Logic cannot create something out of nothing. We cannot reason our way to truth because reason must begin with something that is held to be true. We call them axioms. I can't help but notice that most of the arguments that exist in the religion/philosophy section are a result of people being unable to recognize their own assumptions as just that. We all begin with some assumptions about the world; we must. If you begin with the assumption that God exists and created the world (many do) then you will never be able to find any arguments that contradict that (duh). On the other hand, if you begin with the assumption that your senses and intellect will tell you all you need to know about the world, then you will definitely come to some very different conclusions. Of course, reasoning fallacies occur as well, but it would probably help if people were clear about their axioms.

I know, I'm dreaming. 90% of the population aren't even aware that they make any assumptions about the world, much less are they honest enough to admit what they are. Enjoy the discussions; I just had to say it.

3 Axioms:

Existence exists - There is something, as opposed to nothing. Existence is axiomatic because it is necessary for all knowledge and it cannot be denied without conceding its truth. To deny existence is to say that something doesn't exist. A denial of something is only possible if existence exists.

A is A/The Law of Identity - Everything that exists has a specific nature. Each entity exists as something in particular and it has characteristics that are a part of what it is. Identity is the concept that refers to this aspect of existence; the aspect of existing as something in particular, with specific characteristics. An entity without an identity cannot exist because it would be nothing. To exist is to exist as something, and that means to exist with a particular identity.

Consciousness is the faculty that perceives that which exists. - To be a consciousness, it must be conscious of something external to itself. Only after it is conscious of something external can it identify itself. Descartes argued that consciousness is axiomatic because you cannot logically deny your minds existence at the same time as using your mind to do the denying. Because to be conscious is to perceive something, consciousness requires something outside of itself in order to function; consciousness requires and is dependent upon, existence.

Logic is the art of conforming one's thoughts to the Law of Identity. It is the art of non-contradictory identification.

Logic is used in integrating ideas as well. What this means in practice is combining information clearly, and without contradiction. It must be combined into a specific, identifiable package, that doesn't contradict itself.

These three axioms and logic form the basis of a rational and defensible epistemology.

Yes good point...

Godel made the interesting point that a conclusion of logic can only be of equal or less "weight" than the assumptions. IOW logic doesn't do anything aside from rearranging or discarding information in the assumptions.

Otherwise, we'd have some sort of analog to a perpetual motion machine, except with information, that is pulled out of thin air.

In popular opinion, assumptions are generally demonized as logic fallacies (for example the popular phrase "when you assume, you make an ass out of you and me"), but ultimately, logic is useless without them. Assumptions are actually necessary ... and even good to have.

The questions about evaluating the quality of assumptions should focus on subsets... to make as few as possible that maximize the overall weight of the deductions.

The approach shouldn't be that "assumptions are generally bad," but that that "simplicity is a virtue," since it's less likely two any two assumptions will turn out to contradict one another.

Interesting thread so far. I haven't much to add yet, but I read this article (originally in New Scientist) recently which some here might find of interest:

Source: Impossible Things for Breakfast

Those are 3 good ones, and probably the best place to start. We need a few more, however, to obtain anything truly useful. We can certainly shoot down systems which are not internally consistent, but to form a system we need probably one more, maybe two axioms, and we can't agree on them. That's fine, sometimes there's more than one plausible, logically consistent system. (e.g. geometry:Non-Euclidean geometry - Wikipedia, the free encyclopedia)

Assumptions are necessary, and they are not bad provided we are aware of them and that we state them clearly in the discussion.

I agree. These are three good starting points. It's important to note though that these starting points are not opinions, arbitrary meaningless starting points. They are necessary for thought and any knowledge whatsoever.

First assumption we make when we think that we can understend the world.Without that we can not even begin of thinking.It is assumption because we can imagine that world is too complex and we can not understand it.What we have right now is simplified picture of the world.I know this sounds pesimistic,but it is one of the options.I agree that we need some basic axioms to start with.I think that Goldman have reasonable epistemology.

I think this needs to be a little bit reworked. Descartes aside, this leaves a great big hole in cases such as schizophrenics. How to define a "broken" consciousness? Consciousness cannot be axiomatic because it fails many tests. I am not conscious of many things, that does not mean that they do not exist.

Then again, Maybe I read it wrong.

Consciousness is a can of worms, because it is a product. Neurologists have proved that consciousness is not necessary to perform many daily actions.

