Does Logic use Faith?

[lawtonfogle]

Yes, the thread by the opposite name prompted me to say this, but it is a separate idea. By faith, I am referring to belief without proof in something.

Then, I offer up the formal 7 (if I remember correctly) axioms of logic. They are axioms, therefor unproven. Yet, all logic (both the predicate and prepositional calculus) are derived from them (worse day of logic class ever).

So, we believe they are true, but we have no proof. Now, let me state we do have a need to believe them true, for if they are not, we have a general problem with logic.

So, do not we have faith in these 7 axioms?

(As for the axioms, I do not have the list right now, and I fear I may misquote them otherwise.)

 

[The Nihilist]

There's only one rule of logic that counts, and everything else derives from it. As Aristotle wrote, that is the Law of Contradiction, which says that two contradictory statements cannot be true of the same thing in the same way at the same time. If this is not true, the universe becomes completely incomprehensible. (You are both green and not green and you are not both green and not green and you are someone else but also a desk.) It is impossible to argue for the Law of Contradiction, but it is much more impossible to argue against it, because all arguments inherently rely on it.
So basically, no, it's not about faith. What it's about is that if you disagree with the Law of Contradiction, you're going to sound like a schizophrenic, so just go along with it even if you have reservations.

 

[billwald]

>As Aristotle wrote, that is the Law of Contradiction, which says that two contradictory statements cannot be true of the same thing in the same way at the same time.

True in math but Immaterial in inductive logic?

 

[DailyBlessings]

If this is not true, the universe becomes completely incomprehensible.

Who says the universe is comprehensible?

So basically, no, it's not about faith. What it's about is that if you disagree with the Law of Contradiction, you're going to sound like a schizophrenic, so just go along with it even if you have reservations.

So... threats? That's why we're supposed to believe you?

 

[quatona]

Yes, the thread by the opposite name prompted me to say this, but it is a separate idea. By faith, I am referring to belief without proof in something.

Then, I offer up the formal 7 (if I remember correctly) axioms of logic. They are axioms, therefor unproven.

öklsd 4.yß23 äadöo3 950c.ewö+23, dperoisaaölwk.

 

[The Nihilist]

Who says the universe is comprehensible?

So... threats? That's why we're supposed to believe you?

Well, if the universe isn't comprehensible, then there's no sense arguing about it. But you're here and I'm here, so let's say it is.
I don't think it's a threat to say that you're going to sound like a schizophrenic. After all, you'd be great fun at parties.

 

[Washington]

Yes, the thread by the opposite name prompted me to say this, but it is a separate idea. By faith, I am referring to belief without proof in something.

Then, I offer up the formal 7 (if I remember correctly) axioms of logic. They are axioms, therefor unproven. Yet, all logic (both the predicate and prepositional calculus) are derived from them (worse day of logic class ever).

So, we believe they are true, but we have no proof. Now, let me state we do have a need to believe them true, for if they are not, we have a general problem with logic.

So, do not we have faith in these 7 axioms?

(As for the axioms, I do not have the list right now, and I fear I may misquote them otherwise.)

I don't recall there ever being a specific number of axioms; however, where they are employed it's not as a matter of faith but as an established truth. That they are true is derived from their self evident nature. We define true as being in accordance with what we consider to be the actual state of affairs, and any such "actual state of affairs" is wholly dependent on our perception. If we don't perceive X to be the actual state of affairs we can't/don't say X is true. So to say X is true is to say it's in accordance with the actual state of affairs. Therefore if we assert that Y is axiomatic, we are saying its truth is in accordance with the actual state of affairs. Is it necessary to prove axioms? No. Because proof is used to establish a truth, and axioms are already predicated on truth (not all truth derives from formal proof) proving axioms is unnecessary. The mere fact that axioms are true, functions as a "proof" of their validity. The proof that axioms are true is that they conform to our definition of true: they are in accordance with the actual state of affairs.
So is some kind of faith necessary? No. Faith is a basis for accepting that whose truth is not established, but because axioms are true, faith is unnecessary.

Some say axioms are statements/postulates that are unproven, meaning their truth is unproven. This is true if one insists the proof be formal, but not all truths derive from formal deductions, some are identities such as axioms. The nature of an axiom is identical to the actual state of affairs we accept as true.

 

[billwald]

A century ago Kurt Godel demonstrated that all logical systems are ultimately circular.

 

[quatona]

A century ago Kurt Godel demonstrated that all logical systems are ultimately circular.

I don´t think this is an accurate description of Gödel´s theorems.

 

[peter22]

Billwald

As Aristotle wrote, that is the Law of Contradiction, which says that two contradictory statements cannot be true of the same thing in the same way at the same time.True in math but Immaterial in inductive logic?

Let's imagine that you live in New Zealand and you only ever see white sheep. You induce that because the first and the second and the third and the millionth sheep you see is white, that all sheep are white. Then you go to Scotland and see a black 'contradictory' sheep.

Aristotle's Law of Contradiction is flawed in many respects. A sheep can be both black and white.

 

[Robbie_James_Francis]

Let's imagine that you live in New Zealand and you only ever see white sheep. You induce that because the first and the second and the third and the millionth sheep you see is white, that all sheep are white. Then you go to Scotland and see a black 'contradictory' sheep.

Aristotle's Law of Contradiction is flawed in many respects. A sheep can be both black and white.

How so? A single sheep cannot be both entirely black and entirely white. To say that some sheep are white and others are black is not contradictory.

 

[The Nihilist]

Aristotle's Law of Contradiction is flawed in many respects. A sheep can be both black and white.

You know why that's wrong, don't you?

 

[Stainless]

Yes, the thread by the opposite name prompted me to say this, but it is a separate idea. By faith, I am referring to belief without proof in something.

