The first three logical principles stated are principles of the logic of truth of propositions: x=x (identity), x AND NOT-x is absurd (non-contradiction) and x OR NOT-x (excluded middle). The excluded middle is rejected by advocates of a logic of proof rather than a logic of truth, because we may not be able to prove x or prove not-x. I am not sure about the law of state-contradiction. Presumably this is a law of dialectical logic. Is this equivalent to x=NOT-x? The latter is a logical falsehood by the law of non-contradiction. You could use a special type of NOT operator to avoid a contradiction, but I am not sure what the interpretation would be. If you are trying to capture the idea that objects change with time, then I would use a temporal logic.

to Andrew Powell,

Because of symbols restricted the discussion is blurred, see my paper titiled: atomic proposition and 1-order predicate function for dialectical logic, as an attachment to you.

to Ian Williams Goddard,

As you said the first three is just classical logic, also be called as formal logic and Boolean algebra is its mathematical model, the fourth law is a mathematical technique to expand classical logic become dialectical logic so that solved the problem about logic variable A and NOTA , and proved Boolean algebra is a special case of dialectical logic.

Best regards.

To Yaozhi Jiang

I had a look through your paper, but think you need to clarify what you mean by your positive and negative operators. (I also note that in normal classical propositional logic if (P IMPLIES Q) then (NOT-Q IMPLIES NOT-P), which is called contraposition.) You should provide for any well formed formula an inductive definition of the positive and negative parts and define your T operator in terms of domain and co-domain (which seems to consist of an order pair and integer values). I think your intuition is that negative parts are those that have a normal form with a remaining NOT operator. Can you give an example of a proposition true in dialectical logic that is not true in classical (2 -valued Boolean) logic?

to Andrew Powell,

At first, the contradictory factors postive factor and negative factor is a pair of factor in dialectical logic variable, not seen as a NOT operator; secondly the true-valued operator T is valued on closed interval [-1,+1], and it is a continous function defined on individual domain. See my attachments to you.

Thanks for your comments.

To Yaozhi Jiang

Thank you for the papers. I am finding the definitions of state-contradiction and T difficult. If T is a continuous function then if it is binary valued, it will have to be constant (i.e. T(x) always =0 or always =1). It would be helpful to know which propositions are true in dialectical logic that are not true in classical logic.

to Andrew Powell,

If denote dialectical logic vatiable by X, its true-valued function can denote by T(X),this T(X) is a continous function defined on individual domain, and valued in closed interval [-1,+1], with another word, the true-valued function T(X) of dialectical logic variable X is continous valued from -1 to +1. Not only valued on binary 0-1system like Boolean algebra did.

Best regards.

To Yaozhi Jiang

As I understand dialectical logic, the idea is to generate a new set of propositions when an existing set of propositions yield a contradiction. Many mathematical proofs are in the form "A, A leads to a contradiction, therefore NOT-A". Dialectical logic does not restrict itself to proofs by contradiction. Historically I know Hegel took as his starting point Kant's Antinomies of Pure Reason, where Kant shows that contradictory propositions are possible when exceeding the proper extent of concepts. I think Hegel took Kant's contradictory propositions and proposed an evolutionary approach where the concepts (or strictly ideas) are refined continually until contradictions no longer arise. That is hard to formalise in logical terms since logic tends to study predicates as variables rather than how predicates evolve.

to Andrew Powell,

Your said is correct. There has been an argument focused on for a long time, i.e. logic variable A and its NOTA, Almost logicians think this is not satisfied by non-contradiction law, therefor they never admit dialectical logic is just logic. My two papers as attached to you avoid the predicament via a mathematical technique, i.e.dialectical logic variable includs a dual state sub-variable: positive factor and negative factor, so we can see the result that Aristotelian logic Three Laws is satisfied not only to fomal logic, Boolean algebra, but also to dialectical logic, thus this is source of the Four Laws. From this we can obtain an important result: Boolean algebra is a special case of dialectical logic.

Best regards.

To Yaozhi Jiang

If we are talking about the same dialectical logic, then I think you need to define T and positive and negative parts of a proposition. I confess that I do not understand the law of state-contradiction.

