itself...facepalm... — eodnhoj7

If, and when, "P=P" is used to signify the law of identity, it signifies that P is the same as itself, because that's what the law of identity states. It does not signify that p is equal to P.

Sorry to be the one to inform you of this (though I know others such as brianw have already told you this): you appear to be incredibly, terribly, inept at interpretation. But I know your game, it's intentional, as deception.

Actually it does considering a length observes a connection between specific localized points, I may walk 30 feet from Point A to Point B, where that 30 feet is the connection in space and time with Point A and Point B. — eodnhoj7

How does this indicate that if length is a relation, then all relations are lengths?

If, and when, "P=P" is used to signify the law of identity, it signifies that P is the same as itself, because that's what the law of identity states. It does not signify that p is equal to P. — Metaphysician Undercover

Then "=" is not the same as anything and effectively is nothing but a point of inversion between one P and many P's. "=" is not identified except through P but under the law of identity it must have an identity hence the statement can be inverted to (=)P(=) causing P to have no identity unless referencing P=P. In these respects the law of identity necessitates a circularity.

But this circularity is a fallacy, hence the law of identity is strictly contradictory and a law of dualism.

However "P=P" and "(=)P(=)" are contradictory in the respect they are opposed to eachother as a dualism hence a third element must be synthesized where (P=) as both "P" and "=" where P as a form and "=" as a function of equivocation (connector) exist as one.

The law of idenity if it is to be logical must be:

1. P=P
2. (=)P(=)
3. (P=)

However because of equivocation "equals" "=" "is" etc. must be replaced by a universal variable as well that acts as a connective variable where the variable is not just a form but also a function.

Hence:

1. P(p)P
2. (p)P(p)
3. (Pp)

Sorry to be the one to inform you of this (though I know others such as brianw have already told you this): you appear to be incredibly, terribly, inept at interpretation. But I know your game, it's intentional, as deception. — Metaphysician Undercover

Actually you are confusing your ability for interpretation as memorization. I am simply following the fallacies of logic, unlike you...who is more logical?

Point of Origin as unification of all axioms and all axioms as inversive, as an axiom. — eodnhoj7

Where and how have you arrived at this?

Linear Definition as connection and seperation of axioms, as an axiom. — eodnhoj7

Where and how have you arrived at this?

Circularity as maintenance and dissolution of axioms, as an axiom. — eodnhoj7

Where and how have you arrived at this?

Each law defines the other through collaboration according to Brian. — eodnhoj7

This only applied to those three laws of logic, not every law in existence. Dude, context, please!


archimedes constant (pi), euler's number, pythagoras constant, the golden ratio, etc; are a few common mathematical constants which represent certain mathematical relationships

Is it your testimony that they are all the same? If you think so, then b**s***. If not, then that's the point we've been trying to make. The word relationship does not equate unrelated circumstances.

Now, on to your fallacies:

1. What is an axiom (http://www.importanceofphilosophy.com/Metaphysics_Axiom.html)

Axiom
An axiom is an irreducible primary. It doesn't rest upon anything in order to be valid, and it cannot be proven by any "more basic" premises. A true axiom can not be refuted because the act of trying to refute it requires that very axiom as a premise. An attempt to contradict an axiom can only end in a contradiction.

The term "axiom" has been abused in many different ways, so it is important to distinguish the proper definition from the others. The other definitions amount to calling any arbitrary postulate an 'axiom'. The famous example of this is Euclidean geometry. Euclid was a Greek mathematician who applied deductive logic to a few postulates, which he called axioms. In this sense, "axiom" was used to mean a postulate which one was sure was true. Later, though, it was shown that his postulates were sometimes false, and so the conclusions he made were equally false. The "axiom" he used was basing his geometry on a two dimensional plane. When his work was applied to the surface of a sphere, though, it broke down. A triangle's three angles add up to 180 degrees on a plane; they do not add up to 180 degrees on the surface of a sphere. The point is that Euclid's "axioms" were actually postulates.

True axioms are more solid than that. They are not statements we merely believe to be true; they are statements that we cannot deny without using them in our denial. Axioms are the foundation of all knowledge.
There are only a few axioms that have been identified. These are: Existence Exists, The Law of Identity, and Consciousness.

