When speaking of logic, I am referring to basic conclusions like this one:

All Greeks are Humans.
Socrates is a Greek.
Therefore, Socrates is a Human.

What I am trying to express with my question:

1)Is logic a concept of rational beings? (Assuming False)
alternatively
2)Do all processes follow the laws of logic or do we conclude the laws of logic by observation of natural processes?

3)If !1 in what way does logic exist then? Can we physically explain why Socrates needs to be Human if he is a Greek if Greeks are humans? Is there a physical representative for " = " ?

4)Does Math only exist in the way that Days (as a concept of 24 Hours) exist?

This should probably be in philosophy...
1) Isn´t that clear. The use of a logic defines rationality.
2) Not all formal logics follow the same laws. Science as a method demands a logic in which the statement ((A->B) AND !B)->!A is true, which for instance boolean logic satisfies, but L3 for instance doesn´t.
3) Does logic exist?
4) Isn´t clear either.

I don´t think any of these can be answered without some additional assumptions - and maybe that´s the key to logic: It is what you get when you want to have some basis of evaluating the truth of statements with the minimum of axioms. ZOL is an algebraic ring and in fact the smallest non-trivial ring, it is sound and complete. Under a congruence theory of truth this implies that ZOL is true and thus serves as a stable basis for rational discourse.

Logic is a way of establishing new truths by use of existing truths with valid and consistent relationships.

"Wie die Ethik kann man auch die Logik eine normative Wissenschaft nennen. Wie muss ich denken, um das Ziel, die Wahrheit, zu erreichen? Die Beantwortung dieser Frage erwarten wir von der Logik, aber wir verlangen nicht von ihr, dass sie auf das Besondere jedes Wissensgebietes und deren Gegenstände eingehe; sondern nur das Allgemeinste, was für alle Gebiete des Denkens Geltung hat, anzugeben, weisen wir der Logik als Aufgabe zu. Die Regeln für unser Denken und Fürwahrhalten müssen wir [als] bestimmt denken durch die Gesetze des Wahrseins. Mit diesen sind jene gegeben. Wir können mithin auch sagen: die Logik ist die Wissenschaft der allgemeinsten Gesetze des Wahrseins."

(Frege, Gottlob. "Logik." 1897. In Gottlob Frege: Schriften zur Logik und Sprachphilosophie; Aus dem Nachlass, hrsg. v. Gottfried Gabriel, 4. Aufl., 35-73. Hamburg: Meiner, 2001. S. 38-9)

English translation:

"Like ethics, logic can also be called a normative science. How must I think in order to reach the goal, truth? We expect logic to give us the answer to this question, but we do not demand of it that it should go into what is peculiar to each branch of knowledge and its subject matter. On the contrary, the task we assign logic is only that of saying what holds with the utmost generality for all thinking, whatever its subject matter. We must assume that the rules for our thinking and for our holding something to be true are prescribed by the laws of truth. The former are given along with the latter. Consequently we can also say: logic is the science of the most general laws of truth."

(Frege, Gottlob. "Logic." 1897. In The Frege Reader, edited by Michael Beaney, 227-250. Oxford: Blackwell, 1997. p. 228)

susu.exp wrote:Under a congruence theory of truth this implies that ZOL is true and thus serves as a stable basis for rational discourse.

What is ZOL?

home_ wrote:

susu.exp wrote:Under a congruence theory of truth this implies that ZOL is true and thus serves as a stable basis for rational discourse.

What is ZOL?

Zero-order logic.
It´s what you get when you have two operations and true and false as neutral elements with respect to these operations. It doesn´t allow countably infinite statements (the main thing that gets you to first order logic, or FOL).

RationalVegan wrote:When speaking of logic, I am referring to basic conclusions like this one:

All Greeks are Humans.
Socrates is a Greek.
Therefore, Socrates is a Human.

What I am trying to express with my question:

1)Is logic a concept of rational beings? (Assuming False)
alternatively
2)Do all processes follow the laws of logic or do we conclude the laws of logic by observation of natural processes?

3)If !1 in what way does logic exist then? Can we physically explain why Socrates needs to be Human if he is a Greek if Greeks are humans? Is there a physical representative for " = " ?

4)Does Math only exist in the way that Days (as a concept of 24 Hours) exist?

why you wanna know?
let me know, and i will give you an answer.
alternatively logic is whatever you want it to be.
or perhaps logic is a coherent, self contained system. or maybe it is a self contained systems arrived at from certain axioms, considered true, or provable (earth is round).
does it have weaknesses, yes?
wanna know its greatest weakness?

good question though.

