@salima,
Exebeche wrote:No matter what kind of formal system you use, the same rules appear in all of the systems.
Theages;83643 wrote:That's not true. See e.g. An Introduction to Non-Classical Logic: From If to Is
Too bad, i was curious about a further explanation, but this is only an advertise for a book.
It doesn't explane what you mean.
Theages;83643 wrote: Can you say with any confidence "It is not the case that there are four prime numbers between 10 and 20"? I certainly can't. Most people would think that someone would have to be ignorant or insane to assert that.
Most people would think that someone who assumes the earth is not the center of the universe would have to be ignorant or insane to assert that.
At least this is the kind of argument Galileo Galilei was confronted with when he was taken to the trial.
Do you really not see the mistake you make?
It's totally ok to say you have a preassumption that your deduction is based upon.
This will make your deduction true for all cases in which your preassumption is true.
But you can not use this deduction as a proof for your preassumption to be true.
That's circular reasoning.
salima;83668 wrote:
then what is logic? is it another formal system? other formal systems are subject to logic? has the human mind designed logic or is it inherent in the working of the mind? isnt it in fact a faculty of the mind?
The question what is logic, definitely takes us deep into the rabbit hole.
What i can already say is: No, logic is not another formal system.
Logic deals with formal systems. Predicate logic tries to express the rules of logic in formal systems.
Logic is about the principles a system is based upon.
When we regard the universe as a system we observe the logic of everything, thus universal principles.
However we can also talk about the logic of something very particular.
Let's say a hand pulley block. To explain the principle a hand pulley block is based upon, you will have to describe it's logical structure.
Each system can have it's own logic.
Each different language for example is based on its own logic. Grammar is the formal system that describes it. Grammar however describes the logic of this particular artificial system, valid only for this particular language.
As another example, for playing a game like chess, you will have to learn the rules (principles). Normally after playing a few games a player will recognize the immanent logic of the game from observing how the rules and elements are intertwined in action.
So every system can have its own logic that may have nothing to do with predicate logic which tries to describe the universal principles applicable to all natural systems (and which is almost always referred to by the word logic).
In other words the logic of a system depends on how the system is arranged, how its constituents relate to each other and how the relations of the system's constituents affect the progression of the system's behaviour.
