What Is Logic?

[XxFREEofFILTHxX]

I Know That Logic Is Limited And That We Are Enslaved In Its Confined Boundaries.

I Would Like To Hear Your Opinions,
My Question's Are:
1. What Is Logic And What Is It A Product Of?
2. Does It Define Things Or Is It Being Defined By Other Higher Things?

[dekoi]

1.) Logic is a root of reason. Reason is either 1: a product of human/intellectual developement |or| 2: a Divine gift.

2.) Depends on whether you believe in a central authority or not (God). If you believe in God, and that God created all, then God defines reason. One can refute this, by saying humans have free will and thus, they use their will to define reason. However, reason is based on an objective truth (if in fact, you believe in God). If you are a humanist, then you clearly define your own logic (because you believe you are your own authority).

[Goongyae]

1a. "What Is Logic"

Logic is a reliable method for taking one set of truths and manufacturing new truths from them. Using a finite number of axioms, plus logic, one has access to many truths (though not all). Seeing as how it's impossible to prove the consistency of simple systems like arithmetic, I admit that it's possible logic can also yield false results. The theorem about cutting up a grapefruit into a finite number of pieces and then fashioning a solid sphere the size of the sun comes to mind.

1b. "What Is It A Product Of?"

Logic, like science, is something people invented because it proves useful empirically. Most people who reject logic have died out by now. In particular, the bunga bunga tribe was horribly impaled by their foes when they refused to accept the parabolic trajectories of their javelins.

2. "Does It Define Things Or Is It Being Defined By Other Higher Things?"

It's merely a tool that has proven useful to people. So, the answer is that people are the higher things that have defined their logic. I think suggesting much beyond that would take a lot of hubris.

[Humbucker]

Logic is weighing your behavior against the consequences.The choice is yours.

[wuliheron]

I Know That Logic Is Limited And That We Are Enslaved In Its Confined Boundaries.

I Would Like To Hear Your Opinions,
My Question's Are:
1. What Is Logic And What Is It A Product Of?
2. Does It Define Things Or Is It Being Defined By Other Higher Things?

The term "logic" refers to the catagory of analytical tools based on the principle of Reductio ad absurdium (reduction to the absurd). In turn, this principle is derived from our demonstrably emotive ability to give or find meaning in the world around us.

Logic provides merely one type of description of things among many. For example, natural language is repleat with vague terms such as love, pile, bald, etc. which logic has little to say about.

[XxFREEofFILTHxX]

1. but how did you conclude these statements?
2. Is logic wrong and full of errors?
3. By what do we conclude what is logic, and what is not?
4. On what is Logic based on?
5. What is proof?

[XxFREEofFILTHxX]

Dekoi, The opinion base in the existence god should not make a difference...........what defines logic?

[Prometheus]

I Know That Logic Is Limited And That We Are Enslaved In Its Confined Boundaries.

I Would Like To Hear Your Opinions,
My Question's Are:
1. What Is Logic And What Is It A Product Of?
Logic is an abstract form of reasoning that is based on the model of the Indo-European language grammar. Non I-E languages do not consider, and never developed, logic in the way that it developed in the west.

Logic is a method of formulating thought. It is not a way to prove anthing, except in a theoretical manner. For example, logic could never be used to provide a proof that god exists, because such proof requires axioms, which are beyond the scope of logic.

[dekoi]

Prometheus:
Logic can very much prove something. Proving God does not require axioms; the proofs themselves use logic/reason to build up into a general law (an axiom).

XxFREEofFILTHxX: If God exists, he has defined logic for us. Logic and/or reason, in this case, would be founded on the natural law.

[hypnagogue]

Prometheus:
Logic can very much prove something. Proving God does not require axioms; the proofs themselves use logic/reason to build up into a general law (an axiom).

I think what Prometheus meant to say is that the formal rules of logic alone are not enough to prove anything; we must start with certain premises that we assume to be true (axioms) and manipulate these axioms using the rules of logic to derive further premises. In this regard, Prometheus is quite right. Given no axioms to work with, logic cannot do much of anything, somewhat like a baker cannot do much of anything if he has a recipe but no ingredients.

XxFREEofFILTHxX: If God exists, he has defined logic for us.

This depends on one's definition of God. If the minimal requirements for a God be that it is omnipotent and omniscient, then it's not hard to suppose a kind of omnipotent, omniscient God that has nonetheless not defined logic for us.

Remember that we are talking about an abstract philosophical concept when we use the word 'God.' Perhaps some religions suppose a God who defines logic (whatever that might mean exactly), and in the context of such a religious definition of God your statement would hold. But please keep in mind that PF does not support discussions about God in the context of religion.

[hypnagogue]

XxFREEofFILTHxX, a good introduction to the topic of logic is available on wikipedia.org: http://en.wikipedia.org/wiki/Logic

Please read over this article. It may clear up some lingering confusions you have and help shape any future questions you might have.

[Prometheus]

I think what Prometheus meant to say is that the formal rules of logic alone are not enough to prove anything; ...
Well-phrased.

Prometheus:
Logic can very much prove something. Proving God does not require axioms; the proofs themselves use logic/reason to build up into a general law (an axiom).
Please prove something using logic. You might try proving that god exists, or something simpler. Please indicate how a proof using the rules of logic can prove that anything exists with no axiomatic requirements.

[dekoi]

Prometheus, i must have misunderstood you as Hypnagogue stated.

However, why could axioms not be produced by logic as well? Why do you state they are outside the scope of reason? I can answer this question myself (likely the same answer you will reply with), although it is very vague.


Hypnagogue: imo, i find it very difficult (as well as a professor i know) to express philosophical thoughts regarding an omnipotent power without -- at a latter point -- making a connection with theology. However, i will try :approve:

[cogito]

I think what Prometheus meant to say is that the formal rules of logic alone are not enough to prove anything; we must start with certain premises that we assume to be true (axioms) and manipulate these axioms using the rules of logic to derive further premises. In this regard, Prometheus is quite right. Given no axioms to work with, logic cannot do much of anything, somewhat like a baker cannot do much of anything if he has a recipe but no ingredients.

Not quite. Formal Logic is sufficient for proving all theorems, which by definition can be proven from the empty set of premises. So, it is false that we must start with certain premises merely assumed to be true. We can start with no premises, and derive necessary truths. What is the case is that these theorems are true in any possible world, and hence quite uninformative about the particularities of the actual world (i.e., you can't derive any contingent truths about the actual world).

[Tom Mattson]

Formal Logic is sufficient for proving all theorems, which by definition can be proven from the empty set of premises.

What brand of logic is it that can do this?

Logic, as it is normally understood, consists of rules of valid inferences from one statment to another. How do you reason something from nothing?

[Goongyae]

"Formal Logic is sufficient for proving all theorems, which by definition can be proven from the empty set of premises."

Incorrect, have you not heard of Goedel's theorem? Even in the simple mathematical system of arithmetic it can be demonstrated that there are truths that are impossible to prove.

[cogito]

"Formal Logic is sufficient for proving all theorems, which by definition can be proven from the empty set of premises."

Incorrect, have you not heard of Goedel's theorem? Even in the simple mathematical system of arithmetic it can be demonstrated that there are truths that are impossible to prove.

I'm familiar with both Goedel's incompleteness proof, which proves that all consistent formalizations of number theory will include undecidable propositions (propositions for which the axioms of the system will not allow one to determine their truth-value), and his completeness proof, which proves that first-order predicate calculus is complete and sound. When I used the term 'formal logic', in my original quote, I was referring to first-order predicate calculus (which is what the term 'logic' [in the deductive sense, rather than in, say, a Bayesian inductive sense] almost invariably refers to) and not to extensions of it that require set-theory. I should have been more clear about this, but I'm used to talking about logic with philosophers and not mathematicians. Thanks for keeping me honest! :smile:

[cogito]

What brand of logic is it that can do this?

Logic, as it is normally understood, consists of rules of valid inferences from one statment to another. How do you reason something from nothing?

First-order predicate calculus. You reason from nothing by temporarily assuming some proposition, and seeing what follows from it. You discharge this assumption in various ways. If an assumption leads to a contradiction, then you know that the negation of the assumption is a theorem. If your assumption leads to some conclusion, then you know that the conditional comprised of the assumption as its antecedent and the conclusion as its consequent is a theorem. There are other ways of deriving theorems, but these two methods are very common.