Then, I offer up the formal 7 (if I remember correctly) axioms of logic. They are axioms, therefor unproven. Yet, all logic (both the predicate and prepositional calculus) are derived from them (worse day of logic class ever).

So, we believe they are true, but we have no proof. Now, let me state we do have a need to believe them true, for if they are not, we have a general problem with logic.

So, do not we have faith in these 7 axioms?

(As for the axioms, I do not have the list right now, and I fear I may misquote them otherwise.)

You clearly misunderstand the foundation of Logic.

Logic is not formed by observation, but by declaration.

The intent in logical thought is to form a model of reality from which one can make productive decisions. The model is accepted as helpful constructs for thought, not as any part of observed reality.

The only faith involved is faith in using the axioms declared in order to proceed in thought. When and if any logical argument is found to not conform to observed reality, either the logic is re-written so as to become more useful or an error in the argument is sought out.

Without logical thought, all efforts to reason fail. The human is reduced to an animal. The instincts have their own logic constructs. If those are given up, the animal dies as well.

Faith means sticking to the plan and has nothing to do with what is or isn't real except a hope that the plan will bring real gain.

Example:
Do you have FAITH that 1 centimeter is really 1/100th of a meter?

-- It is only a matter of faith when using the declarations for measuring reality for the purpose of constructive thought and communication. It has nothing to do with the "real existence" of a centimeter or its relation to a meter.

 

[The Nihilist]

You clearly misunderstand the foundation of Logic.

Logic is not formed by observation, but by declaration.

The intent in logical thought is to form a model of reality from which one can make productive decisions. The model is accepted as helpful constructs for thought, not as any part of observed reality.

The only faith involved is faith in using the axioms declared in order to proceed in thought. When and if any logical argument is found to not conform to observed reality, either the logic is re-written so as to become more useful or an error in the argument is sought out.

Without logical thought, all efforts to reason fail. The human is reduced to an animal. The instincts have their own logic constructs. If those are given up, the animal dies as well.

Faith means sticking to the plan and has nothing to do with what is or isn't real except a hope that the plan will bring real gain.

Example:
Do you have FAITH that 1 centimeter is really 1/100th of a meter?

-- It is only a matter of faith when using the declarations for measuring reality for the purpose of constructive thought and communication. It has nothing to do with the "real existence" of a centimeter or its relation to a meter.

What you're describing sounds a lot more like how science works than how logic works.
Here's a good thing to know about contradiction. If you look around you and see nothing contradictory, then everything's fine. Otherwise, you're on acid.

 

[Stainless]

What you're describing sounds a lot more like how science works than how logic works.
Here's a good thing to know about contradiction. If you look around you and see nothing contradictory, then everything's fine. Otherwise, you're on acid.

Science is based on demonstration - observation from which very little deductive logic is permitted so as to reduce doubt.

The only things declared in Science are stated as such in the beginning of any experiment. Logic is similar to that degree, the axioms are declared, not observed.

The experiment in Science depends on the faith of the person executing the hypothesis to follow the process until the experiment is done. What he deduces from there is additional reasoning and might vary from person to person.


Logic is by declaration and faith that such declarations will yield usefulness.

Science is by demonstration/observation and faith that what is being observed is as declared (controlled environment).

Religion is by acceptance that no more experimenting is required on your part and thus having faith in doing what has been suggested.


The existence of God was an already accepted axiom now challenged by those who wish to disperse the religious.

 

[The Nihilist]

what are you talking about

 

[peter22]

You know why that's wrong, don't you?

Somebody got my joke. Sorry, it wasn't very funny.

 

[ArnautDaniel]

Yes, the thread by the opposite name prompted me to say this, but it is a separate idea. By faith, I am referring to belief without proof in something.

Then, I offer up the formal 7 (if I remember correctly) axioms of logic. They are axioms, therefor unproven. Yet, all logic (both the predicate and prepositional calculus) are derived from them (worse day of logic class ever).

So, we believe they are true, but we have no proof. Now, let me state we do have a need to believe them true, for if they are not, we have a general problem with logic.

So, do not we have faith in these 7 axioms?

(As for the axioms, I do not have the list right now, and I fear I may misquote them otherwise.)

Oh the question is much deeper and more complicated than you put it here.

First off there are many systems of logic not all equivalent to the one you learned in your introduction to logic class (I'm just guessing that is the class you are referring to, no attempt to be mean there). And there are debates in mathematics as to how it should all be logically formulated.

As another poster indicated, the point of a logic is to ensure non-contradictory reasoning. That said, there are differing logics that allow you to include more or fewer non-contradicting propositions in your system depending on what you consider rigorous.

As there isn't a single logic, but rather various logics, the one you choose doesn't so much represent faith, as a chosen philosophy.

 

[JonF]

Without logical thought, all efforts to reason fail. The human is reduced to an animal. The instincts have their own logic constructs. If those are given up, the animal dies as well.

If you are still speaking of formal logic, this is false.

Faith means sticking to the plan

and has nothing to do with what is or isn't real except a hope that the plan will bring real gain.

I don’t think the OP is all that familiar with philosophy so he might be miss-stating his position. I think he isn’t referring to the arbitraryness of the axioms of “logic” but rather the transcendental nature of predicate calculus systems.

 

[JonF]

I don't recall there ever being a specific number of axioms; however, where they are employed it's not as a matter of faith but as an established truth. That they are true is derived from their self evident nature.

this isn't true.

for example how self-evident is:
There exist an omega set which is a finite set of elements called operators or binary logical connectives. The set omega is partition into disjoint subsets, where the order of the partion is equal to or less than cardnalitiy of the natural numbers, and there is a well defined set omega-j in which is defined to be a subset of the union of omega cross n, which each logical operator or connective is relatied to it's arity.