At bottom, logic operators like 'if' 'and' 'or' 'not' can be reduced to one operator:



and all basic logical theorems can be derived from one fundamental axiom like:


For example from this, you can define all the basic logical operators, and propositional logic theorems, such as DeMorgan's laws.

Of course this system does not include quantifiers like 'all', or modal operators like 'possible', ... this would require a more complex system. But still, spelled out like this, a few questions become apparent:


1. what is logic?

2. is this the only system of logic that can be defined?

3. what is the foundation for this logic?

4. if something is "proven," how do we know the proof is itself valid?

Probably a good idea to read Sheffer stroke - Wikipedia, the free encyclopedia. Also, note that it is non-associative. Good to have your mind that a|b=(not (a and b))
Hmmpf, this is far from straightforward; Use web-searching powers and pen and paper, why are.these true: (is just using the tables i guess.)
(not A) = A | A,
(A and B) = (A | B) | (A | B),
(A or B) = (A | A) | (B | B),
(A if then B) = A | (B | B) = A | (A | B).
Last one is not very clear to me yet. (only if it equals true)
And also. what does the axiom mean here: (U|(U|(V|(U|U)))); (U|(U|(if V then U)))=(if U then (if V then U)) huh? (used the last one given by wikipedia.

Also, I read somewhere that logic can also be based on sets (although that book didnt really go into that :/) Perhaps i will try see if i can find something about it.
Furthermore, In http://socialdiscussion.com/religion....html#post9679, the link Impossible Things for Breakfast given in that post, note that discussing about that is maybe offtopic, as it is not logic as we use. Also, I doubt any of us knows shit about it.(yet)

The middle expression reduces to "not (and and not-b)," which is exactly what we want for (mathematical) implication: the implication is true at all times unless the hypothesis (A) is true and the conclusion (B) is false.

lol being second year in an electronic engineering degree, ive seen waay too much boolean logic.

Meaning that we have paradox in very basis of logic and that make me feel uncomfortable.

logic is an illusion made and used by us lying in the eye of the beholder.

That's one one of the things I learned while getting my doctors degree in maths.

Reading the book, not sure i was right about sets in previous post.
@MRiGnS: Could be true, but that case in unargueable. Thinking about it, how did you arrive at this conclusion?(as in events, not as in logic) Considering that learning is being argued the learned, by another person or by reality, it would seem to me that such a thought just pops into existence.
In discussion, one could, instead of assuming logic, decide that communications can either bring over a point to people or not. People can decide for themselves what points and how to communicate. Other people can think whatever they think about it. Only thing is that, if people select things, it becomes more like a popularity contest. On the other hand, logic just happens to convince people, but has no special place except in the minds of the people. (damn i used logic in this statement )

define:logic - Google Search


reasoning i guess

So we can say that world exsist and we understand because

1. prestablished harmony
2.we are part of the world and that is why we can understand it
3.existence of the world is ilusion in my mind

If I take third there is no discusion because all is ilusion and I discus with myself.From epistemological point of view this is is not fruitfull and because of that reject.
For first and second I will use Ockham's razor wich leaves me with second.

From that I can see that logic is not just ilusion.It is not perfect but it is not ilusion.

Did I used logic right now?