Does Logic use Faith?

[Patashu]

I may as well assume that the axioms of logic hold, because if they do not hold the universe is not rational and self-consistent and, not only would humans be impossible, no knowledge could be gained from observation (as there would be no rules followed by this unlogical universe)

 

[JonF]

I may as well assume that the axioms of logic hold, because if they do not hold the universe is not rational and self-consistent and, not only would humans be impossible, no knowledge could be gained from observation (as there would be no rules followed by this unlogical universe)

this is not true - there are many logic systems with different axioms in each. And this doesn't address the question: why does logic an a prior object bear on the a postori the way it does?

 

[The Nihilist]

this is not true - there are many logic systems with different axioms in each. And this doesn't address the question: why does logic an a prior bear on the a postori the way it does?

Can you name some of the different logical systems? Or can you explain some of the differences in the axioms?

 

[JonF]

Can you name some of the different logical systems? Or can you explain some of the differences in the axioms?

sure how about: Second Order, Fuzzy logic, Deontic

 

[The Nihilist]

sure how about: Second Order, Fuzzy logic, Deontic

Ok, I have no objection to your claims so far. What are your thoughts on the solution to the question posed? I have my own, but I'd rather hear yours first.

 

[keith99]

Logic no more relies on faith than does using a lever.

Thinking logic gives all answers needs as much faith as thinking a lever can do all jobs.

 

[JonF]

Ok, I have no objection to your claims so far. What are your thoughts on the solution to the question posed? I have my own, but I'd rather hear yours first.

Logic as a system requires no faith other than the common faith that you are about to rationally think and deduce, and that you can determine tautology.

The transcendental nature of logic systems does though. The fact that this purely abstract a priori entity has a sort of necessary bearing on the a postori world is something pretty weird. See the transcendental argument for the existence of God. There are some questions that can’t be answered by deductive reasoning, appeals to evidence, induction, or even abduction - for example try to justify why you believe “what happens in the past determines what happens in the future” without assuming first that it is true, or try to even offer evidence it’s false. You can’t. The proposition “Events in the real world must be logically consistent if the event in question adheres to a particular logic systems axioms” is another such statement. I have faith that is true, but what I don’t have is a guarantee.

 

[JonF]

I may as well assume that the axioms of logic hold, because if they do not hold the universe is not rational and self-consistent and, not only would humans be impossible, no knowledge could be gained from observation (as there would be no rules followed by this unlogical universe)

i want to comment more on this post: so it's true because you don't like the alternative? Isn’t this a justification you would criticize a Christian for if they used it to defend their beliefs?

 

[quatona]

i want to comment more on this post: so it's true because you don't like the alternative? Isn’t this a justification you would criticize a Christian for if they used it to defend their beliefs?

Looks like you are doing your best to use logic to arrive at your conclusions. What do I make of that?

Axioms are not accurately described as "something we accept because we don´t like the alternative". It´s more like something we accept because there is no workable alternative.

 

[JonF]

Looks like you are doing your best to use logic to arrive at your conclusions. What do I make of that?

Axioms are not accurately described as "something we accept because we don´t like the alternative". It´s more like something we accept because there is no workable alternative.

Looks like you are doing your best to use logic to arrive at your conclusions. What do I make of that?

That I hold logic as a first principle?

Axioms are not accurately described as "something we accept because we don´t like the alternative". It´s more like something we accept because there is no workable alternative.

This is just not true. How much experience do you have working with axiomatic logic systems, calculus’s, and set theory? It’s highly arbitrary, some logics are more useful than others . Also you did post an alternative (an inconsistent universe), one you don’t believe in, but also one which you can’t offer evidence against or for. I don’t believe in that universe because of my faith, you don’t why?

 

[quatona]

That I hold logic as a first principle?


This is just not true. How much experience do you have working with axiomatic logic systems, calculus’s, and set theory? It’s highly arbitrary, some logics are more useful than others . Also you did post an alternative (an inconsistent universe), one you don’t believe in, but also one which you can’t offer evidence against or for. I don’t believe in that universe because of my faith, you don’t why?