Best Regards

to Andrew Powell,

There are very important conception, i.e. contradiction in dialectical logic. Dialectical logician think that all of varieties are produced by contradiction consisted of one couple of postive factor and negative factor, of cause this is the simplest case. In my paper I call dialectical logic variable as state-contradiction and express the dialectical logic variable by X+- , Its true-valued function by a state-dual, i.e. T(X+-)=(a,a-1). The Law of State-contradiction is that if replace the formal logic variable with dialectical logic variable, then all of properties in formal logic can be transformed easily into properties in dialectical logic.

Best regards.

to Ian Williams Goddard,

As you said, science of logic is First Part in "The Eneyclopaedia Logic(English translation version)", its author George Wilhelm Friedrich Hegel(1770/1831) is a great philosopher after Francics Bacon and Rene Descartes. Hegel is also a successor of Aristotle in dialectical logic. The main viewpoints in dialectical logic are that in objective world all things are variant and the variance is caused by contradiction.

As for the Fourth Law by one statement, it is that"the variable of dialectical logic is just the variable of formal logic under my definition ".

Making some semantics text knowledge mathematically is a main direction of science.

Best regards.

to Williams Goddard,

In a simple statement, dialectical logic is such a logic that its proposition's true-valued function is both poartial-true and partial-false, but it includs Boolean algebra as its special case. dialectical logic is suitable to variant process, and dialectical logician think of the variance is caused by contradictions.

As for Buddhist logic, it indeed had known some properties of dialectoical logic, in Chiese ancient philosophers such as Laozi, Mozi, and Zhuang zi, they all had known some properties of dialectical logic.

To Yaozhi Jiang

I think what I am finding difficult is that you are saying that T (truth) applies to a proposition and has values in the closed interval of real numbers from -1 to 1 and yet you are also saying that T on positive and negative parts is an ordered pair of (I think) real numbers. And you do not say what the positive and negative parts of a proposition are. Let us take the proposition A OR NOT-A. I think this has positive part A and negative part NOT-A. Then is it true that (X OR NOT-X) if and only if X if and only if NOT-X? No, because if X is false, then we have "True if and only if False", which is false.

Going back a dialectic as a conversation, it is true that if my opponent (Socrates say) forces me into a contradiction, I can revise my hypothesis and see if that survives Socrates's testing. Generally such an approach involves analysis of the concepts (or predicates) and is of course an excellent logical method. But I am not convinced that you should ever accept contradictions. For Kant, an antinomy simply meant that you were using a concept beyond its range of applicability. As I said before, "ideas" for Kant are concepts that lead to error, to antinomies. I think Kant was correct in his attitude towards antinomies.

to Andrew Powell,

Firstly, true-valued function of dialectical logic proposition is variant and partial-truth or partial-falsity, so I defined the dialectical logic true-valued function by a state-dual, i.e. the positive factor of state-dual is its partial-truth and the negative factor of state-dual is its partial-falsity. it is necessary to remember that dialectical logic do not allow any logical contradiction as well as formal logic does, but state contradiction caused process changing is absolutely necessary.

If we say "somebody is a gentleman." This is a proposition P, then in fact the man which is with 90% advantage and 10% disadvantage, thus the true-valued function of proposition P is T(P)=(0.9,-0.1), and if the percentage is changing depend on some variable, then this just a simplest dialectical logic example.

Secondly, dialectical logic variable A never include some factor contradict with A itself, at least under my definition, but the dialectical logic variable consists of two factor contradict each other, i.e. the positive factor and negative factor, of cause this the simplest case.

Ancient Greek philosopher Socrates and Gemany philosopher Kant, both of them are great philosophers, they are great all over the world.

Best regards.

To Yaozhi Jiang

Are you saying that the positive and negative parts of a proposition are related to the likelihoods of the proposition being true and false respectively? I can see how that would work for a logically true or logically false proposition, but how would that work with a proposition such as "I will win at a game of chance this evening"?

Best Regards,

Andrew

to Andrew Powell,

Dialectical logic, includes formal logic as its special case, can express all expessed by formal logic, and also can express all unexpressed by formal logic, and can operated in hybrid with formal logic. Dialectical logic includes fuzzy theory and probability theory, but it is not similiar with the both above, because of the state contradiction.

Thanks for your attention.

to Ian Williams Goddard,

Aristotleian the Three Logic laws are satisfied by partial-truth and partial- falsity,

See my attachment to you.