Logic is a little tweeting bird, chirping in a meadow. Logic is a wreath of pretty flowers which smell bad.

susu.exp wrote:

home_ wrote:

susu.exp wrote:Under a congruence theory of truth this implies that ZOL is true and thus serves as a stable basis for rational discourse.

What is ZOL?

Zero-order logic.
It´s what you get when you have two operations and true and false as neutral elements with respect to these operations. It doesn´t allow countably infinite statements (the main thing that gets you to first order logic, or FOL).

Any recommended reading on this subject? Thanks!

I think a rather good thing to do rather than just read is to look at Zmod2 - i.e. a system where you have 0 for the class of all even numbers and 1 for all odd numbers and then see what you get with the two operations of addition and multiplication.
Then note the equivalencies:
1 ~ true
0 ~ false
* ~ AND
+ ~ XOR
See if you can derive any conjective you want (normal OR, negation, implication, etc.) from this.
Then ask what quantifies like "for all" would look like in this system and if you can come up with a formula that doesn´t have a fixed value.
Apart from that, there are good entries on algebraic structures on Wiki and Mathworld.

Shhhh....! Don't tell the Christians, Jews, Muslims, or Mormons. They might try logic and corrupt it.

Well, I'm just a lowly Christian, and I'd hate to corrupt logic, but to my understand logic is a set of symbols together with rules for forming 'sentences' with them (for instance, '3 + =' is not a valid sentence in arithmetic) and a set of rules of inference (for instance, substition and modus ponens) used to derive theorems (i.e., sentences that are valid inferences from valid sentences).

But, hey, what do I know?

Grace wrote:Shhhh....! Don't tell the Christians, Jews, Muslims, or Mormons. They might try logic and corrupt it.

Logic is fairly commonly used in various branches of Jewish theology, e.g. in Halakhic reasoning, for one.

CliveStaples, so, as a "lowly Christian," with so many errors, lies, contradictions, and absurdities found in Christian culture and literature, how does one make logic work?

Grace wrote:CliveStaples, so, as a "lowly Christian," with so many errors, lies, contradictions, and absurdities found in Christian culture and literature, how does one make logic work?

From what I know there is no need to accept all the contradictions to call yourself a Christian. Modern Christians tend to believe in the parts of "christian culture" they sympathise with only. So I am assuming that is the case here.

But the Christian did not exactly answer in regard of the actual question(s) I asked, so reading appears to be a problem nevertheless. Thus, the veil of sarcasm is not quite appropiate.

From the knowledge I´ve accumulated here I would say that I can now fairly conclude for myself, that Logic is the way from A,B=>C, with => being a rational concept without actual substance but it´s actual components being somewhat represented in both A,B and C, just like in physics, where you first assume that you have some sort of field, just to then later discover that the field is much rather a component of the interacting physical objects.

RationalVegan wrote:
From the knowledge I´ve accumulated here I would say that I can now fairly conclude for myself, that Logic is the way from A,B=>C, with => being a rational concept without actual substance but it´s actual components being somewhat represented in both A,B and C, just like in physics, where you first assume that you have some sort of field, just to then later discover that the field is much rather a component of the interacting physical objects.

This almost sounds like word salad.

Logic is one tool that is used to reference
the physical world but it has limits : as
the following are objectively true but
are also devoid of reason however
which is quite interesting I find

A Faraday cage
Quantum mechanics
The Galileo experiment
Physics at centre of black hole
Aerodynamic ability of a bumble bee
Infinity existing between two finite points
Non physical dimension as part of the Universe

surreptitious57 wrote:Logic is one tool that is used to reference
the physical world but it has limits : as
the following are objectively true but
are also devoid of reason however
which is quite interesting I find [...]
Aerodynamic ability of a bumble bee

If you're referring to the claim that science can't explain why the bumble bee can fly - that it physically shouldn't, - the flight capability of the bumble bee has been scientifically explained. Whosoever didn't originally understand it had a mistaken model either of physics or of bumble bee flight, and therefore got a mistaken result.

"This almost sounds like word salad."

Lay off, he's just a boy!

Logic is essentially a formal means of differentiating between valid and invalid reasoning. However, it has a broader remit than simply identifying particular cases of each: it seeks to determine the nature of classes of argument, not simply individual instances of those classes.

A somewhat terse, dense, but ultimately highly informative book on the subject, is Methods of Logic by Willard Van Ormand Quine. Even if you find it heavy going, it's worth persevering with, because at the end, you'll discover that the remit of analytical logic is even broader than this, not least because analytical logic introduces some set theory axioms into the mix, and from that point, allows you to define the concept of 'number' from more fundamental entities. But I'm jumping ahead of the game by a massive amount here.