Make a proposal how we can have a conversation without axiomatically accepting logic, and we will get talking.

I haven´t posted anything about an inconsistent universe, btw. Apparently you are confusing me with somebody else.

 

[JonF]

Sorry you quoted me talking to someone else, hence the problem.

I absolutely agree that logic needs to be axiomatically accepted. We can absolutely converse without logic, we can’t reason. I.e. the truth value of statements can’t be determined without some system of logic, but the statements can still be made.

The problem with your position is that it doesn’t explain why logic does what it does, or why we even have logic to begin with – it just gives reason why it’s a good thing.

If I were to ask you, “how does electronic communication work?” and your response was, “I’d like to see you ask me that without electronic communication because I’m in another country” That isn’t an answer.

 

[quatona]

Sorry you quoted me talking to someone else, hence the problem.

Ok.

I absolutely agree that logic needs to be axiomatically accepted. We can absolutely converse without logic, we can’t reason. I.e. the truth value of statements can’t be determined without some system of logic, but the statements can still be made.

But they can´t be assumed to have any meaning.
I´m not talking about the truth value of statements, I am saying that without the axiomatic acceptance of logic statements aren´t even statements.

The problem with your position is that it doesn’t explain why logic does what it does, or why we even have logic to begin with – it just gives reason why it’s a good thing.

I didn´t intend to explain it, in the first place, and I can´t explain it. That´s the particularity about an axiom like this - it defies rationalization and justification. It is simply the neccessary basis for any abstraction, explanation or statement. It´s not a good thing, it´s a necessary thing.

If I were to ask you, “how does electronic communication work?” and your response was, “I’d like to see you ask me that without electronic communication because I’m in another country” That isn’t an answer.

Firstly, you didn´t ask me how logic works.
Secondly, logic is not a device like electronic communication. It is thecognitive prerequisite for any attempt of an explanation. This self-reference exactly points to it being a necessary axiom.
If you ask me to explain logic you expect the explanation to be logical. And there you already have your answer.
However, if you are content with an explanation like "qweproitu viur390 vcljkr", I´ll concede you have a point and give you this answer.

 

[ArnautDaniel]

Sorry you quoted me talking to someone else, hence the problem.

I absolutely agree that logic needs to be axiomatically accepted. We can absolutely converse without logic, we can’t reason. I.e. the truth value of statements can’t be determined without some system of logic, but the statements can still be made.

The problem with your position is that it doesn’t explain why logic does what it does, or why we even have logic to begin with – it just gives reason why it’s a good thing.

If I were to ask you, “how does electronic communication work?” and your response was, “I’d like to see you ask me that without electronic communication because I’m in another country” That isn’t an answer.

Comparing logic to communication equipment is looking at it in entirely the wrong way.

Logic is simply syntax (not semantics, that is no content whatsoever). It simply allows you take a set of propositions (no idea what they mean, and it doesn't matter) assign true and false values to the propositions (no idea where those came from), and then construct other propositions so that all the propositions form a consistent set of propositions (that is you can never find a proposition that is both true and false).

That's it.

Asking why logic works is like asking why chess "works". Chess is just a set of rules and so is logic.

"Why does chess work?" Well chess consists of a set of rules that make for an enjoyable game, there are other sets of rules out there, but most of them make for dull games.

"Why does logic work?" Well we chose a set of rules that seem to be useful.

"How do we know they are useful?" Well that is an entirely different question, but has nothing at all to do with logic per se.

 

[JonF]

But they can´t be assumed to have any meaning.
I´m not talking about the truth value of statements, I am saying that without the axiomatic acceptance of logic statements aren´t even statements.

You are wrong predicate calculus doesn’t come from logic, logic is defined in predicate calculus. If what you are saying is true, how does one understand the axioms of logic in the first place?