[wuliheron]

1. but how did you conclude these statements?
2. Is logic wrong and full of errors?
3. By what do we conclude what is logic, and what is not?
4. On what is Logic based on?
5. What is proof?

1) Demonstrably, words only have meaning according to their use in a given context. Hence the term logic could be used by someone to refer to a love of chickens, but obviously that is not the context used here. The implied context is the normal uses of the word, which includes both formal and informal logic.

Because all types of logic normally refer to the concept of reason, the foundation of logic is obviously the concept of the absurd because reason has no demonstrable meaning outside the concept of the absurd. That is, the idea that some things are just impossible, undesirable, and meaningless. When analyzed, every form of logic thus far investigated has been based on the principle or axiom of Reductio ad Absurdium.

In turn, the concept of meaningful/meaningless demonstrably arises from our ability to emote. My computer can do endless logical functions flawlessly, but it cannot place logic in any kind of meaningful context. It is an idiot savant which cannot tell the difference between the logical and the irrational.

One famous case study involves a man who lost the ability to emote due to a head trauma. He could not hide his condition for any length of time whatsoever. Like a computer with an incredible number of preset responses, all he had left was his memories of how to respond. Any novelty whatsoever always threw him for a loop (Danger Will Robinson, does not compute!)

2) Logic is a specific type of tool and, as such, is limited by definition. Still, I call a wrench "wrong" or "full of errors" when I attempt to do something with it that it was not designed to do. However I can use it occationally as a hammer or whatever, something it was not really designed to be used as. If I use logic for something it simply cannot do, it is my use of the tool that is "wrong" or "full of errors", not the tool itself.

3) See answer #1

4) Ditto

5) Again, demonstrably words only have meaning according to their function in a given context. Logically speaking, logic cannot be used to prove it's own axioms because this would violate the principle of reductio ad absurdium. Hence, the ultimate proof for logic is whether or not it fits our ideas of the absurd. Whether or not we feel it is absurd.

[dekoi]

If logic requires some sort of earlier premises, would that not cause us to assume there is an original, absolute, and objective truth or premise in everybody?

[hypnagogue]

If logic requires some sort of earlier premises, would that not cause us to assume there is an original, absolute, and objective truth or premise in everybody?

I'm not sure exactly what it would mean for there to be a premise literally residing in a person, let alone an original, absolute, or objective one. That seems to be a poor way to phrase your question.

[Prometheus]

We can start with no premises, and derive necessary truths.
Please provide an example where you start with no premises and then derive some necessary proof, however you want to define necessary.

[Prometheus]

Prometheus, i must have misunderstood you as Hypnagogue stated.
That happens to us all.

However, why could axioms not be produced by logic as well?
Because that is not the way that logic works. Do you know what an axiom is?

Why do you state they are outside the scope of reason?
Please cite where I said that anything is outside the scope of reason, or where I discussed reason at all.

[Prometheus]

If logic requires some sort of earlier premises,
You seem to be unclear as to what logic is and what an axiom is. Nobody, I believe, here said that logic requires earlier premises. As well, that is not a true statement. Why? What do you think that a premise is? It is a word that implies a relationship using logic.

We are talking about axioms. Logic does not require axioms, and has nothing to do with axioms. It is the attempt to apply logic to the real world, to which formal logic does not apply, that requires axioms. As these axioms cannot be applied within the confines of formal logic, logic cannot be applied to the real world as a method of establishing proof.

would that not cause us to assume there is an original, absolute, and objective truth or premise in everybody?
Let me try to be clear about my response to your question. NO.

[cogito]

Please provide an example where you start with no premises and then derive some necessary proof, however you want to define necessary.

OK, here you go.

Notation:

P: some arbitrary proposition
~: negation symbol
v: disjunction symbol
#: contradiction symbol

The numbers in the parentheses on the far left of each line refer to those hypothetical suppositions that are operative. The text in brackets on the right refers to that rule of first-order predicate calculus that allows for what is written on each line of the derivation.

(1) 1. ~(P v ~P) [hypothetical supposition]
(1,2) 2. P [hypothetical supposition]
(1,2) 3. P v ~P [from 2, by disjunction introduction]
(1,2) 4. # [from 1 and 3, by contradiction introduction]
(1) 5. ~P [from 2 and 4, by negation introduction]
(1) 6. P v ~P [from 5, by disjunction introduction]
(1) 7. # [from 1 and 6, by contradiction introduction]
8. ~~(P v ~P) [from 1 and 7, by negation introduction]
9. (P v ~P) [from 8, by negation elimination]

Note what happened on steps 5 and 8 of this derivation. On step 4, I discharged that hypothetical supposition that P. Thus, on step 5, the number "2" no longer appears in the parentheses on the left. This means that the hypothetical supposition introduced on line 2 is no longer operative. On step 7, I discharged the hypothetical supposition that ~(P v ~P). Thus, on step 8, the number "1" no longer appears int he parentheses on the left. This means that the hypothetical supposition introduced on line 1 is no longer operative. The conclusion, the Law of the Excluded Middle, is derived from no premises at all. Any conclusion derivable from no premises is a necessary truth. Hence, the conclusion is a necessary truth. This particular conclusion goes by the name "The Law of the Excluded Middle".

[Les Sleeth]

I Know That Logic Is Limited And That We Are Enslaved In Its Confined Boundaries.

I Would Like To Hear Your Opinions,
My Question's Are:
1. What Is Logic And What Is It A Product Of?
2. Does It Define Things Or Is It Being Defined By Other Higher Things?

Personally, I can't see how whether or not logic proves propositions or produces truth, etc. has anything to do with your questions (although they might be interesting side issues). In my opinion, there are very definite answers to both of your questions.

It is easier to answer the questions in reverse of the order you asked them:

2. Does It [logic] Define Things Or Is It Being Defined By Other Higher Things? This is an good metaphysical question, but we don't need God to decide it (even if some sort of consciousness might be behind order). To decide the metaphysical question all we need to know is whether order is significantly influential in reality, and it is. That is precisely why math can predict certain situations in advance of observing the situation. Human consciousness might be what defined "logic" for communicating about it, but consciousness was merely giving a name to a way reality operates. So ultimately, it was a higher thing, reality, that gave us the order which the logic operations of consciousnes reflect.

1. What Is Logic And What Is It A Product Of? Logic is order embodied in the conscious process of reason. Logic is a product of our consciousness of reality's order.

[Tom Mattson]

First-order predicate calculus. You reason from nothing by temporarily assuming some proposition, and seeing what follows from it.


Perhaps I'm not understanding you, but these two sentences seem to directly contradict each other. I do not see how you can reason from nothing and at the same time reason from an assumed proposition. Is that assumed proposition nothing? Does it come from the empty set of premises?

[Prometheus]

Please provide an example where you start with no premises and then derive some necessary proof, however you want to define necessary.
OK, here you go.

(1) 1. ~(P v ~P) [hypothetical supposition]
(1,2) 2. P [hypothetical supposition]
(1,2) 3. P v ~P [from 2, by disjunction introduction]
(1,2) 4. # [from 1 and 3, by contradiction introduction]
(1) 5. ~P [from 2 and 4, by negation introduction]
(1) 6. P v ~P [from 5, by disjunction introduction]
(1) 7. # [from 1 and 6, by contradiction introduction]
8. ~~(P v ~P) [from 1 and 7, by negation introduction]
9. (P v ~P) [from 8, by negation elimination]



You claim that you have derived a necessary proof, whatever necessary means. Please be so kind as to tell me what you have proven, as I have no idea. It seems that you are attempting to demonstrate a structural relationship, rather than dealing with content. You seem not to have attempted to represent content at all.

I notice that although you claimed to be able to start with no premises, you begin with 2 premises, in both 1 and 2.

Let me ask you some questions. You began as follows, did you not?
Notation:

P: some arbitrary proposition
~: negation symbol
v: disjunction symbol
#: contradiction symbol

Therefore, your very first line begins with a premise, which you offered to do without.

More importantly, your subsequent lines use the concepts of negation, disjunction, and contradiction. Did you define these concepts here? If not, then how can you use them? Are you assuming such concepts as given, or as defined elsewhere? This violates your conditions, as you claimed that you could provide a proof where nothing is accepted as given.

Therefore:
1. You have proved nothing of content, but only of structure.
2. You used terms that were not self-evident or defined herein, thereby violating the condition that you accepted of not requiring anyting as given.

