Logic is generally seen as a prescription for arriving at truth - as long as our methods of reasoning are sound, our conclusions will be.
Unfortunately, by accepting this line of thought one ties conclusions to methods of reasoning.

In 1829, Nickolai Lobachevsky published a small book on geometry whose conclusions would radically change the history of geometry. For over 2000 years, our knowledge of geometry was essentially based on the work of Euclid of Alexandria. All of Euclid's theorems are based on five postulates - by these five, he goes on to give a system which, with modification, has formed the basis for our knowledge of geometry. Yet the fifth postulate was incomplete. What Lobachevsky did, and which revolutionized geometry, was to replace that fifth postulate.
Euclidian and non-Euclidian geometry are radically different for this reason. Yet neither is "false" - both are internally consistant.

By simply changing one postulate one can radically arrive at different "true" conclusions. Apply this to the study of logic - logic defines a structure of reasoning and criteria by which bad methods of reasoning are weeded out. Change the criteria and what is accepted as a valid conclusion and what is accepted as invalid can change radically.

Simply put, logic's stance as a self-referential system undermines it. Nihilists believe that a thing is only what it is, and its values or associations are not indicative of the thing in-itself. Compare this to formal logic, which values the reasoning that we follow as valid or invalid. Logic is inescapable - even illogical or magical thinking is a form of logic - but the idea that we can arrive at truth by creating the proper methods to do so seems antiquated.

(I should say that I'm thinking of formal and philosophical logic when writing this.)

Logic for me is a set of rules constructed from experience and consistency.
So logic leads to ‘truth’ that is always subjective because it is tied to the experiences and awareness of every individual.
The search for ’ absolute truth’ or ‘objective truth’ should be left aside as a myth so that we may focus our attentions in finding a superior ‘subjective truth’.
Man sees what he is looking for; let him look for greatness.

Amazing, no comment from the peanut gallery so far.

Wanderer:
Well that's so and I agree, but formal logic posits a set of rules that is allegedly objective.
Of course, accepting that set is a subjective act. You see what I'm getting at? Not only our truth but our logic is subjective. It seems obvious enough, doesn't it? But the conclusions are breathtaking. Or perhaps that's just me, I've spent much of my life dedicated to rational methods of thought. The implications of this subjectivity did profoundly change everything for me when I discovered them.

"While we may believe
our world - our reality
to be that is - is but one
manifestation of the essence"
-Varg Vikernes

The objective is merely a set of subjectives decided upon. This is what allows different conclusions. Also they are not both "true" unless view within their contexts. The two rules are mutually exclusive.

Logic is generally seen as a prescription for arriving at truth - as long as our methods of reasoning are sound, our conclusions will be.

It may be seen that way, but that's incorrect. Sadly, it will still be seen that way regardless.

Unfortunately, by accepting this line of thought one ties conclusions to methods of reasoning.

No, by accepting that line of thought, one misses the usefullness and thus the point of logic. Conclusions are always tied to methods of reasoning, especially since all methods of reasoning contain at minimum, one subjective judgement.

In 1829, Nickolai Lobachevsky published a small book on geometry whose conclusions would radically change the history of geometry.
Beautiful. You gotta love big thinkers.
For over 2000 years, our knowledge of geometry was essentially based on the work of Euclid of Alexandria.
"our knowledge" as in the populations knowledge is still based on Euclid's thinking. Non-Euclidian geometry is of little utility to the average person.

Euclidian and non-Euclidian geometry are radically different for this reason. Yet neither is "false" - both are internally consistant.

I think this serves as a clue to the nature of logic, as I'll describe below.

By simply changing one postulate one can radically arrive at different "true" conclusions. Apply this to the study of logic - logic defines a structure of reasoning and criteria by which bad methods of reasoning are weeded out. Change the criteria and what is accepted as a valid conclusion and what is accepted as invalid can change radically.

Recognize that logic is a transform.

You put in assumptions (1=1, what I see is real, the measurement of angle is representative of reality, etc.), logic is used to process them, you get results.

Those results are wholly based on the assumptions.

