What Are the Origins and Limitations of Logic?

[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 let's 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 doesn't 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.

 

[quantumdude]

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 doesn't 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 possesses 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.

(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]

The Abrsact Angle

ok Logic is a descriptive term meaning a process or steps that's 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 don't have to get a phd on it,mother nature doesn't 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.

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 . 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 don't 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.