[cogito]

Perhaps I'm not understanding you, but these two sentences seem to directly contradict each other. I do not see how you can reason from nothing and at the same time reason from an assumed proposition. Is that assumed proposition nothing? Does it come from the empty set of premises?

Do understand what a conditional statement is? It is a statement of the form "if X, then Y". Here's an example:

Suppose, hypothetically, that Tom is 6 feet tall. If so, then Tom is taller than all those shorter then 6 feet. So, if Tom is 6 feet tall, then he is taller than all those shorter than 6 feet. Now, does this little argument actually commit me to claiming that Tom is, in fact, 6 feet tall? No, it doesn't. The argument shows one necessary consequence of an assumption, without taking any position on the truth of that assumption. Go look up the truth-tables for conditional statements if you are still confused.

[cogito]

You claim that you have derived a necessary proof, whatever necessary means. Please be so kind as to tell me what you have proven, as I have no idea. It seems that you are attempting to demonstrate a structural relationship, rather than dealing with content. You seem not to have attempted to represent content at all.

I notice that although you claimed to be able to start with no premises, you begin with 2 premises, in both 1 and 2.

Let me ask you some questions. You began as follows, did you not?

Therefore, your very first line begins with a premise, which you offered to do without.

More importantly, your subsequent lines use the concepts of negation, disjunction, and contradiction. Did you define these concepts here? If not, then how can you use them? Are you assuming such concepts as given, or as defined elsewhere? This violates your conditions, as you claimed that you could provide a proof where nothing is accepted as given.

Therefore:
1. You have proved nothing of content, but only of structure.
2. You used terms that were not self-evident or defined herein, thereby violating the condition that you accepted of not requiring anyting as given.

Wow. You've never taken a course in logic, have you? There are no premises in the above argument There are temporary suppositions in sub-proofs that are discharged through the use of the appropriate deductive rules. Here is a tutorial on the subject:

faculty.washington.edu/smcohen/120/Chapter6.pdf

In the argument provided, the truth of the conclusion does not depend on the truth of any of those temporary suppositions. What the proof shows is that if a certain statement is true, then it leads to a contradiction just by virtue of its syntactic structure. Hence, the negation of that statement is true just in virtue of its syntactic structure. Hence, any statement that has that syntactic structure is true. Hence the conclusion of the argument is necessarily true.

Now, the conclusion of the argument, expressed in English, is that any proposition is either true or not true. Hardly informative, I know. This is why I claimed earlier that logic doesn't tell us interesting stuff about the world. By itself, all logic can do is establish truths that hold in every possible world; it cannot establish anything idiosyncratic or contingent about any particular world.

Yes, I've used the rules of deduction in the proof above. Are you claiming that the rules of deduction are premises to the above argument? If so, then you are using 'premise' in a completely different way than anybody who has studied formal logic. If you equate rules with premises, then you will be committed to the claim that proofs are impossible to construct, as they would require an infinite number of lines. For more information on this consequence of your equating rules to premises, please look up "Carroll’s Paradox ".

[Prometheus]

Dude, take a course on the subject. :smile:
Dude, what a quaint word.

Your proof proves nothing at all in the sense that I am speaking. Your proof proves that within the rules of logic there are relationships of logic. How incredibly wonderful of you. I said that logic can prove nothing in the real world, and you attempt to prove that relationships of logic can be proven.

Take a look at any of my posts in this thread before you came along with this. I said that logic cannot be used to prove anything in the real world. Your example is off that topic.

[Tom Mattson]

Do understand what a conditional statement is?


Yes, and I understand your symbolic proof, and I understand truth tables. What I am not understanding from your previous discussion is how you can derive necessary truths from an empty set of premises.

When you say, "There are no premises in the above argument,", it begs the question: Why don't you consider your "hypothetical suppositions" premises?

[cogito]

Dude, what a quaint word.

Your proof proves nothing at all in the sense that I am speaking. Your proof proves that within the rules of logic there are relationships of logic. How incredibly wonderful of you. I said that logic can prove nothing in the real world, and you attempt to prove that relationships of logic can be proven.

Take a look at any of my posts in this thread before you came along with this. I said that logic cannot be used to prove anything in the real world. Your example is off that topic.


Your claim is false. The above proof proves that a proposition must be either true or false. That applies to every world, including the real one.

[cogito]

Yes, and I understand your symbolic proof, and I understand truth tables. What I am not understanding from your previous discussion is how you can derive necessary truths from an empty set of premises.

When you say, "There are no premises in the above argument,", it begs the question: Why don't you consider your "hypothetical suppositions" premises?

Hypothetical suppositions are not premises because their actual truth value has nothing to do with the proof. The premises of an argument are such that their actual truth value is essential to the establishment of the argument's conclusion. Again, take the example of a conditional proof. A conditional proof starts by saying "Let's see what would follow if P was true. Now, if P was true, Q would follow. So, we know that the conditional claim if P, then Q is true, regardless of whether P is, in fact, true".

Hypothetical suppositions are agnostic as to the actual truth value of what is supposed, whereas premises are declarations that some statement has a particular truth value. When, in formal logic, a hypothetical supposition is discharged, it is thereby shown that the truth of the conclusion does not rest upon that supposition.

[Les Sleeth]

Hypothetical suppositions are not premises because their actual truth value has nothing to do with the proof. The premises of an argument are such that their actual truth value is essential to the establishment of the argument's conclusion. Again, take the example of a conditional proof. A conditional proof starts by saying "Let's see what would follow if P was true. Now, if P was true, Q would follow. So, we know that the conditional claim if P, then Q is true, regardless of whether P is, in fact, true".

Hypothetical suppositions are agnostic as to the actual truth value of what is supposed, whereas premises are declarations that some statement has a particular truth value. When, in formal logic, a hypothetical supposition is discharged, it is thereby shown that the truth of the conclusion does not rest upon that supposition.

I don't want to put words in Prometheus' mouth, but I understood his statement about logic not producing proof as meaning it doesn't produce proof about external reality. Everybody knows one can produce a proof within the system of logic, but all it tells you is if the logic is correct. Logic without empirical data really can prove nothing about external reality, just as Prometheus said.

[Prometheus]

Your claim is false.
Which claim are you referring to?

The above proof proves that a proposition must be either true or false.
This is not true at all, or, if true, it is not meaningful. Propositions are based on words, and whether the words are true or false in the context of logic, they cannot be used to provide a definitive, objective proof about the real world.

That applies to every world, including the real one.
Then I ask you again. Please use your logic example, or another example, to prove on the basis of logic that something exists in the real world. In the example originally provided, for example, you might try to use logic to prove that god does, or does not, exist.

[Tom Mattson]

Cogito, it is certainly the case that we are using two different definitions of the word "premise". In the logic textbook to which I am referring (Logic by Robert Baum), the term "premise" is used to describe not only particular statements, but also schemata whose truth values are unspecified. If you are using the term "premise" to refer exclusively to statements whose truth values are determinate, then that's fine. I just want to get it straight that that's what you mean.

But even so, there are some unresolved points of confusion here.

Hypothetical suppositions are not premises


Well, they certainly do not come from the empty set of premises.

Your initial claim was:

"Formal Logic is sufficient for proving all theorems, which by definition can be proven from the empty set of premises."

You were asked for an example, but you have not delivered.


because their actual truth value has nothing to do with the proof.


Doesn't it? Your conclusion is certainly analytically true, but had you not started with a prem---...errr....hypothetical supposition that was analytically false, you would not have arrived at that conclusion.

[Prometheus]

The premises of an argument are such that their actual truth value is essential to the establishment of the argument's conclusion.
Perhaps you might enlighten me about a point in logic that is unclear to me. Consider the following:

All blees are blahs
All blahs are blips
Therefore: All blees are blips

I am under the impression that the conclusion is true, given the premises, and that the real life truth value of the premises is irrelevant to the value of this logic. Are you saying that if it is not true that all blees are blahs in real life, then the logic is flawed?

[Prometheus]

I don't want to put words in Prometheus' mouth, but
Thanks. This is my point.

[Tom Mattson]

Perhaps you might enlighten me about a point in logic that is unclear to me. Consider the following:

All blees are blahs
All blahs are blips
Therefore: All blees are blips

I am under the impression that the conclusion is true, given the premises, and that the real life truth value of the premises is irrelevant to the value of this logic.


But you can't have it both ways. Either the premises are given (as true), or they are not. There's no difference between "the truth value" and "the real life truth value".

