O death, where is thy sting? O grave, where is thy victory?
I distrust logic due to my distaste for its dirty laundry (constructs such as Russell's Paradox). So, anyway, what is an assumption? Is an assumption part of a logical system? Is it a chicken/egg kind of thing? It might be similar to how when constructing Peano's axioms one can not pin down which axioms specifically define the Prime numbers because prime numbers are defined in terms of the operations on the integers. So Primes are a feature of the setup... maybe assumptions are similar. Am I blabbering? Probably... I certainly can appear to know something about math but you probably see right through my undergrad degree!
Your question is improper. The axioms and theorems of logic are the means to demonstrate the truth or falsity of a spoken or written argument that has been asserted to be true. No, it is not true that logic is learned inductively nor is it learned through empiricism.
Your last statement is an argument in the form of a question, the axioms of logic are not able to be applied to a question since nothing in a question is being asserted to be true. to apply the axioms and theorems of logic your question needs to be rephrased into a declarative form and its fallacy becomes immediately apparent. i.e., "Irrationality is rationality"
"empiricism is irrational"
Therefore: Impericism is rational.
also the axioms of logic that demonstrate truth or falsity of a spoken or written assertion are not able to be applied to numbers. This is also easily demonstrated, While it is true that because 2+2=4, therefore 4=2+2. It is not true that because all roses are flowers therefore all flowers are roses.
I hope this helps,
Axioms are not a means to demonstrate anything except for what can be derived from those axioms.
We learn everything inductively. We are wired from birth to learn by that manner. Children ask thousands of questions, testing, trying to determine which questions always give the same answer and which have answers that change. They learn speech in the same manner. They also learn some logic by this same manner well before it gets formalized in ninth-grade geometry.
Axioms, including the axioms of logic, are assumed true. They are not proven true. How can they be? Because they are consistent with logic? Circular reasoning if I've ever heard any.
No, I never said nor implied that "Impericism [empiricism?] is rational." Far from. I would have thought that you of all people understood that rational and logical are synonyms. You far too often jump to unnecessary conclusions.
What are derived from axioms are theorems. axioms are not derived inductively. Axioms are universally and eternally self evidently true. It is the application of the axioms and theorems of logic to a conclusion derived from a declarative statement that are able to necessarily demonstrate the tuth or falsity of the conclusion.
Of the five forms of human discourse: a prayer; a command; a question; a wish; a declarative; only the declarative is asserting something to be true. It is only the declarative that is a subject for logical examination.
I agree you have not said empiricism is rational, because you have not said anything. You have only asked questions. I rephrased your questions into declaritive statments so that they could be logically examined, and demonstrated to be false, therefore I have not jumped to unnecessary conlusions. If you feel my rephrasing is not accurate, then you rephrase them into declarative statements and I will apply the axioms and theorems of logic to your statements and demonstrate them as false. what I do understand is that rational and irrational are antonyms just as are logical and illogical, they are not able to be equated.
And how do you know that "Axioms are universally and eternally self evidently true?"
You don't know that they are true. You assume them to be true.
Fortunately you are in error, I do know that axioms are true and are not inductively derived. I need no assumptions or induction to know a contradiction can not be true.
The fact is, God created a world in which we can be sure that things are true through experimentation. As far as things being ALWAYS true, in the natural world we CAN determine truth through experimentation and how our experiments show consistent results. If they do, then we can proclaim them to be true.
But because God is God, and He can bend things to His will outside the natural realm, the only way we can determine truth in the realm in which we do NOT live is to take His word for it.
I believe in logic only within the natural realm. I do not have enough experience with the supernatural to proclaim that logic holds in the same way there as it does here. So an axiom determined on the earth is not necessarily the same in another realm.
So Jeff, are you arguing this point (about logic) theologically, or naturally?
Your first paragraph says it all.
If Doug's first paragraph says it all, what all does that paragraph say? "The fact is, God created a world in which we can be sure that things are true through experimentation."
Am I to understand that you affirm that through experimentation man can prove as true that God created the earth? - That God created man?
Has this experimentation ever conclusively been accomplished, by whom and when?
My first paragraph only said part of it. I went on to state that the supernatural cannot be proven through natural means. So I am in agreement with Tom in his statement that what is OUTSIDE nature cannot be proven by nature.
So where is this discussion going? I don't see the conflict between anyone here.!
Jeff and I are diametrically opposed in the function and application of the axioms and theorems of deductive logic as the only means of demonstrating truth.
Jeff is on record in stating that truth is obtained experiencially by induction. I deny that any truth can be learned experiencially or inductively.
You believe that NO truth can be determined experientially? Then how DO you find truth?
I don't understand why you would take this position?