Simply put, logic's stance as a self-referential system undermines it.

That is a matter of opinion. If you misunderstand the application of logic, then yes you're correct. Otherwise, it's a reflection of expectation to say that it is "undermined". It is as effective as the assumptions employed to yield the pertinent transform (disregarding the skill of application).

Nihilists believe that a thing is only what it is, and its values or associations are not indicative of the thing in-itself.

That is simply common sense. I have no idea why you associate that with nihilists, but you read more than I do so maybe you have good reason. Regardless, as you elude to below, you had to use logic to reach that conclusion.. how can you be sure it's valid?

Compare this to formal logic, which values the reasoning that we follow as valid or invalid.

You must not be referring to binary logic (which is quite formal)? Reasoning, IMO, is much more broad than logic, and actually gave birth to the concept. Reasoning is not formal. Aspects of it might be, but all in all, reason incorporates intuition and faith. Formal logic doesn't value anything. It is susceptable to flawed assumptions.

Logic is inescapable - even illogical or magical thinking is a form of logic - but the idea that we can arrive at truth by creating the proper methods to do so seems antiquated.

I'd say you're mistaking logic for reasoning in that case, but the terms are often used interchangably. You are apparently not using terminology the same way I do.

Speaking of truth: I see two fundamental types of truth. The objective and subjective. For instance the truth that the truth is based on your assumptions, or rather.. that it's context dependent. That is a truth that transcends itself, yet still adheres to itself. Its truth depends on the context in which it is stated, yet it is applicable even if you fail to acknowledge the validity of the context.

The thing is: The truth is abstract. The only thing making something "true" is a structure in your head which validates or invalidates the stuff you present it. As such, there may be rules, there may be absolutes, but they have little bearing on the physical world unless forged there by force of will. The physical world will determine what is. This is often a useful tool when people assert truth via their will. If you want to hurt me, you can hit me. You will create a common context and assert a truth in doing so, manipulating the physical world to do so.

I'll stop before I get lost in all of that.

Xev sez:
Simply put, logic's stance as a self-referential system undermines it. Nihilists believe that a thing is only what it is, and its values or associations are not indicative of the thing in-itself. Compare this to formal logic, which values the reasoning that we follow as valid or invalid. Logic is inescapable - even illogical or magical thinking is a form of logic - but the idea that we can arrive at truth by creating the proper methods to do so seems antiquated.

The natures of even our most basic concepts are cloudy enough that I don't believe that there is any way to arrive at truth, or even recognize it if you were sitting on it. Many of our deeply held beliefs are conventions; often we have conventions even for things that we consider to be "true", and there is no way to discover what truth underpins them.

Consider numbers, for instance. People have many different ideas of what numbers are - linguistic representations of arrangements or properties - but numbers still enjoy a different status in our language from other symbols.

When we say "A", we know that's a sound (convention) for a written symbol (convention) that we use to communicate words (convention) in our language (convention).

When we say "1", we know that's a sound (convention) for a written symbol (convention) that we use to communicate... this is where it gets foggy. It could be:
Representation of an ARRANGEMENT - a single thing.
Representation of a PROPERTY - a single thing has the property of being single.

I'm not sure which of these it is, but it represents a problem:

When we say "Apple", we know that - if humans had never existed but apples did - there would still be apples but they would not have the name "apple". Apple is a real thing (for the sake of argument). "Apple" is a conventional term that dies with us when we die.

When we say "1", we know that - if humans had never existed but objects did - there would still be single objects but they would not have the name "1". There would still be 1 of the object, even though the name "1" doesn't exist. "1" is just a name for its single-ness. "2" a name for the number of 2 things, &c.

So it seems to make sense that numbers can exist without an intelligent observer/speaker, where names can't.

Consequently numbers seem to make the most sense as being names for arrangements - think of 1,2,3,4 the same way you think of inside, outside, above, below - states of arrangement.

But is this how we think of numbers really? Not really; by convention we handle numbers as abstract entities for mathematical use. But that doesn't change the fact that they appear to exist without us, as arrangements of physical objects.