But in any case, the truth value of any proposition is irrelevant to the validity of any logic. Deductively valid arguments can have false conclusions, provided that at least one premise is false.


Are you saying that if it is not true that all blees are blahs in real life, then the logic is flawed?

I think you need to look at cogito's symbolic proof again. The conclusion of that argument is a tautology, meaning that there is no possible instantiation of that schema that can render its truth value false.

While it may be the case that "All blees are blips" is false, it is certainly the case that "All blees are blips or all blees are not blips" is true.

But as I said, you can only "prove" a tautology if you start with a contradiction. I don't question the validity of cogito's proof, but I do question his claim that he can prove something from nothing.

[Prometheus]

But in any case, the truth value of any proposition is irrelevant to the validity of any logic. Deductively valid arguments can have false conclusions, provided that at least one premise is false.
I agree, and this is my point.

But you can't have it both ways. Either the premises are given (as true), or they are not. There's no difference between "the truth value" and "the real life truth value".
I don't want it both ways. Given the premise that all blees are blahs, it is possible to use logic. However, the truth value in real life is irrelevant. In other words, it is not significant to logic whether or not this statement has any truth value in real life. As for truth value at all, that is irrelevant. If this proposition is made, then it is assumed to be true for the purposes of the argument, and for the purposes of the logical argument there is no meaning in questioning whether it might be false in some real world test.

[Tom Mattson]

I agree, and this is my point.


OK


I don't want it both ways. Given the premise that all blees are blahs, it is possible to use logic. However, the truth value in real life is irrelevant. In other words, it is not significant to logic whether or not this statement has any truth value in real life. As for truth value at all, that is irrelevant. If this proposition is made, then it is assumed to be true for the purposes of the argument, and for the purposes of the logical argument there is no meaning in questioning whether it might be false in some real world test.

Right, but one of cogito's points is that his conclusion (unlike yours) is necessarily true. In other words, it is not possible for any statement of the form P V ~P to be false, no matter what statement you insert for the logical variable P. On the other hand, the conclusion of your syllogism is contingent.

[Prometheus]

Right, but one of cogito's points is that his conclusion (unlike yours) is necessarily true. In other words, it is not possible for any statement of the form P V ~P to be false, no matter what statement you insert for the logical variable P. On the other hand, the conclusion of your syllogism is contingent.
I have no problem with that. I am still thinking from the standpoint that what he has presented has no ability to demonstrate proofs about the real world. It is an interesting game with words, but that is what I accepted as given at the beginning of this thread. Can he use this to prove that, for example, god exists or does not exist? My goal is not to challenge the tenets of logic, nor to debate it, but to discuss its limitations.

[Tom Mattson]

I have no problem with that. I am still thinking from the standpoint that what he has presented has no ability to demonstrate proofs about the real world.


But he already admitted that he can't do that.


What is the case is that these theorems are true in any possible world, and hence quite uninformative about the particularities of the actual world (i.e., you can't derive any contingent truths about the actual world).


The way I see it, the only issue still in dispute is the "something from nothing" claim.

[Prometheus]

But he already admitted that he can't do that.
Then I guess that there never was any real disagreement, although it seemed so.

[cogito]

I don't want to put words in Prometheus' mouth, but I understood his statement about logic not producing proof as meaning it doesn't produce proof about external reality. Everybody knows one can produce a proof within the system of logic, but all it tells you is if the logic is correct. Logic without empirical data really can prove nothing about external reality, just as Prometheus said.

And, again, that claim is false. The Law of the Excluded middle applies to external reality. Hence, a proof of the Law of the Excluded Middle proves something about external reality.

[cogito]

Which claim are you referring to?


This is not true at all, or, if true, it is not meaningful. Propositions are based on words, and whether the words are true or false in the context of logic, they cannot be used to provide a definitive, objective proof about the real world.


Then I ask you again. Please use your logic example, or another example, to prove on the basis of logic that something exists in the real world. In the example originally provided, for example, you might try to use logic to prove that god does, or does not, exist.


I am referring to your claim about logic not being able to prove anything about the world. The Law of the Excuded Middle applies to the world, hence your claim is false.

Now you seem to be changing what you were asking for. Now you want to a proof that not only applies to the actual world, but a proof that something exists in the actual world. Not all claims that describe the actual world are claims concerning what exists in the actual world. For instance, the claim "For all X, X is identical to itself", describes every world, including the actual, but it is silent on what exists in the actual world.

I will provide a proof that shows that something exists (though it'll involve quantifiers, which I'm not sure you are familiar with), if you admit that the proof I provided earlier describes the actual world. I'll not play a game with you wherein I refute one of your claim just to have you aver that you were claiming something else all along.

As far as a proof of God goes, Kant already proved it is impossible to proof that God exists, and impossible to prove that God doesn't exist.

[cogito]

Cogito, it is certainly the case that we are using two different definitions of the word "premise". In the logic textbook to which I am referring (Logic by Robert Baum), the term "premise" is used to describe not only particular statements, but also schemata whose truth values are unspecified. If you are using the term "premise" to refer exclusively to statements whose truth values are determinate, then that's fine. I just want to get it straight that that's what you mean.

No, I am not using 'premise' to refer only to statements with determinate truth values. A premise may have a indeterminate truth value (e.g., the measurement will be "spin-up", Tom will drink a beer tomorrow, etc.). A hypothetical supposition may have a determinate truth value (e.g. (P & ~P)). The distinction I'm drawing is a different one. Premises are suppositions that are not discharged in the course of the proof. The conclusion relies on them in that it is the assumption of their truth that allows the derivation of the conclusion. When a conclusion is derived from a hypothetical supposition that is discharged, it means that regardless of the truth of the hypothetical supposition, the conclusion follows. It means that it doesn't matter if the hypothetical supposition is actually true, because the conclusion doesn't rely for its justification on supposition's being true. In your logic book, look up the use of subproofs, or the use of conditional proofs, and let me know what you find. It could be that this is just a difference of terminology.



Well, they certainly do not come from the empty set of premises.

Your initial claim was:

"Formal Logic is sufficient for proving all theorems, which by definition can be proven from the empty set of premises."

You were asked for an example, but you have not delivered.

Since they are not premises, the proof follows from no premises. Hence, the proof follows from the empty set of premises. No premises = Empty set of premises. Of course suppositions were used, but these were discharged. Rules of inference were used as well, but these aren't premises, and claiming that they are leads to Carroll's Paradox, which leads immediately to wholesale skepticism.



Doesn't it? Your conclusion is certainly analytically true, but had you not started with a prem---...errr....hypothetical supposition that was analytically false, you would not have arrived at that conclusion.

Yep, it's called an indirect proof, or reductio ad absurdum. You can't work an indirect proof from no premises unless you start with the negation of a theorem.

[Les Sleeth]

And, again, that claim is false. The Law of the Excluded middle applies to external reality. Hence, a proof of the Law of the Excluded Middle proves something about external reality.

First, thanks for the logic demonstration, I reread everything you wrote, saw your point, and realized I regularly rely on hypothetical suppositions. Good stuff.

I'll nitpick on your above point however regarding what logic tells us about external reality. Wouldn't you say that to recognize A is either A or not A is a general truth about external reality derived from experience? If we were mere brains in a jar, just exchanging ideas and never experiencing external reality, then we really would not know if Tom could both be 6 feet and not 6 feet. As far as we would know, Tom might simultaneously exist in two modes which walk around at 6' and 4' so that Tom really is both 6' and not 6' (and how about Schrodinger's cat???? :wink:).

So logic hasn't revealed anything by itself about external reality; generalized experience first established how reality works, and from that we inferred a general principle of logic which we can use without looking at reality again, or so we assume.

The reason we can assume that relates back to my original post about logic being order embodied in the conscious process of reason, and a product of our consciousness of reality's order. If we weren't able to count on reality operating consistently, then we also couldn't assume order would prevail and that logic could be relied on without fresh observation.

[Prometheus]

I am referring to your claim about logic not being able to prove anything about the world. The Law of the Excuded Middle applies to the world, hence your claim is false.
My original point was that logic could not be used to prove existence in the real world, such as the existence of god. I would also accept the existence of trees or whatever. You jumped in the middle of this thread with your statements, leading off on a tangent. I accept you arguments about logic having rules that describe the structure of logic.