2. The Law of Identity (http://www.importanceofphilosophy.com/Metaphysics_Identity.html)

A is A: Aristotle's Law of Identity
Everything that exists has a specific nature. Each entity exists as something in particular and it has characteristics that are a part of what it is. "This leaf is red, solid, dry, rough, and flammable." "This book is white, and has 312 pages." "This coin is round, dense, smooth, and has a picture on it." In all three of these cases we are referring to an entity with a specific identity; the particular type of identity, or the trait discussed, is not important. Their identities include all of their features, not just those mentioned.

Identity is the concept that refers to this aspect of existence; the aspect of existing as something in particular, with specific characteristics. An entity without an identity cannot exist because it would be nothing. To exist is to exist as something, and that means to exist with a particular identity.

To have an identity means to have a single identity; an object cannot have two identities. A tree cannot be a telephone, and a dog cannot be a cat. Each entity exists as something specific, its identity is particular, and it cannot exist as something else. An entity can have more than one characteristic, but any characteristic it has is a part of its identity. A car can be both blue and red, but not at the same time or not in the same respect. Whatever portion is blue cannot be red at the same time, in the same way. Half the car can be red, and the other half blue. But the whole car can't be both red and blue. These two traits, blue and red, each have single, particular identities.

The concept of identity is important because it makes explicit that reality has a definite nature. Since reality has an identity, it is knowable. Since it exists in a particular way, it has no contradictions.


=> Therefore, any 'thing' (e.g. a line) can only be that 'thing' (e.g. a line) due to its own unique/distinct IDENTITY.

Before I proceed to the law of non-contradiction, something you might want to understand:

3. Irrational Epistemology (http://www.importanceofphilosophy.com/Irrational_Main.html)

Irrational Epistemology
Epistemology is the study of knowledge, and how we come to achieve it. A proper epistemology allows us to gain valid understanding of the world, and identify incorrect ideas. An epistemology based on reason is our means of successfully acquiring knowledge. An irrational epistemology, though, impairs the functioning of the mind. The more irrational it is, the less valid the knowledge one has is.

Since philosophy is a kind of knowledge, an irrational epistemology is the destroyer of a rational philosophy. It is makes it difficult or impossible to get other parts of the philosophy right, since it is prevents the proper functioning of the mind.

Like all misbegotten notions, most irrational epistemological theories or assumptions are not practiced consistently. The result would be an inability to deal with the world. Instead, an irrational epistemology is practiced inconsistently. It impairs the mind when it is used, but it is often ignored allowing limited real use of one's mind.

The following is a list of common epistemological mistakes or flawed systems. It is not an exhaustive list, since there are an infinite number of ways one can be wrong (and only one way to be right).

Faith
A Priori Knowledge
Philosopher's Deduction Fallacy
Subjectivism
Polylogism
Determinism
Fallacy of the Second Standard
Skepticism


=> In bold are your mistakes too.

Point of Origin as unification of all axioms and all axioms as inversive, as an axiom. — eodnhoj7


1. Where and how have you arrived at this?

Linear Definition as connection and seperation of axioms, as an axiom. — eodnhoj7


2. Where and how have you arrived at this?

Circularity as maintenance and dissolution of axioms, as an axiom. — eodnhoj7


3. Where and how have you arrived at this?

Each law defines the other through collaboration according to Brian. — eodnhoj7


4. This only applied to those three laws of logic, not every law in existence. Dude, context, please!


archimedes constant (pi), euler's number, pythagoras constant, the golden ratio, etc; are a few common mathematical constants which represent certain mathematical relationships

Is it your testimony that they are all the same? If you think so, then b**s***. If not, then that's the point we've been trying to make. The word relationship does not equate unrelated circumstances.
4 minutes ago

1. All axioms are defined through further axioms, and as defined through further axioms they are connected to them where all axioms effectively exist as extensions of each other as one axiom. All axioms are a point of origin forth further axioms with all axioms in themselves being a center point of origin.

2. If one axiom, through definition progresses to another axiom (lets say one definition in a dictionary leads to another), this new axiom is relativistically seperate from the prior axiom in the respect it progresses past its point of origin as a point of origin in itself. In a seperate respect (and you can look at a dictionary again for this example) From a macroscopic view all axioms are defined by what they are connected too where one axiom is directed to another with this secondary axiom being directed back to its origins. They are directed towards eachother through eachother as eachother as 1 axiom observed through multiple connected parts.