There are similar conventions in geometry and other fields that are often considered to be "representative of the world"; they sometimes serve to demonstrate those aspects of the world that we are unable to analyze to any degree.

Poincare had an example of a geometric convention that cannot be broken out of to find the "truth" - you can read about it briefly <a href="http://mcs.open.ac.uk/tcl2/nonE/CABRI2001/PDiscMod.html">here</a>, it's just a thought experiment really...

On the basis of these unbreakable conventions I must agree that truth is not a fish that you can catch.

So it seems to make sense that numbers can exist without an intelligent observer/speaker, where names can't. (bbh)

i fail to see the difference unfortunately. as with the requirement that an observer is required to name that which is apprehended, so is his presence required in order to quantify the same

if there is no observer, distinctions cannot be made b/w 1/2/3/4

ja? no? :confused:

The physical world will determine what is. This is often a useful tool when people assert truth via their will. If you want to hurt me, you can hit me. You will create a common context and assert a truth in doing so, manipulating the physical world to do so.
And this is where I disagree. The physical world is non existent without the observer. A physical world is realizable only within the viewpoint of the individual. Again, there is no objective that is not based on a subjective. One takes the subjective, and unconflicting with other subjectives, presupposes its truth. That subjective then becomes an objective.

Logic takes a set of subjectives and asserts their objectiveness within a specific context. A such, on earth, gravity is 9.8m/s^2. And within this context, we say that value is the objective. Or perhaps that, when cut, a living person bleeds. Again, within this context, that becomes an unconflicted subective, and hence an objective. One can follow logically and assert therefore that "I cut A. Therefore, A is bleeding". And other factors, unconsidered, "A is not cut. Therefore, A is not bleeding."

Logic is merely formalized reasoning that yields a truth, every sungle time-- as long as viewed within its context. The physical of the tree therefore is entirely dependent on the assumptions made by the subject.

Spookz - if there are no observers, but one single object (in a certain region of the universe we are considering), say a rock, there will still be a single rock. It doesn't need to be observed for there to be 1 of it.

thefountainhed - though the theory is that any logical statement represents a truth value, there are serious problems with this view. One of the most basic is this:

Hamlet's great-grandfather's eyes are blue.

Is that statement true? False? No mention was made of Hamlet's great-grandfather by Shakespeare in any known writing, and he's dead and can't be asked. There is no fact of the matter where this is concerned, so the sentence can't be true or false.

Another is that we still have great difficulty logically quantifying natural language...

--So it seems to make sense that numbers can exist without an intelligent observer/speaker, where names can't.

I do not believe you can reach that conclusion. A number is an abstraction based on a physical; in the same way, a name is an abstraction based on a physical. 1, X, deux, are all names. What they define is not realizable unless one counts. And to count, one must distinguish and differentiate between specifics. As such, one needs naming to count. The two are not mutually exclusive.

So, without an observer, there cannot be 1 object?

Edit: if numbers are only names, then what are they labels for?

Without an observer, there is no conception of 1. The observer must distinguish and classify to associate 1. One of what? Earth, oranges, etc? There must be classifications.

Numbers are names needed for a realization of the abstract called counting. Again, how does one count 10 of anything? One must first classify what is being counted.

10 oranges 10 objects 10 x

After the classification, one then distinguishes between the individual pieces and assigns numbers 1, 2, 3, etc to distinguish. The final result therefore becomes the count, plus the classifier(s). Numbers are a tool; they are a naming convention. This is what allows for different kinds of representation for numbers.

thefountainhed - though the theory is that any logical statement represents a truth value, there are serious problems with this view. One of the most basic is this:
The theory is true only within a specific context. The logic within sphere A, may not necessarily apply to that of sphere B. However, within their specific spheres, they necessarily reach the true conclusions.

Hamlet's great-grandfather's eyes are blue.
Is that statement true? False? No mention was made of Hamlet's great-grandfather by Shakespeare in any known writing, and he's dead and can't be asked. There is no fact of the matter where this is concerned, so the sentence can't be true or false.
That sentence cannot be considered logical unless one presupposes its truth. It then becomes truth, a priori. If one cannot know that it is true, then it is not logical.