For instance, the claim "For all X, X is identical to itself", describes every world, including the actual
Using the logic that you describe, I will accept "For all X, X is identical to itself" as being true. However, I still completely fail to find any real world value to this statement. Are you saying that this statement by itself proves something about the real world, or are you saying that you can substitute X with a substitution that will prove something about the real world? I am not sure what you suggest that this statement proves, and as I see it, it proves nothing.

I will provide a proof that shows that something exists (though it'll involve quantifiers, which I'm not sure you are familiar with), if you admit that the proof I provided earlier describes the actual world. No to both.

As far as a proof of God goes, Kant already proved it is impossible to proof that God exists, and impossible to prove that God doesn't exist.
I do not believe you. Kant cannot have proven this. You are leaving out the context for his proof in your statement.

[XxFREEofFILTHxX]

If we need axiomic requirements for logic, then if axioms are based on false asumptions then what good is logic? Moreover, how do we know if axioms are true, and how do you prove them to be true, or what system do we use to back these asumptions up with? you would have to base it off previous axioms and logicical theories which derived from axioms and logic itself. Because it was clearly said you cant base things off nothing, so what did reason start with?
so what i mean to ask is what is the first asumption which we base our entire system off of?

[Prometheus]

If we need axiomic requirements for logic,
Axioms are not only not required for logic, they are not appropriate. It is for this reason that logic is not appropriate to the real world. Logic is a method of establishing relationships. In order to map this to the real world, axioms are applied. The appropriateness of the logic is then dependent upon the value of the axioms. It is for this reason that logic cannot be used to prove the existence of god, for example, because the axioms cannot be proven. Logic can only say that if we accept such and such as axiomatic, we can then use logic to "prove" that god does/does not exist.

if axioms are based on false asumptions then what good is logic?
Logic is about structure, not about content.

Moreover, how do we know if axioms are true, and how do you prove them to be true,
By defiinition, we don't and we don't.

[Les Sleeth]

I do not believe you. Kant cannot have proven this. You are leaving out the context for his proof in your statement.

Whether you accept Kant's argument or not, it has been well demonstrated that trying to use logic to confirm or disprove the existence of God is a colossal waste of time. It is the same problem found with two people arguing if a mountain exists which neither of them have seen. The argument inevitably become circular, and nothing is ever resolved until each goes to where the mountain is supposed to be and looks. And then guess what, the argument ends instantly. Either the mountain is there or the mountain isn't. This is exactly what those thinkers realized who started advocating empiricism. Experience and know, that's what we've discovered works.

[Les Sleeth]

Because it was clearly said you cant base things off nothing, so what did reason start with?
so what i mean to ask is what is the first asumption which we base our entire system off of?

I say it is experience. That is the source of everything real (i.e., conceptually corresponding to reality) we are reasoning with. Think about it, if you had absolutely NO experience of reality . . . no sights, sounds, smells, feelings . . . and were confined strictly to what you could think, you'd have noticed no trends from which you could generalize to form principles. (Actually we have evidence of this in children who were deprived of experience from being locked in a closet, or something similar.)

[Prometheus]

Whether you accept Kant's argument or not, it has been well demonstrated that trying to use logic to confirm or disprove the existence of God is a colossal waste of time.
I never said that I have any problem with Kant's argument. I quite agree that logic cannot prove the existence of god. In fact, I made this very point in my first post of this thread.

What I did not buy is cogito's phraseology, wherein he claimed that Kant made a proof without including the context, which you supplied, of logic.

[SlySpy]

How could you refute the law of non-contradiction :confused:

And what about this syllogism:

1. An omnipotent being exists
2. This being can create a rock heavier than it can lift (from 1)
3. This being can lift any rock it creates (from 1)
Cl. An omnipotent being cannot exist (from 2 and 3 via contradiction)

This way, by supposing a proposition that does not have to relate to the observed world is it not possible to formulate a negative conclusion about the world?

[wuliheron]

How could you refute the law of non-contradiction :confused:

And what about this syllogism:

1. An omnipotent being exists
2. This being can create a rock heavier than it can lift (from 1)
3. This being can lift any rock it creates (from 1)
Cl. An omnipotent being cannot exist (from 2 and 3 via contradiction)

This way, by supposing a proposition that does not have to relate to the observed world is it not possible to formulate a negative conclusion about the world?

Check out Fuzzy Logics and Neutrosophy. Fuzzy logic allows for multiple truth values and has proven applications in the real world. Neutrosophy adds a third catagory of Indeterminate.

[Les Sleeth]

How could you refute the law of non-contradiction :confused:

And what about this syllogism:

1. An omnipotent being exists
2. This being can create a rock heavier than it can lift (from 1)
3. This being can lift any rock it creates (from 1)
Cl. An omnipotent being cannot exist (from 2 and 3 via contradiction)

This way, by supposing a proposition that does not have to relate to the observed world is it not possible to formulate a negative conclusion about the world?

While I wrote my answer, I see Wuli said some of it, but here it is anyway.

I don't want to challenge the law of non-contradiction, but I will challenge the assumptions used in that syllogism, which I've seen many times, to show how while you’ve demonstrated impeccable logic, you’ve said nothing conclusive about the “world” other than what the syllogism assumes in the first place (the truth of non-contradiction).

To be omnipotent means to be in possession of all the power there is. However, it doesn't tell us if there is a finite or an infinite amount of power to be in possession of; also, all-powerful doesn't mean “omni-capable,” i.e., that the omnipotent being can do anything it wants (analogously, a powerful weightlifter isn't necessarily intelligent).

We know a lot of "power" is packed into matter, so it follows that the omnipotent being uses power to create the rock. If the pool of power being drawn from is finite, then the rock could get so big at some point that the power used up creating the rock doesn't leave enough for lifting, and so an omnipotent being in a finite power pool could create a rock that was not liftable. If, on the other hand, the pool of power being drawn from is infinite, then the rock could never get so big that there wasn't enough power left to lift the rock, and in that case the omnipotent being could not create a rock that was not liftable.

Thus we can see that we can’t draw conclusions about reality without sufficient facts, and facts are given to us by experience. As I pointed out before, we couldn’t even assume non-contradiction if we’d not observed reality behaving that way.

[SlySpy]

Check out Fuzzy Logics and Neutrosophy. Fuzzy logic allows for multiple truth values and has proven applications in the real world. Neutrosophy adds a third catagory of Indeterminate.
I am aware of fuzzy logic, but I'll have to look into neutrosophy. And even then, wouldn't an argument refuting the law of non-contradiction require that very law? If you could, can you show me an example where this can be done without relying on the law of non-contradiction (to be consistent.)

[wuliheron]

I am aware of fuzzy logic, but I'll have to look into neutrosophy. And even then, wouldn't an argument refuting the law of non-contradiction require that very law? If you could, can you show me an example where this can be done without relying on the law of non-contradiction (to be consistent.)

Every type of logic is based on reductio ad absurdium, reduction to the absurd. Even the law of noncontradiction is based on this principle. However, at one time people considered the idea that the earth is round absurd. The only way around this problem is to use emperical evidence to prove or disprove such logical axioms.

There are numerous examples of logics that work in the real world, and all of them incorporate variations on the law of noncontradiction. As occured with the advent of quantum mechanics we can protest all we want and claim it makes no sense whatsoever, but there will always be Neil's Bhor around to remind us to "Shut up and calculate". :tongue2:

[Mazuz]

Truth is always relative. Existence is always relative. I exist relatively to this world as this world exists relatively to me.

[Rainer]

Every type of logic is based on reductio ad absurdium, reduction to the absurd. Even the law of noncontradiction is based on this principle.

Not every type.

Forgive me if I am mistaken, but I believe it is the Law of Non-contradiction that lets Reductio ad Absurdum function.

This is how it works in my mind: When you show that a hypothesis's or premise's implication is absurd, (or, according to the Greek version, "impossible") you are using a short-hand version that subsumes more fundamental rules: such as the Law of Non-contradiction, and most fundamentally, the Law of Identity.

For example, you show that the ultimate conclusion of a axiom/premise is absurd and then you say that it is false; this is the process of Reductio ad Absurdum. This jump covers the Law of Non-contradiction, which says that contradiction cannot exist in the same respect and at the same time. Which is only valid because A = A.

Could you mean that Reductio ad Absurdum is a far more common kind of logic? And because it is deductive in nature, it is often the basis for more complex logic...ya? Or have I missed something?