You must be included in that 90%. You are making the assumption that all that exists (truth) is logical, and that logic can take you to it.

It is this assumption that has stopped conventional science from acknowledging many of the mysteries it cannot explain logically. It doesn't know how to get there in any rational way, so it doesn't go there. It creates an atmosphere of denial.

This is where intuition comes into play. Intuition allows us to make leaps which defy logic. Such leaps are a component of genius - they are what allows some people to grasp what others miss. It is taking something on faith.

Many people dismiss intuition itself, for the same reason. They can't understand it. Or, they think that leaps of logic are not valuable.

It is valuable to take such leaps, to work on faith. However, after you take them, it is also important to see what it has brought you. Does your new model, born of intuition, WORK? Does it allow you to build new toys, even if you can't explain how those toys work? Does it allow you make verifiable predictions? Does it give you greater insight into the data, leading you to more developments?

Some people never use intuition. Some people use intuition, but never look back to see if it has produced an observable advantage. Both approaches are incomplete.

Most of the great developments in science come from intuition. It is when people STOP thinking that they get their greatest insights. Einstein's theory of relativity came to him while he was riding on a train. It was a leap of logic he couldn't explain. Yet he went back and worked with real data and developed the theory, which in turn WORKED (produced benefits).

It is a mistake to believe everything in the universe is necessarily logical or rational. It is an assumption, and as you observe, you will only find the logical and rational as a result. You will dismiss whole swaths of reality that don't fit in your logic box.

Really, I believe everything is ultimately logical - the universe makes sense. But it is a wild, huge sense, which we cannot always appreciate with our simple understandings. This is where intuition, leaps of logic, insights, help us to bridge the gap. They are not necessary because the universe is illogical. They are necessary because our 'logical thinking' is often limited is ways we do not see. Once we make the leap, then we can go back and follow the logic. We will say 'of course!'

The theory of relativity is logical. Yet it also seemingly defies 'common sense', and leads on to conclusions which may at first appear irrational (and did to many physicists).

Some Einstein quotes to ponder...

“Logic will get you from A to B. Imagination will take you everywhere.”

“We can't solve problems by using the same kind of thinking we used when we created them.”

“No problem can be solved from the same level of consciousness that created it.”

“The only real valuable thing is intuition.”

“Imagination is more important than knowledge. For knowledge is limited to all we now know and understand, while imagination embraces the entire world, and all there ever will be to know and understand.”

“The intuitive mind is a sacred gift and the rational mind is a faithful servant. We have created a society that honors the servant and has forgotten the gift.”

I don't think bns said that. The problem he brought up was that people were basing arguments around assumptions without first validating that assumption. You are quite right in that intuition and leaps of logic are necessary to further our understanding, but once that leap is made it is also necessary to go backwards to validate it.

But it is not necessary to validate it logically, which bns implied.

For example, no one can logically explain why computers work. Electricity is poorly understood, if at all, let alone why or how QM operates as it does. People USE computers, and use QM models, and use electricity, but that doesn't mean they can follow or derive them logically from a known set of principles. We simply don't understand enough to do so. Nevertheless, we use the results.

Logic is no necessary ingredient in the exploration of truth. The truth may very well include that which is illogical and irrational.

It would explain a lot, if many of your ideas were in the intuition state. Like your conspiracy theories?
“Logic will get you from A to B. Imagination will take you everywhere.” Einstein
And that is its problem also, indeed as you said, confirm/debunk hunches.

Electricity and QM are quite well understood. It is the physical reality that poses us with complication theory can not really overcome. Things are build empirically. With pondering, one could think up principles of workings, but building it is another matter.
Ok, QM still has big interpretation problems, but so has Probability theory.

I do indeed use intuition to move more quickly in my understandings, and this partly explains why people sometimes have problems following my logic. Even if they look at the same information, they may not follow where I go with it.

Yet as I said, it is important to then see if the intuitive leap brought you somewhere useful. I'm not suggesting that one rely on intuition and abandon reason. Nor is the intuition 'needed'. It is merely convenient. It speeds things up.

For example, with 9/11 some people will not entertain the idea because they can't believe it (it seems illogical). They won't walk with you. They refuse to budge. Their mind is closed - they 'know it all'. A leap of intuition or faith might say, "Okay, let's pretend the official story is hoaxed. What can we now see?" By walking the path, you see the issue from a new perspective. You drop the denial and suspend disbelief long enough to be exposed to other views. It is the people who have been willing to do this who see through the hoax.