One can presuppose these truths:

1. All members of Hamlet's family have blue eyes.
2. A great grandfather is a family member.

Therefore, the statement "Hamlet's great-grandfather's eyes are blue." becomes a truth-- within the context of the objectives it is based upon.

Another is that we still have great difficulty logically quantifying natural language...
What do you mean by natural langauge? The language of speech?

Without an observer, there is no separation of the 1 from its environment. There may be one of something you classify as A. But without you the something is not A, or B, or anything. It is merely part of the tao so to speak.

Then how many environments are there?

well, you can hypothesize that there is an environment without the need for an observer, but you can only reach the conclusion that there is one environment if you observe (or imagine) it. otherwise there is only the "is" and nothing can be said of it.

Then how many environments are there?

One, you ask that I count, and two, you ask that I classify. The subject must be present for both events to take place.

Not so, unless you're claiming that the universe has no nature without an observer. Do you believe that only observation makes things real? I believe that there is an objective universe, whether we see it truly or not.

And this is where I disagree. The physical world is non existent without the observer. A physical world is realizable only within the viewpoint of the individual.

Yes and no, sadly. From my assumption of the plausibility of cause and effect, I assume that the physical/naturalistic world existed in time prior to my observance of it. To me, this is a matter of faith. I don't have faith that this is indeed true, but that it is reasonable based on my comprehension of what it is to be. So while you can validly argue your point all day, I circumvent your point with an assumption.

In other words, I think you are right that it is "realizable only within the viewpoint of the individual" but that this does not mean it is "non existant" without that observer. It simply means it hasn't been observed.

Again, there is no objective that is not based on a subjective.

Sorry but here I have to laugh. You're telling this to Mr. Annoying Subjectivity Man? Preaching to the choir brother.

Have you forgotten that just because you can't see it - that don't mean it ain't there? My pa taught me that there. Ah-hyuck.

What is the "nature" of the universe unless the observer is able to conceptualize that nature?

Is the universe an extremely cold place, cold place, warm place, etc. You get it? A nature is of the universe cannot be discussed with the subject. It is non existent within an experience.

I believe that there is an objective universe, whether we see it truly or not.

What is this objective universe? If you do not know it, then on what basis do you base your belief?

Your subjective experiences still take place within a context, which would indicate that on some level there is some form of objective existence - of yourself if nothing else.

certainly but if you can't observe it, you can't make observations about it. :D

this is the nature of tao

It does not indicate that there necessarily exists an objective outside of the self. Yes, the self exists. Hence, the subjective. That is inapplicable however, to an objective of the universe.

That doesn't matter - what matters is whether it can be there or not.

Edit: You squiggly punks! I'll pin you down to numbers yet!

Apologies to Xev - I s'pose this isn't exactly what you were looking for. On the other hand metaphysics is always a can of worms, and truth a can of invisible, incorporeal, unverifiable worms that cannot be detected in any way.

---That doesn't matter - what matters is whether it can be there or not.

Of course it matters. We spent half a bloody hour talking about it. But that is the entirely of the notion. The self is the only verifiable. So yes, one can say an objective universe may or may not exist. It is irrelevant. In fact, I can argue that one can only say an objective universe cannot exist, but I suppose it is uniomportant really. Perhaps another time.

Sorry, that was addressed to wes's post:
certainly but if you can't observe it, you can't make observations about it

Shoulda made that clearer.

BUT in any case it's not irrelevant, since your mind was already able to conceive of more things than there are. It is possible for you to abstract concepts as well, and thinking about something is not the same as observing it - no?

So if it's possible to think about the context you exist in, and how it would be if you didn't exist (which you can think about, if not observe) then we can think about the properties of that context. That's why it's important.

I use irrelevant in the sense that it tells us nothing about the nature of an objective truth.

Solipsism can't be disproved, but then you run into the problem of defining yourself as an observer. I suppose I will dig around for something that might actually refute solipsism.

