Logic and Dialectical Reasoning

[Pattern-chaser]

No, it was a means to point to the communist aim with BLM.

I rather think "BLM" says it all: Black Lives Matter. No communism, or capitalism either, just a plea for justice and equality, both deserved.

[Arjen]

It isn't pattern Chaser, but this is not the topic for it. Let me say that there is a large difference between the founders, "anti"fa and the people that demonstrate peacefully just hoping to do some good. I am discussing with Greta to start a real topic about BLM, due to emotions getting high over this topic. But, she is not against it. I have collected a load of data. For sure it's a shocker.

[Arjen]

I wonder if, in practice, and for reasons that are purely pragmatic, we should embrace "illogical thinking"? Such 'thinking' plays an enormous part in human social culture, and without it, we cannot understand it or participate in it. Just a thought....

A few things:
1) Logic is an activity of the brain. Thinking without logic is impossible if taken literally
2) Illogical thinking often means "intuitive" responses. Of course, this is also an activity of the mind and in that way "logical". Intuition is, according to Kant. the collection of categorical properties of human thought. That means, without scrutiny of the conscious thoughts. In some cases, this produces very valueable insights that we can't understand until later, when further experiences reveal what we intuitively already knew.

[Sculptor1]

Oppss.. Error
People are naturally generous, people are naturally energetic and like work.
People are not naturally greedy, nor are they naturally lazy.

These statements have exactly the same empirical value as the ones you give above.

But, I made no effort to assert that any of those statements were true. I only gave them as examples of the types of things people often *think* are true, while clearly saying that I think the truth is more complex and difficult to understand.

No I get that. But you do agree that the converse of these statements are also true.

[Sculptor1]

No I am not misunderstanding at all.
Since no two things are can be same X=X cannot compare two things that are the same.
What is does is compare two similar things which share in common characteristics which are considered significant, ignoring differences which are thought unimportant.

Mathematicians sometimes start off by stating the obvious, so that it's there to be seen and read. "X = X" simply says that X is identical to itself; it is equal to itself; and this is always the case. This is a precursor to, for example, saying that X is (or is not) equal to some other quantity, distinct from itself.

Like most axioms, and this one is Euclidian, they are bold statements, not empirically true. Things taken as true to press an argument inside an abstract conceptual space. But other Euclidian assumptions are not borne out by physical evidence. Circles, integers, straight lines, parallel lines are all conceptual: none exist in reality. Models only.

[Pattern-chaser]

Even more honest than axioms, these are defined to be true, so that further reasoning can follow. Just like you saying something like "In this topic, I use the term xdr to mean kjsafjhwegytfg" (assuming the nonsense was proper words).

[chewybrian]

But, I made no effort to assert that any of those statements were true. I only gave them as examples of the types of things people often *think* are true, while clearly saying that I think the truth is more complex and difficult to understand.

No I get that. But you do agree that the converse of these statements are also true.

Yes, you are right. People are complex and can have parts of their personality that are each a bit of that person's makeup despite the fact that they seem contradictory, or maybe even seem to be mutually exclusive in theory. I suppose you can box it all up by saying we often make the fundamental attribution error, deciding that behavior is fully indicative of character, when it is more often a response to the situation. It is not a strong foundation to any argument or line of thinking to begin with "people are...", or even "James is...".

[Sculptor1]

No I get that. But you do agree that the converse of these statements are also true.

Yes, you are right. People are complex and can have parts of their personality that are each a bit of that person's makeup despite the fact that they seem contradictory, or maybe even seem to be mutually exclusive in theory. I suppose you can box it all up by saying we often make the fundamental attribution error, deciding that behavior is fully indicative of character, when it is more often a response to the situation. It is not a strong foundation to any argument or line of thinking to begin with "people are...", or even "James is...".

Obvioulsy "James is..." , is an easier thing than "People are...". But humans more than any other species owe more to culture than genetics.

[detail]

So, one first needs to define, and my understanding is imperfect, but I'll have a go, borrowing heavily...

https://www.coursera.org/learn/mindware ... -reasoning

...and someone (or everyone) can correct me if I miss the mark.

-------------------------------------

Logic begins with assumptions we hold to be true that transcend situations. It seems to hold sway in the West.

---X=X. X is always X and never something else.

---X is not not X. Not X and X are always mutually exclusive and only one can be true at a time.

---There is no middle. X is the case or not X is the case, but not some other thing in the middle.

-----------------------------------

Dialectical reasoning begins with the assumption that none of those assumptions above could ever be true. It has greater footing in the East.

---Reality is change (change is the only constant).

---Change involves contradiction, so contradiction is everywhere, always.

---The whole is greater than the sum of its parts. Parts have value only in relation to the whole. Context always matters.