Definition exists through seperation and connection.

3. All axioms circular back to their origins with this circularity being a constant. While this is deemed as a contradiction in western logic due to a lack of progressive defintion, the axiom is maintained through an oscillation where they are connected as one. This connection of the axioms through a circulation cause them to dissolve into a further axiom as one axiom in itself. For example 1+2 and 2+1 observe a circulation between the two where one is directed towards two and two directed towards 1 (through "+" as an active function) resulting in one defined the other and connected as "3" with 3 being the dissolution of +1 and +2 into a new axiom.


4. But the laws of logic must describe every law in existence other wise the laws are not logical.

4. On Contradictions (http://www.importanceofphilosophy.com/Metaphysics_Contradiction.html)

Contradiction

A contradiction arises when two ideas each make the other impossible. Contradictions don't exist in reality because reality simply is as it is and does not contradict itself. Only our evaluations of reality can contradict each other. If you think you have found a contradiction, then check your premises. Either you're mistaken about it being a contradiction or one of the contradicting concepts has been improperly formed.

If the content of your knowledge contains contradictions, then some of your knowledge is in error. Because in order to be successful in reality one must know reality, success requires correct knowledge. It is therefore important to continually search for and root out contradictions in your knowledge in order to make sure that your knowledge corresponds to reality. The two primary methods for doing this are logic, the art of non-contradictory identification, and integration.

Address above. However the Law of Identity is fault being P=P would require "=" to be defined under the same law in which it is not. It is void of meaning, hence the law contradicts itself.

4. On Contradictions (http://www.importanceofphilosophy.com/Metaphysics_Contradiction.html)
Contradiction

A contradiction arises when two ideas each make the other impossible. Contradictions don't exist in reality because reality simply is as it is and does not contradict itself. Only our evaluations of reality can contradict each other. If you think you have found a contradiction, then check your premises. Either you're mistaken about it being a contradiction or one of the contradicting concepts has been improperly formed.

If the content of your knowledge contains contradictions, then some of your knowledge is in error. Because in order to be successful in reality one must know reality, success requires correct knowledge. It is therefore important to continually search for and root out contradictions in your knowledge in order to make sure that your knowledge corresponds to reality. The two primary methods for doing this are logic, the art of non-contradictory identification, and integration.

con·tra·dic·tion
[ˌkäntrəˈdikSH(ə)n]
NOUN

a combination of statements, ideas, or features of a situation that areopposed to one another.
"the proposed new system suffers from a set of internal contradictions"
a person, thing, or situation in which inconsistent elements are present.
"the paradox of using force to overcome force is a real contradiction"
the statement of a position opposite to one already made.
"the second sentence appears to be in flat contradiction of the first" · [more]
synonyms:
denial · refutation · rebuttal · countering · counterstatement · opposite · negation · gainsaying · confutation

http://www.bing.com/search?q=contradiction+definition&qs=n&form=QBLH&sp=-1&pq=contradiction+definition&sc=8-24&sk=&cvid=C2C1F9EB4C8540CDB6CFC492CF5E2A6B

The multiplicity of sources leads to the definition of contradiction as subject to equivocation as each source must be defined by another source, etc.


All contradiction arises through a dualism leading to opposition between variables. The law of identity, because "=" is not defined, is subject to this dualism.

I am simply following the fallacies of logic, unlike you...who is more logical? — eodnhoj7

If you think that the law of identity, is a logical fallacy then it's quite clear that you are being illogical.

Then, it is as I said before, you are using unfounded premises which are deemed fallacious by every law of logic. Hence, illogical.

Address above. However the Law of Identity is fault being P=P would require "=" to be defined under the same law in which it is not. It is void of meaning, hence the law contradicts itself. — eodnhoj7

Do you see any "=" in the explanation given for law of identity? Stop dreaming, pinch yourself and wake up. There is no hiding behind misunderstood equations with me. Read, understand and know you are mistaken!