1. What Is Logic And What Is It A Product Of?
2. Does It Define Things Or Is It Being Defined By Other Higher Things?

1. Logic is noncontradictory identification of percepts and conceptual units.

Reason is cognitive effort--logic is the process.

2. Neither. Both options assume that reality is subjective--an asssumption without basis; an assumption that never will have a basis. Reality is objective.

As far as a proof of God goes, Kant already proved it is impossible to proof that God exists, and impossible to prove that God doesn't exist.

And Kant is a fool, imbecile, idiot, and wrong--all at the same time and in the same respect.

I am referring to your claim about logic not being able to prove anything about the world. The Law of the Excuded Middle applies to the world, hence your claim is false.

The Law of the Excluded Middle does not refute the analytic-synthetic distinction--which is what Prometheus is asking you to refute.

[cogito]

Every type of logic is based on reductio ad absurdium, reduction to the absurd. Even the law of noncontradiction is based on this principle.

This is false. Without the Law of Non-contradiction, Reductio ad Absurdum wouldn't establish anything. The final line of any Reductio is an explicit contradiction, something of the form (P & ~P). This wouldn't be sufficient for proving the negation of the assumption leading to the contradiction unless the Law of Non-Contradiction held.

[cogito]

And Kant is a fool, imbecile, idiot, and wrong--all at the same time and in the same respect.

That is a fabulous argument! Thanks!

The Law of the Excluded Middle does not refute the analytic-synthetic distinction--which is what Prometheus is asking you to refute.

You should go back and re-read this thread. Earlier, I claimed the following:

...logic doesn't tell us interesting stuff about the world. By itself, all logic can do is establish truths that hold in every possible world; it cannot establish anything idiosyncratic or contingent about any particular world.

The claim of mine that you quote says merely that the Law of the Excluded Middle (and, by extension, logic itself) tells us about the actual world. My claim is still true, as not all facts about the actual world are contingent.

Cheers!

[Rainer]

You should go back and re-read this thread. Earlier, I claimed the following:

Whoa there! I didn't say anything about your case; I only spoke on Prometheus's case. He wants to know if logic can show us anything meaningful and worthwhile about the world, his case is that it doesn't.

I would need to hear a few more thoughts from you before I comment on your case...so far I am pretty sure I agree with it.... If you read my verbose explanation in response to wuliheron you'd see that we agree in regard to Reductio ad Absurdum.

...logic doesn't tell us interesting stuff about the world. By itself, all logic can do is establish truths that hold in every possible world; it cannot establish anything idiosyncratic or contingent about any particular world.

Such as the Law of Identity?

[XxFREEofFILTHxX]

For shure we cannot prove nothing then,
we cannot prove if God exists or doesnt exist so we are all in a stalemate.
If you can do any then, P R O V E IT!

which none will do...............

phylosophers didnt do it then and we cannot do it now.

[XxFREEofFILTHxX]

Quote:
Originally Posted by cogito
As far as a proof of God goes, Kant already proved it is impossible to proof that God exists, and impossible to prove that God doesn't exist.



And Kant is a fool, imbecile, idiot, and wrong--all at the same time and in the same respect.


RAINER is even far more an idiot for not realizing this.......hahaaha.

IF YOUR NOT AN IDIOT THEN PROVE IT SO THAT WE MAY ALL SEE....

BUT I COMPLETELY DOUBT THAT YOU WILL EVEN CONVINCE YOURSELF BECAUSE YOU KNOW WELL THAT IN YOUR OWN MIND THAT NOONE HAS DONE SO.

[wuliheron]

This is false. Without the Law of Non-contradiction, Reductio ad Absurdum wouldn't establish anything. The final line of any Reductio is an explicit contradiction, something of the form (P & ~P). This wouldn't be sufficient for proving the negation of the assumption leading to the contradiction unless the Law of Non-Contradiction held.

Words only have demonstrable meaning according to their function in a given context. This is not simply an opinion, but an emperical fact. In addition, what various cultures and individuals believe to be absurd differs.

Again, there is more than one kind of logic, and more than one kind of logic that has emperically established applications in the real world. The statement that only those which incorporate the law of the excluded middle are valid is, by it's own standards, a reductio ad absurdium argument rather than an emperical fact or any kind of verification of the universality of the law of non-contradiction.

[Tom Mattson]

Again, there is more than one kind of logic, and more than one kind of logic that has emperically established applications in the real world. The statement that only those which incorporate the law of the excluded middle are valid is, by it's own standards, a reductio ad absurdium argument rather than an emperical fact or any kind of verification of the universality of the law of non-contradiction.

I didn't think we were talking about all the different kinds of logic. I thought we were talking about Aristotelian logic, which you have repeatedly claimed is based on reductio ad absurdum. Of course, this is not the case: reductio is possible within Aristotle's logic because of the rules of that system, as cogito said.

[Rainer]

Again, there is more than one kind of logic, and more than one kind of logic that has emperically established applications in the real world. The statement that only those which incorporate the law of the excluded middle are valid is, by it's own standards, a reductio ad absurdium argument rather than an emperical fact or any kind of verification of the universality of the law of non-contradiction.

No one has claimed Aristotelian logic as being the only valid form of logic.

Every type of logic is based on reductio ad absurdium,

We were addressing this statement. This is incorrect, as we've explained: Not every type of logic relies on it. As you can see, there is logic that does not require Reductio as its foundation.

For shure we cannot prove nothing then,
we cannot prove if God exists or doesnt exist so we are all in a stalemate.

Nothing is a concept without meaning. It is merely a relational concept--we know what existence is, and its opposite is nonexistence; this is sufficient when working with the non-existence of things.

All we need is to establish the rules in which existence is possible, and then apply those rules to understand what can and cannot exist.

We are not in a stalemate at all. One can prove that God does not exist quite easily. However, it is pointless to do so for those who rest entirely on dogma--such as Kant followers and religious folks.

IF YOUR NOT AN IDIOT THEN PROVE IT SO THAT WE MAY ALL SEE....

Existence is primary to consciousness; and as a corollary fact, all existents must possess idenity--things with identity have definite qualities and quantities. God has indefinite quantities (being infinite in every quality; omnipotence, omniscience, etc.), therefore God fails to meet the most basic requirement for an existent: Identity.... Essentially, God is not an existent.

That is the short hand version--you need to think about it for a day or two. If you come back with a response that seems to have completely ignored one word of what I said up there, I will point it out--it will be a sufficient response. But, if you want me to clarify a particular point, I will.

[wuliheron]

No one has claimed Aristotelian logic as being the only valid form of logic.

We were addressing this statement. This is incorrect according to the cases we've shown you: Not every type of logic relies on it. As you can see, there is logic that does not require Reductio.

Please present an example of a logic that does not incorporate reductio ad absurdium. Even the case of Aristotles logic, he formulated the law of the excluded middle using reductio ad absurdium arguments. Such were common for centuries before the first formal logic of Aristotle was conceived.

[Rainer]

All I said was that Reductio was NOT the basis of one type of logic!

I didn't say that it didn't incorporate Reductio arguments!

The Law of the Excluded middle was not formulated via Reductio. Think of Reductio ad Absurdum being an application of Aristotle's laws.

(An yes, chronologically Reductio ad Absurdum was a favorite game on the intellectual playground for years before Aristotle was born--but technically it didn't have a formal justification until after Aristotle; without such a formal justification of the Reductio ab Absurdum argument with Aristotle's basic laws of logic, Reductio could not technically be taken as serious.)

[wuliheron]

You need to study the history of philosophy more. Before Aristotle there was no such thing as formal logic, and reductio ad absurdium was routinely used as a formal proof. In fact, it was the entire foundation of Aristotle's formal logic.

http://www.iep.utm.edu/r/reductio.htm

In addition, every kind of formal logic incorporates some variation of the excluded middle, thus they are all founded ultimately upon reductio ad absurdium.

Where did you think formal logic and the excluded middle came from? Under a cabbage patch? Why do you think people still use them? Just because they are internally self-consistent?

[hypnagogue]

I have decided to split the extended discussion between Les Sleeth and Rainer that was originally developed in this thread into a new thread called Synthetic and Analytic Logic (http://www.physicsforums.com/showthread.php?t=50300).

(Unfortunately, it was pretty much impossible to split into a separate thread without having some of the discussion directly pertinent to this thread spilling over into it. But for the most part the new thread deals with a more or less independent topic.)