-----------------------------------

So first, have I got a general idea of the two ways of looking at the world and the way they differ (seemingly drastically)? Then, if so, what does it all mean for us? Is one way of looking at the world necessarily more correct or more useful? Are they mutually exclusive, or would we benefit from trying to use both at once? Do you have a preference for one outlook over the other, or are you willing and able to use both? Is the use of either situational, where one is better under certain conditions, and the other better in other conditions?

Well even if you stay in abstract logic, there is more than first order logic. If one implements a kripke structure , logical variables depend on the situation the logical values of a variable depend on the state. There are operators like possible and necessary for a modal logic.
The wikipedia writes :

Let AP be a set of atomic propositions, i.e. boolean expressions over variables, constants and predicate symbols. Clarke et al.[3] define a Kripke structure over AP as a 4-tuple M = (S, I, R, L) consisting of

a finite set of states S.
a set of initial states I ⊆ S.
a transition relation R ⊆ S × S such that R is left-total, i.e., ∀s ∈ S ∃s' ∈ S such that (s,s') ∈ R.
a labeling (or interpretation) function L: S → 2AP.
Since R is left-total, it is always possible to construct an infinite path through the Kripke structure. A deadlock state can be modeled by a single outgoing edge back to itself. The labeling function L defines for each state s ∈ S the set L(s) of all atomic propositions that are valid in s.

A path of the structure M is a sequence of states ρ = s1,s2,s3,... such that for each i > 0, R(si, si+1) holds. The word on the path ρ is a sequence of sets of the atomic propositions w=L(s1),L(s2),L(s3),..., which is an ω-word over alphabet 2AP.

With this definition, a Kripke structure (say, having only one initial state i∈I) may be identified with a Moore machine with a singleton input alphabet, and with the output function being its labeling function.[4]

// On this basis one can define higher order logics like doxastic logic, that believes of a proposition are somehow stated. So logic is nothing fixed.
The way of reasoning can then be classified on the basis of a Kripke structure and doxastic logic. :\\

To demonstrate the properties of sets of beliefs, Raymond Smullyan defines the following types of reasoners:

In accurate, inaccurate, stable , modest , queer, reflexive,normal reasoners etc. //
See for this wikipedia doxastic logic. So dialectics is nothing trivial , but even from the viewpoint of abstract logic s.th. very complicated.
But the philosphical dimension implements in addition a even more complex feature.

[Arjen]

I want to add that, while it is true that a lot of things are easier to define in some 2nd order logic systems, still the logical principles remain the same. In the end, all logic is, is a way to formalise thought. People just invated ways to write it down. Then, in order to simplify more complex formulations, people deviated from and expanded on first order logic.

Perhaps the most interesting thing to me is if logic can be reduced to a single mental activity. I mean we place observations into a logical syntax. And then we apply more and more complex operations. But, for example if and only if can be reduced to if, then plus not if, then. That way eliminating if and only if. Leaving less operators. More complex operators make complex formulations easier, is all.

If then can be reduced to x and y or not x and not y, thus eliminating if then. I think it can be done with the and operator as well.

How far can the reduction go?

[chewybrian]

I want to add that, while it is true that a lot of things are easier to define in some 2nd order logic systems, still the logical principles remain the same. In the end, all logic is, is a way to formalise thought. People just invated ways to write it down. Then, in order to simplify more complex formulations, people deviated from and expanded on first order logic.

Perhaps the most interesting thing to me is if logic can be reduced to a single mental activity. I mean we place observations into a logical syntax. And then we apply more and more complex operations. But, for example if and only if can be reduced to if, then plus not if, then. That way eliminating if and only if. Leaving less operators. More complex operators make complex formulations easier, is all.

If then can be reduced to x and y or not x and not y, thus eliminating if then. I think it can be done with the and operator as well.

How far can the reduction go?

I agree that all logic boils down to that very simple idea. When presented with an obvious truth, I must accept it, and if this truth has clear implications, I must accept the implications in the bargain. If I can't do this, I am not logical.

However, I think the dialectical stance is that 'obvious truth' is a subjective judgement. Further, as we are all unique, even if the facts are conceded, the implications might vary, as we all have different priorities. Then, the only fact is that life is messy and the only implication is that we must work to find the best possible compromise.

[Arjen]

We are subjects, so all we assert is subjective. I think you mean this in the in the objective <-> subjective distinction from the other topic?

[detail]

Perhaps one should choose like in the doxastic logic of belief an Operator D acting on a Kripke structure , that additionally somehow indicates that this is a dialectic proposition which should be somehow dependendt on the status s of the world and the mapping pi in this state of the logical variables . But what properties should have a dialectic operator which is not the Belief , the necessary or the possible operator then ?

[Arjen]

detail I am getting the impression that you are better versed in Logic than I. May I ask what you studied in logic?

[detail]

I just cite for you the Hans von Dittmarsch pdf ""An Introduction to Logics of Knowledge and Belief "".
It was edited by:

Hans van Ditmarsch
Joseph Y. Halpern
Wiebe van der Hoek
Barteld Kooi

It was at that time available for free.