Then you can decide which view brought you the most insight, explained the available facts the best, etc. There need be no faith at this point - just direct logic and reason.

As bns observed, everyone has assumptions, and often they don't see them. (For example, "Elected officials would never orchestrate 9/11.") Intuitive leaps help you to see your assumptions, and try different ones.

QM is a model. What exists of the model is well understood. What it is modeling is not. As for electricity, I'll stand by my statement that it is not well understood. Models of it achieve various goals, but the underlying 'why does it work this way' is unclear. And it must be, because QM is incomplete.

Classical mechanics is well understood too. It too is incomplete, not being complete does not mean it is not well understood. It is true for a certain range of measurements.
As to why, not being able to answer why does not mean a model is incomplete. A-priory, why might well be an question that is still to be asked for a complete theory. (but one will never be able to prove that a theory exactly mirrors reality.)
I still do not have read moonshine better then so far, but i do not think all the intuitive leaps have been backed up by evidence/logic yet. I am sure there are conspiracies going on, but that does not mean we can hope to uncover them with what we know.

I do not know what exactly you think when talking about a leap of intuition. Sounds like thinking up hypothetical situations, assuming for sake of argument, etc. Not something that society is completely unaware of.

Existence exists - There is something, as opposed to nothing. etc.,etc.

A is A/The Law of Identity - Everything that exists has a specific nature. Each entity exists as something in particular and it has characteristics that are a part of what it is. etc.,etc.

Consciousness is the faculty that perceives that which exists. - To be a consciousness, it must be conscious of something external to itself. Only after it is conscious of something external can it identify itself. etc.,etc.

While these sound great and succeed in establishing a basis for something, i don't think that something is logic. All that seems to be established is that we exist -in a universe of many things -and we are able to make the claim that 'we exist'. A fairly vague basis, I think. It is also based on the perception that we know the truth of existence which, until we can no longer classify anything as 'unexplained', is incomplete.

Classical mechanics is well understood too. It too is incomplete, not being complete does not mean it is not well understood. It is true for a certain range of measurements.
As to why, not being able to answer why does not mean a model is incomplete.

Does that mean an incomplete sentence is true even if we understand the given words in a sentence? ( Cheese is ___ it is also __. True or not?) Is a house without a roof, even though we know it is a house, able to be called such when it doesn't fulfill the basis tenants of shelter? Is it also possible that, having no roof, that house may be having a second floor added? (I've seen this done, very neat :P) In which case, our previous understanding and use of knowledge about square footage, building height, volume and living capacity, all change drastically. Is not an incomplete model subject to similar flaws, all of which only serve to prove we may yet be mistaken? These model may be incomplete due our attempt to mold observation to theory instead of fitting theory to observation.

Granted, I'm not a well read man, but it seems that a lot of philosophical ideas are being used in the discussion of logic(truth, perception, existence, intuition, etc.). Perhaps our incomplete models are based on our inablity to properly combine or divide the two ( :P I jest-interesting thought though). I have a high regard for logic, so please don't get me wrong, but true logical thought has always been beyond me. Much to my fortune it seems.

@ punkinside

That is truth.Existence of external world doesn't depend of our consciousness or knowledge of it.But without consciousness we are not able to know the world.

@ DemandingMore

Let say this is unfair example.But I can also say it is bad example,because that is sentence without sense,so I can not say anything about it.I can tell you this;we can write all logical statments as disjunction and in that case I don´t need to know all elements of infinite statment.I just need to kow that first one is truth and by disjunction infinite statment is true.Is it complete knowledge even possible is another question.

I admit that particular example is over-simplified and, therefor, flawed. The House example remains true, I feel. Isn't logic the means by which we can go from one point to another in order to understand or explain things? Is an explanation with holes a complete one, or simply an expanded theory?
I ask these questions because I don't know the answers. Most of you here seem to have an extensive background in logic where I have none, so these may be silly things to ask to you, but seem like good questions to me. Please, I look forward to having them answered.

We see something without a roof and we say :˝This house doesn´t have a roof.˝How do we know that is a house if doesn´t have basic characteristic of house?Because it is houselike.This is just one way to answer your question.Your general position is that incomplete knowledge is not knowledge at all which lead to paradox.If you don´t have all knowledge you can not have knowledge at all.

Yes but that doesn´t mean that we know or understand everything.Logic itself have problems which is difficult or maybe impossible to solve.