[kouga]

XxFREEofFILTHxX, a good introduction to the topic of logic is available on wikipedia.org: http://en.wikipedia.org/wiki/Logic

Please read over this article. It may clear up some lingering confusions you have and help shape any future questions you might have.
this does clear up the question of what logic is but brings a question of, what knowledge do we have and how do extend it??

[Rainer]

what knowledge do we have and how do extend it??

Epistemology, Induction. Not Logic.

[Dayle Record]

Logic's beginning, was the beginning of the end of purely impulsive human behavior. Logic was the beginning of human self programming, that allowed more sophisticated survival skills, to evolve, delay of gratification, tool making, planning, sharing, storing. Without logic, none of these things would have superseded time present impulsive behavior. Development of logic, coincided with the first understanding of time, past and future. The if implies the future, the then implies the past. The birth of logic, the arising of the moment wherein circumstance does not dictate immediate behavior, was a singularity of sorts.

Perhaps this happened when humans on the sidelines of emotionally charged events, had to make survival choices. This could come witnessing the killing of a parent, or spouse, or child, when a human flees a scene, over coming the impulse to fight for the life of a beloved in a hopelessly mortal situation; or perhaps the exact opposite happened. Perhaps the human overcomes all urge to flee, and stands and struggles for a clan member. Perhaps this occurred in procuring a mate, realizing that trying to overcome a more successful rival physically, would possibly have negative result. Fear of death overcomes impulse.

Logic is an accounting procedure, weighing right and left brain information, the sensed and the intuited, the known, and the desired, the unknown and the emotional response to the unknown, memory and its projection on new information.

Logic is one of the differentiators between sentience and non sentience. Lots of animals use logic on a daily basis, not only humans.

[QI]

ok Logic is a descriptive term meaning a process or steps thats leads us from A to D, visiting B and C on the way.

The Trip from A to D might start as just that. "If that is true, Then this also must be true" we mave have no greater understanding that this intuition.

ie "If the speed of Light is constant then time must vary" I was 13 when this hit me in a physics lesson .. It was only 13 years later on that I began to undestand why it was true.

The understanding is us defineing the logical steps to get from A to D where we find that er have had to visit B and C on the way.

so with my understanding above,

1, We define the logic to something that we are tring to understand. It is a product of our own attempt to understand our own thought processes
Logic is then used to teach these steps to others.

Every set of data as numerous interpritations and understandings there for more than one logic can be applied to the same senario.

2, We define the original logic there all other login that is generated by clever math or lateral thinking is also defined by us . was we have limited our view point to a bound set of logic formerly created by us.

If we could say that there were only one logicl answer to a question then the answer defines the logical path from teh question to the answer. As there is no such thing as a 100% accurate answer then it is purely based on our own interpritation.


ok so I rambled a bit. but that can be me at times.

2,

[juju]

Hi,

Logic without intuition is sterile, intuition without rationality is futile.

juju

[Thor]

The laws of nature are absolute and inviolate. They are realities governed by the attributes of everything which exists.

Logic is the interpretation of those laws. The process of logic evaluates reality within the parameters of three basic criteria - quality, quantity and dimension (relative position and configuration). By observing, defining and comparing the nature of that which we seek to understand, we derive knowledge which can be applied to familiar circumstances to predict the outcomes of the processes within those circumstances. When valid logic is used to simultaneously consider all known variables, it generates conclusions which fit all of the parameters of our observations.

Logic is; however, only a derivative - a derivative of reality. As in calculus, when you integrate a derivative or 'differential' equation an instance of definition is lost and the result always includes an arbitrary constant - an unknown factor without which the original values cannot be determined.

Logic is a vital tool in understanding the nature of existence, but it is imperfect. It requires definition. Concepts such as infinity are undefined and beyond the realm of reason, and when logic is used to solve the riddles of reality, it invariably leaves behind an unknown arbitrary constant.

There may be facets of reality which are undefined and beyond the realm of logic, but they are not CONTRARY to it. That which is contrary to *logic is false.

[Philocrat]

I Know That Logic Is Limited And That We Are Enslaved In Its Confined Boundaries.

I Would Like To Hear Your Opinions,
My Question's Are:
1. What Is Logic And What Is It A Product Of?
2. Does It Define Things Or Is It Being Defined By Other Higher Things?

Let me make it easier for you. Logic exists because 'SEQUENTIALISM' and SIMULTANEITY' are, and have always been, at war. I call this 'CAUSAL RELATIONAL WAR'. You end this war, and Logic (like magic) everporates with it! As I have made it clear elsewhere, reconciling sequentialism with simultaneity would be one of the greatest human achievments in every known intellectual descipline. In computer science, there has always been this illusive assumption that when you get a computer to do many things at once, that you are in real terms undermining sequentialism and helping simultaniety to win this causal relational war. Well, this is not true. Even with the use of parallel computers, this is still not true.

The fact that you use superfast computers to reduce the number of logical steps in a procdure or event from more to less, can infact create an illusion that sequences of logical steps needed to complete a given task is being actually eliminated from the steps. The fact is that some of the things that appear as being done at once are actually being done sequentially, it is the speed of the computer that creates the illusion of simultaneity.

Ok, a parallel computer may in actuality reduce the number of logical steps in a single formula from 200 steps to say 10 steps, through simultaneous multi-processing capability, but my investigation of this shows that it is naturally impossible (at least for the time being) to completely eliminate sequentialism from the process.

So, logic reliance on sequentialism creates what is known in science as spatio-temporal histories on the causal pathways of things and events. When things and events on their causal pathways get intertwined, they create complicated logical pathways and spatio-temporal histories that may require a combination of sequential and simultaneous steps to fully account for.

[Philocrat]

There is also the problem of OPPOSITES. Logic also relies on the existence of oppisite things and events. This is what creates logical and cuasal pathways along with their spatio-temporal histories in the first place. You must have heard of such terminologies or notions as 'beginning and end', open and close, 'this or/and that', 'me or/and you' 'them or/and us' 'from here to there' and so on. Well, these are the logic creators. They make logic! However, sequentialism does not permit true opposites to share the same space both in logical space and in the real world. I use the term 'TRUE OPPOSITES' advisedly, because there are so many things that naturally appear opposed to each other that in actuality are not. We naively declare and asign oppsite terms to things that often have clear and accountable middle terms. In such cases, poeple naively rush to actioning those things, forgetting about their similarities which may render their natural differences non-opposive and irrelevant.

What I also found out is that in making judgements about what is opposed to what, you may very well end up having to consider existent middle terms. You cannot just rush to judge that they are wholly opposed when they are not. For example, if you rush to war with someone you think is naturally opposed to you, but only to later found out that your natural similarity to the supposedly opposed far outweighs your opposed differences, what would be the logical consequence of this?

Well, the moral here is that opposites may naturally enliven logic, but at the human level you are naturally empowered to be cautious and always think of the middle terms, incase they exist and turn out to be that which serves you better.

PROBLEM: If you freeze all opposites and their middle terms or possibilties into singularity proper, such that all internal relational parts everporate, so will logic that previously ruled them and their relationships.

[Philocrat]

The last one is the problem of 'FORMS'. As I have pointed out time and time again in this forum, Natural Forms are spooky creatures. The forms that things take when they come into existence set the rules of logic and mathematics. Since they set these rules, they are naturally above these rules. It is as if they are saying, 'the rules that we set are inadequate to explain us'. Questions that are constantly being asked are these:

1) Can Logic and Mathematics exist outside forms? For example, if the natural form that our current universe take were to suddenly change, would the same logical and mathematical rules still hold or reign supreme?

2) Is Formless existence possible? If so, would it still be governed by logic and mathematics?

3) Is it possible to finally derive at a thing or things with unchanging forms?

These are questions that make logic what it is - spooky! We do logic according to what is naturally written into forms. That we can go beyond this limit, I personally doubt it. This is why, whenever the issue of human perfection turns up everywhere in the debate, I keep on saying that creating a perfect being or a perfect state of being may very well involve interfering with the way things naturally are......their forms. This project if we were to ever dare and brave enough to enact it, would be a quantum shift of a monumental scale. Logic as we currently know it would for the first time earn its keeps!

[philocrazy]

LOGIC--According to-->websters dictionary is
"the science or art of reasoning"
All you logical people out there are either scientists or artists
and you dont have to get a phd on it,mother nature doesnt need it either (phd)

Philosopher Philocrazy

[logicalroy]

I am new here and I bet not a single person who has posted here has taken more than a year of LOGIC. Has anyone taken any LOGIC classes with a professional instructor? This does not include those of you who appear to me to be self taught. According to most of you LOGIC is wishy washy. That is because you were not properly trained. If you were properly trained you would know what it is. Most of the posts here are WRONG.