I

didn´t intend to explain it, in the first place, and I can´t explain it. That´s the particularity about an axiom like this - it defies rationalization and justification. It is simply the neccessary basis for any abstraction, explanation or statement. It´s not a good thing, it´s a necessary thing

Firstly, you didn´t ask me how logic works.
Secondly, logic is not a device like electronic communication. It is thecognitive prerequisite for any attempt of an explanation. This self-reference exactly points to it being a necessary axiom.
If you ask me to explain logic you expect the explanation to be logical. And there you already have your answer.
However, if you are content with an explanation like "qweproitu viur390 vcljkr", I´ll concede you have a point and give you this answer.

You are misunderstanding my question, I’m not asking you to explain why a particular logic’s axioms work – but why logic is transcendental in nature.

 

[JonF]

Comparing logic to communication equipment is looking at it in entirely the wrong way.

No more absurd than saying you can’t have communication without logic. The whole point of my comparison was to show how silly it is.

Logic is simply syntax (not semantics, that is no content whatsoever). It simply allows you take a set of propositions (no idea what they mean, and it doesn't matter) assign true and false values to the propositions (no idea where those came from), and then construct other propositions so that all the propositions form a consistent set of propositions (that is you can never find a proposition that is both true and false).

First of all, logic isn’t syntax, it isn’t grammatical in origin.

Secondly that’s not what logic is. That’s what deductive boolean logics do. All you have done is give a description of what one type of logic does.

Asking why logic works is like asking why chess "works". Chess is just a set of rules and so is logic.

"Why does chess work?" Well chess consists of a set of rules that make for an enjoyable game, there are other sets of rules out there, but most of them make for dull games.

"Why does logic work?" Well we chose a set of rules that seem to be useful.

"How do we know they are useful?" Well that is an entirely different question, but has nothing at all to do with logic per se.

You are confusing my question, I have been stating this since the beginning, the question isn’t “why are we able to make constructions from a set of logic axioms” the question is “why is a set of logic axioms transcendental?” Read your description of logic again (that isn’t what logic is, it’s what logic does). Why does logic do this? Why if logic abstractly says something must be true, does it follow in the real world?

 

[ArnautDaniel]

First of all, logic isn’t syntax, it isn’t grammatical in origin.

It absolutely is grammar. There is no content to logic per se. Just as the grammar of a language allows you to construct grammatical sentences with no meaning, logic allows you to construct meaningless propositions.

The only thing that might be "defined" in logic (and then only in a structuralist sense) is what one means by "true". Even then I'd argue that one decides what they mean by "true" and then selects the meaningless logic that best formalizes that meaning of "truth".

Secondly that’s not what logic is. That’s what deductive boolean logics do. All you have done is give a description of what one type of logic does.

Give me an example of a logic that my analysis doesn't apply to and we'll see.

You are confusing my question, I have been stating this since the beginning, the question isn’t “why are we able to make constructions from a set of logic axioms” the question is “why is a set of logic axioms transcendental?”

There is no single set of logical axioms. So they aren't "transcendenal". There are multiple logics.

Two common examples are classical logic and intuitionistic logic which differ in that intuitionistic logic rejects the Law of the Excluded Middle.

Developments in Topos Theory could make one argue that intuitionistic logic is genuinely more fundamental than classical logic, even though I suspect the Law of the Excluded Middle would be one of your "transcendental logical axioms".

Moreover quantum mechanics would seem to obey a non-classical logic (probably something like intuitionism), so what "transcendental axioms" do you have in mind?

Read your description of logic again (that isn’t what logic is, it’s what logic does). Why does logic do this? Why if logic abstractly says something must be true, does it follow in the real world?

Well as there is no single "logic", how do we know which of the various logics says things that must be true about the real world?

Does the real world follow the Law of the Excluded Middle? Yes or no.

 

[quatona]

You are wrong predicate calculus doesn’t come from logic, logic is defined in predicate calculus.

Please explain "predicate calculus" and why you rephrase my statement with concepts I haven´t used.

If what you are saying is true, how does one understand the axioms of logic in the first place?

We don´t "understand the axioms of logic". We are trying to put into words that which determines our thinking. An absurd process, actually.

You are misunderstanding my question, I’m not asking you to explain why a particular logic’s axioms work – but why logic is transcendental in nature.

Well, I haven´t said anything about logic being "transcendental in nature".