"While we may believe
our world - our reality
to be that is - is but one
manifestation of the essence"
-Varg Vikernes

Lost Wisdom.

Holy shit, you know Burzum? Nobody, even my "metalhead" friends, know Burzum. I say "Burzum" they wonder who the hell I'm talking about. "He killed a man? Wicked! Let's go listen to SYL!" (Then again, I used to be as bad. I thought Cradle of Filth was black metal and Deicide was "wicked heavy" just for being anti-Christian)
Det Som Engag War. The album is almost painful for me to listen to. My favorite album by Vikernes has to be Hlidskjalf. Angry in parts, full of lonesome rage and tremendous beauty.

But umm, on topic, so many methods can be used to arrive at "a" truth. But formal logic eventually becomes self-referential, a system that is useful for proving things but not for much else. Logic is a tool, use it as one rather than as an end in itself.

Solipsism can't be disproved, but then you run into the problem of defining yourself as an observer. I suppose I will dig around for something that might actually refute solipsism.

Doesn't it work best on a practical matter? I know I don't define the world around me because I can't fly. I'd desperately love to fly (without mechanical aid) but I am limited.
Maybe the best argument against it is to ask who a solipsist is arguing with.

A solipsist argues with himself/herself apparently. :)


Everybody is free to believe what he or she wants. But my main
problem with the "all-is-subjective" type of
approach is that it's completely useless. It takes you nowhere: if
you're just a little practical you can't take it seriously. It's a
possible theoretical stance but both its predictive power and its
utility value is nil. On top of it, sooner or later it turns into
solipsism if you want to remain consistent. And as Xev just
pointed out rightly solipsism has its own absurd features. But I
repeat, everybody is completely free to choose his or her
favourite set of beliefs, at least theoretically. If the train is
coming, even the stubborn solipsist jumps aside.

It's a possible theoretical stance but both its predictive power and its utility value is nil. On top of it, sooner or later it turns into solipsism if you want to remain consistent.

Perhaps you can give an example of any stance that isn't fundamentally solipsistic?

Perhaps you can give an example of any stance that isn't fundamentally solipsistic?

One rooted in common sense.
As proteus noted, jumping out of the way of a train.

One rooted in common sense.
As proteus noted, jumping out of the way of a train.

You mean one without thought eh?

EDIT:

Do you see what I mean?

The application of reason requires solipsism.

I don't think that is a bad thing at all. It's merely regonizing that reason is the manipulation of symbolic abstracts as they relate to other symbolic abstracts, all of which are fundamentally solipsistic, in the sense that a dictionary is analagous to a book about solipsism.

Meh. I suppose I'm saying I'm agnostic, which leads to solipsism, which I escaped by faith in reason. To me, it is reasonable to believe you exist, though I cannot ever 100% confirm my belief.

So I think that when you trancend instinct, you are inherently indulging in solipsism. "I think therefore I am" damnit. It gets weird to me though in that really as far as I can tell: Even if you don't think, you am until you aint. Of course, that's assuming you existed at all blah blah, which goes in circles, which is why it's weird. IMO, this is the boundary of logic. Solipsism is the foundation.

"I assume that I am"

"I assume it is reasonable to be reasonable"

"I therefore assume my sensory input is reflective of a medium in which I am"

"I sense that you exist"

"I therefore assume that you exist"

I think that is perfectly reasonable, and flexible in that I realize that I've made assumptions that could prove not to be true.

Glen Benton and his boyfriends "satanism" is a schtick designed by their record company. They talk about fucking jesus at gigs and in front of fans, but spend every other moment inserting dildos into each other and reading "Better Homes and Gardens".

Doesn't it work best on a practical matter? I know I don't define the world around me because I can't fly. I'd desperately love to fly (without mechanical aid) but I am limited.

That still does not disprove solipsism in any way. I can assume everything is in my head, but that doesn't mean I can consciously control every aspect of reality. Think of it as paralysis: a paralyzed person has the ability to move their limbs, but cannot because of a certain misfire in their brain.