[Les Sleeth]

I am new here and I bet not a single person who has posted here has taken more than a year of LOGIC. Has anyone taken any LOGIC classes with a professional instructor? This does not include those of you who appear to me to be self taught. According to most of you LOGIC is wishy washy. That is because you were not properly trained. If you were properly trained you would know what it is. Most of the posts here are WRONG.

:rolleyes: Why don't you just participate and show us all how brilliant you are on a post-by-post basis? My experience has been, people recently trained and puffed up with their new degree or course grade have neat technical aspects in their brain, but it doesn't necessarily mean they can translate those principles for real situations.

Stop condescending, stop making claims, stop bragging . . . show us what you can do. We are happy with our little family here; if you aren't all that impressed, then why not go where you are happy?

[Problem+Solve=Reason]

We should start from the ground up, it is simple logic to do so :wink: . Just think very simply about it at first, for that is where logic is born, from the abc's of a 1st grader to the theory of relativity by Einstien.

Gravity makes objects fall down. Black is dark, white is bright. 1+1=2 and 6^3=216.

We all know these things, to a certain degree, but the gist is the same. I would say that logic is a product of common knowledge. Logic is in every subject of education, and logic is the only way one can understand anything that they are being taught.

Logic is a human tool for solving the everyday problems that come about. Thousands of years ago humans communicated with each other, communicating for instanse "hunt fish with a pointed stick", well that became logic then. If one wants to hunt fish safficiantly he must get a POINTED STICK, and use it a certain way.

I am a strong believe in God. But I also believe that logic (even if given to us by God) is a tool that humans have developed for simple survival reasons, now I serves a varity of reasons as well as survival.

I also believe we can not learn a more advanced subject before we know the simple machanics for a simple but prfound reason. For us to learn something more than the basics we need reason, and reason comes from the logic that we attained before. I.E. we take algebra before adv alg, and pre-calc before calc. We blindly jump into math not know any reason behind it. Then we start to get reasons for it, and build a logic in our head. After we have enough of that logic, we may apply it to a more advanced forum of mathematics.

I would say reason also excists as a survival mechanism. It keeps society on the straight and narrow. We dont understand things because we do not have reason behind them. Reason keeps logic consistant with the world, which is the perpose of logic, to solve the problems that come up in this world. Society needs logic, in that way reason is used as a survival mechanism.

I will review and edit what I have wrote later, but I am out of time now. Thanks for reading....

----- nwO ruoY evaH ,deeN oN <----?eeS I tahW eeS uoY oD

[Les Sleeth]

Just think very simply about it at first, for that is where logic is born, from the abc's of a 1st grader to the theory of relativity by Einstien.

Gravity makes objects fall down. Black is dark, white is bright. 1+1=2 and 6^3=216.

We all know these things, to a certain degree, but the gist is the same. I would say that logic is a product of common knowledge. Logic is in every subject of education, and logic is the only way one can understand anything that they are being taught.

Logic is a human tool for solving the everyday problems that come about. Thousands of years ago humans communicated with each other, communicating for instanse "hunt fish with a pointed stick", well that became logic then. If one wants to hunt fish safficiantly he must get a POINTED STICK, and use it a certain way.

I think you are making a good point. It is surprising to hear a child barely old enough string together words say (essentially) "because of that, this is true" and be correct. We are born into a universe, into a body and brain, and into environments that are highly ordered, which is why logic works. It is both part of us and we it from our inception. I think people can be led away from their natural logic by desires, desires which make them manipulate logic to reach conclusions that will get them what they want. So even if one manages to be logical from point to point, the overall argument turns out not to make sense.

Consider our new logic "expert." What is the logic of his argument? It seems to be "I am trained, educated . . . you all are stupid." Well, why does he want to say that? What are we supposed to do with that information? Bow down before him? Never speak again? Shoot ourselves? All I see is someone who wants to inflate his ego using the very old tactic of bragging on himself while demeaning others. I mean, if he is so smart, why not come here like so many others do and offer to help people understand? That's the spirit of PF, not "I'm smarter than you."

It's a good thing to be logical, but it's meant to be honestly applied to real living situations to help us understand, improve the quality of life, become better human beings . . . It's degraded to mere opportunistic sophistry when someone is relying on it selfishly.

[phoenixthoth]

Let me take a shot in the dark; I apologize if someone else has said this:

Logic is a language equipped with an alphabet, words, and a grammar.

[loseyourname]

Logic is a language equipped with an alphabet, words, and a grammar.

Whether or not that's true it isn't a definition. Many languages can have an alphabet, words, and grammar without being logic.

[phoenixthoth]

What's the definition of the word definition and how is that not a definition?

Anyways, you can be more specific by specifying the actual alphabet, words, and grammar.... That will pin it down from a general language to a specific language.

It is a definition, just not a very specific one.

[loseyourname]

What's the definition of the word definition and how is that not a definition?

Anyways, you can be more specific by specifying the actual alphabet, words, and grammar.... That will pin it down from a general language to a specific language.

It is a definition, just not a very specific one.

It seems to me that the word definition implies that it be definite, which in this context means specific to the word being defined. You only listed a set of parameters that are present in logic. I'd say they are necessary conditions for system x to be considered a system of logic, but not sufficient conditions. A definition should list both necessary and sufficient conditions for system x to be considered a system of logic. You needn't specify the language of the system to do this.

I'd probably define a system of logic thus:

Any system x is a system of logic if and only if it gives a mathematical method for computing truth values of complex propositions and arguments given the truth values of the simple propositions from which these are constructed.

[Problem+Solve=Reason]

Whether or not that's true it isn't a definition. Many languages can have an alphabet, words, and grammar without being logic.

Well it wouldnt be logical to spell "logik". But then again it would be logical to say logic with a k; you wouldn't know the difference in the spelling of the word, just the sound. Logic has more than one context, that is important to notice.

----- nwO ruoY evaH ,deeN oN <----?eeS I tahW eeS uoY oD

[honestrosewater]

Any system x is a system of logic if and only if it gives a mathematical method for computing truth values of complex propositions and arguments given the truth values of the simple propositions from which these are constructed.Do "mathematical" or "computing" have any meaning outside of logic? I like the idea of following unbreakable rules- "mathematical method"="set of unbreakable rules" and "computing"="following". Whattya think?

[Problem+Solve=Reason]

I like the idea of following unbreakable rules- "mathematical method"="set of unbreakable rules"
That is true for human logic simply because we have been taught to belive that, and that only. Although, I'm sure these rules can be broken by different sets of logic. The logic you possess is not the only logic that can come about. For instance, you may not understand a person's idea, while the person that has the idea may completely understand it himself, and he may also be able to structure his idea so it conforms to your logic.
We all have different logic that we use to solve everyday problems, it just so happens that humans have built a sort of uniform logic that most see as the ONLY logic. This is simple not true.
We are taught to gain uniform logic, not logic itself.

----- nwO ruoY evaH ,deeN oN <----?eeS I tahW eeS uoY oD

[honestrosewater]

That is true for human logic simply because we have been taught to belive that, and that only.
What is "human logic"?
The rules are rules of the system. What system of logic breaks its own rules?

[Problem+Solve=Reason]

What is "human logic"?
The rules are rules of the system. What system of logic breaks its own rules?
I'm not saying that society would break it's logic, just that it can be broken. I am just trying to point out that we all do not have the exact same set of logical rules (although we all see the same things with our eyes, which allows for us to have a uniform logic quite easily. While it is different to have a uniform logic about lets say, english, simple because we all are not born with the same thought of what language should be).
Human logic is for example: math, science, language, and anything that is thought of in the same way by humans. Like I said earlier Gravity makes objects fall down. Black is dark, white is bright. 1+1=2 and 6^3=216.We all know these things, to a certain degree, but the gist is the same.. Those are very simple examples of human logic. Any piece of logic that is in accordinence with the majority of people can be considered human logic.
I hope you understand a bit better....

----- nwO ruoY evaH ,deeN oN <----?eeS I tahW eeS uoY oD

[honestrosewater]

Problem+Solve=Reason,
Okay, we are using different definitions. I was talking about loseyourname's definition which I like except for what I mentioned.