Before I proceed to the law of non-contradiction, something you might want to understand:

3. Irrational Epistemology (http://www.importanceofphilosophy.com/Irrational_Main.html)

Irrational Epistemology
Epistemology is the study of knowledge, and how we come to achieve it. A proper epistemology allows us to gain valid understanding of the world, and identify incorrect ideas. An epistemology based on reason is our means of successfully acquiring knowledge. An irrational epistemology, though, impairs the functioning of the mind. The more irrational it is, the less valid the knowledge one has is.

Since philosophy is a kind of knowledge, an irrational epistemology is the destroyer of a rational philosophy. It is makes it difficult or impossible to get other parts of the philosophy right, since it is prevents the proper functioning of the mind.

Like all misbegotten notions, most irrational epistemological theories or assumptions are not practiced consistently. The result would be an inability to deal with the world. Instead, an irrational epistemology is practiced inconsistently. It impairs the mind when it is used, but it is often ignored allowing limited real use of one's mind.

The following is a list of common epistemological mistakes or flawed systems. It is not an exhaustive list, since there are an infinite number of ways one can be wrong (and only one way to be right).

Faith
A Priori Knowledge
Philosopher's Deduction Fallacy
Subjectivism
Polylogism
Determinism
Fallacy of the Second Standard
Skepticism

=> In bold are your mistakes too.


The premised does not give a self-maintained definition of reason, hence is built on contradictory foundations as this "perspective"

is a statement of:

Faith
A Priori Knowledge
Philosopher's Deduction Fallacy
Subjectivism
Polylogism
Determinism
Fallacy of the Second Standard
Skepticism

Taking it an authoritative statement is a fallacy according to the standard laws of logic.

Arguing contradiction is a logical conclusion is the fallacy which is being highlighted. That you can't realise that shows I should not waste any more time on you.

YOU WIN.

The Prime Triadic Nature of the Axiom:

Actually the premises I argue are original, progress to eachother and further axioms, while maintaining themselves as logical and structured through self-referencing.


1. All axioms are points of origin; hence all axioms as progressive linear definition and circularity are points of origins. The point of origin progresses to another point of origin through point 2 and cycles back to itself through point 3 with this linear progression and circularity originating from themselves, through eachother and point 1.

Point 1 is original and exists through points 2 and 3 as points 2 and 3.

As original Points 1,2,3 are extension of eachother as one axiom, while simultaneously being nothing in themselves as points of origin that invert to further axioms respectively; hence originate as 1 and 3 through 1 and 3 as 1 and 3 laws

2. All axioms are progressive linear definition; point 1 and 3 progress to point 2 as respective points of origin observed in point 1 while this linear progression from one to another through alternation and exists as circulation between points 1 and 3 to point 2 and point 2 progressing to points 1 and 3.

Point 2 is definitive and defines points 1 and 3 with points 1 and 3 defining point 2.

As definitive Points 1,2,3 progress from one to another and are inherently seperate. As seperating one from another they are connected under a common function of "seperation"; hence are defined as 1 and 3 through 1 and 3 as 1 and 3 laws.

3. All axioms are maintain through a circularity, as linear alternation through point 2, and points of origin as point 1, with point 1 and 2 circulating through each other as point three while circulating through themselves as each other. Point 3 maintains itself as circular and maintains points 1 and 2 as circular while points 1,2 and 3 circulating through eachother maintain eachother.

Point 3 is circular and exists through 1 and 2 as 1 and 2.

As circular Points 1,2,3 are maintained through eachother as eachother as one axiom, while simultaneously dissolving into further axioms as eachother; hence they circulate as 1 and 3 through 1 and 3 as 1 and 3 laws.

Arguing contradiction is a logical conclusion is the fallacy which is being highlighted. That you can't realise that shows I should not waste any more time on you.

YOU WIN. — BrianW

Win what exactly? your position contradicts itself as well as the "irrational epistemology" you argue. The nature of the axiom is defined above.

Contradiction does not occurs in a triadic logic.

What happened to having sources? I seem to have given you quite a few. So, when do I get yours?

You provided none that fits the requirements I set: They cannot be subject to circularity or equivocation.

Well then, consider me amazed. Either all philosophers who adhere to those laws of logic are blind making you the only sighted philosopher or...

Adieu

You tell me...do all philosophers adhere to those laws?