Holy shit, you know Burzum? Nobody, even my "metalhead" friends, know Burzum. I say "Burzum" they wonder who the hell I'm talking about. "

I read the Lords of Chaos book and thought I would check out the bands. I found Burzum and Emperor to my liking, because I enjoy classical. My favorite would have to be Hvis Lyset Tar Oss, simply because of the atmosphere of it. Hlidskjalf was a fine album too, but some of the songs seem like filler. Frijo's Golden Tears is an excellent example of romantic structure, being more about feel than form. Det Som was alright in my opinion, but it was more 'metal' than the other works. I'm not a big fan of anything other than classical really, but I have some black metal bands I enjoy for the intensity and spirit.

Hastein: does the true solipsist allow for the possibility of anything outside their own consciousness? I would read solipsism as saying "the only thing that exists is your own mind" - which would mean that the solipsist was the entire universe. In this case even your "paralysis" would only be a product of your own world view, which would mean that with sufficient effort you should be able to change it.

I generally agree with the common sense view of the universe, that is, "we can't control things because they are seperate from us + we developed/have senses and self-control to protect ourselves from injury caused by uncontrollable things."

In this case even your "paralysis" would only be a product of your own world view, which would mean that with sufficient effort you should be able to change it.

Of course, I agree. I'm sure there are plenty of people who are trying to alter reality just by thinking about it (this is the basis for some magick practices) Yes, but the fact that they can't makes their theory tricky. It is impossible to disprove solipsism, but it is also impossible to prove it. My philosophy is that even if solipsism is true, it doesn't really change anything, because your reality is the same either way.

Think of it as paralysis: a paralyzed person has the ability to move their limbs, but cannot because of a certain misfire in their brain.

The solipsist doesn't allow for material, and that includes their own brain. We're not just talking about just Cartesian brain-in-a-vat evil genius stuff, we're talking about your mind being the only thing that is real. It sounds like you're talking about something more complicated, or at least allowing for a "real" universe beyond your own consciousness. Not so?

You lost me, but I'm sure you are correct. Xev made the point that a solipsist couldn' do whatever they wanted just by thinking about it. I stated that this doesn't disprove the theory, it just means the solipsist doesn't know how to alter reality to their will because something is hindering them.

Euclidian and non-Euclidian geometry are radically different for this reason. Yet neither is "false" - both are internally consistant.

By simply changing one postulate one can radically arrive at different "true" conclusions. Apply this to the study of logic - logic defines a structure of reasoning and criteria by which bad methods of reasoning are weeded out. Change the criteria and what is accepted as a valid conclusion and what is accepted as invalid can change radically. There are no changes in the rules of logic between Euclidian and non-Euclidian geometry. They reach different conclusions by applying the same rules of logic to different initial conditions. The fact that both are correct and useful doesn't mean that logic is relative and changeable, it's just an acknowledgment that in some spaces parallel lines never intersect, and in others they do. Since different types of space have different properties, it makes sense that you would use different systems to model them. This is no different than acknowledging that some cars are made by Ford and others are made by GM, and that they have different properties.

Nasor:
The fact that both are correct and useful doesn't mean that logic is relative and changeable, it's just an acknowledgment that in some spaces parallel lines never intersect, and in others they do. Since different types of space have different properties, it makes sense that you would use different systems to model them.

Perception being influenced by system, I'm not sure how any of this critiques what I've written.

Hastein:
That still does not disprove solipsism in any way. I can assume everything is in my head, but that doesn't mean I can consciously control every aspect of reality. Think of it as paralysis: a paralyzed person has the ability to move their limbs, but cannot because of a certain misfire in their brain.

Good point, but I'm not trying to disprove solipsism there as to show that it is an impractical (less valid) way of thinking. One might have a somewhat more exciting mental life, but the cost would be jumping off a building thinking one could fly.
One could say, and this is something of my origional point, that there are no real 'truths' - only more or less useful ways of approaching the universe.

I read the Lords of Chaos book and thought I would check out the bands. I found Burzum and Emperor to my liking, because I enjoy classical

It's gratifying to see how much black metal incorperates of classical - especially Romantic - music. I think Bathory's 'Blood Fire Death' album was dedicated to Wagner (not that I'm a huge fan of Wagner)
Classical was my first love, along with industrial and 80s synth-pop (is that the word?) like New Order and the Cassandra Complex.

There are no changes in the rules of logic between Euclidian and non-Euclidian geometry. They reach different conclusions by applying the same rules of logic to different initial conditions. The fact that both are correct and useful doesn't mean that logic is relative and changeable, it's just an acknowledgment that in some spaces parallel lines never intersect, and in others they do. Since different types of space have different properties, it makes sense that you would use different systems to model them. This is no different than acknowledging that some cars are made by Ford and others are made by GM, and that they have different properties.

It is true that the same logic is used in Euclidean geometry and non-Euclidean geometry, namely, classical first order predicate calculus. (If you need set theory as well, you need to move to second order logic, but as far as I remember Hilbert's axioms can be stated in pure first order terms, though I might be wrong here.) But the claim in Xev's original post that several logics are conceivable is also true. Here is short list of logics that have an accepted status today and are different from classical logic: many-valued logic (admitting at least three truth-values besides classical True and False; here, the sky is the limit, there are even infinite-valued logics), probability logic (formally a variant of infinite-valued logic), fuzzy logic (created by an engineer to model vague concepts), intuitionistic logic (Heyting's logic, in which the classical law of excluded middle is not accepted), free logic (the domain of discourse can be empty - this is prohibited in classical logic), the huge family of modal logics, i.e., the logics of necessity and possibility - a class of inferences ignored by classical logic (historically the first of this family was C.I. Lewis' "logic of strict implication" in his systems S1 - S5), intensional type-theoretic logic (Richard Montague's logic to model a broad class of inferences made in natural language), various logics to treat counterfactual implications of the form "If it were the case that A, then it would be the case that B" (David Lewis in his "Counterfactuals" examines 26 such logics - their semantics is based on a topological generalization of the semantics of modal logic first given by Kripke in the sixties), default (or non-monotonic) logics (here the monotonicity principle of classical logic is given up), deontic logic (a variant of modal logic dealing with obligations and permissions), the logic of common sense reasoning (initiated by Minsky and subsequently developed by AI people and philosophers), dynamic logic (Pratt's idea of modelling abstract computer programs), temporal logics (Prior's "linear time" systems and the subsequent developments using branching future), and the list could be much much longer than this. (I didn't mention quantum logic because I don't really know it, but surely it is not a classical system either.)

The landscape is perplexing and one mode of inference judged valid by one of the above logics may well be judged invalid by the other. The natural question arises: which one of them is the real logic? And this question does remind one of the similar question: which geometry is the real geometry? In the case of logic, the choice of a particular logic depends on what type of inferences you want to capture. But valid inferences are not dreams, so each and every logic in the above list seems to cover something of a logical reality (though this concept is not fashionable nowadays). David Lewis had a long series of arguments against the view that thinking about possibilities and necessities can ever be reduced to our mental and linguistic operations. His "modal realism" may be too far-fetched, but I think the case is very similar here to the case with geometry: according to physics, cosmic space is non-Euclidean, so Euclid's original system does not describe reality adequately. In other words, the real geometry of our world seems to be Riemannian. In the same vein, it might well turn out some day that classical logic does not describe reality adequately but some other logic does, probably one still to be discovered.

Xev

Your first post seems true. It's a strange topic. We know that (logically) it is impossible to prove anything about reality from within any axiomatic system (within any possible universe). Nevertheless we can know things to be true. Goedel proved both of these things.

If our systems of logic are all flawed then I'd say it does not matter too much. However if our rationality is an illusion then we're dead in the water. We might as well assume that we are rational, or at least capable of being rational.

In some doctrines there is a perfectly good reason why we cannot prove anything about reality, this being that reality has no true or false attributes. (Buddhism, Spinoza etc) In these doctrines (belief-systems, affirmations, whatever) our epistemology is entailed by our ontology. This is impossible to prove ex hypothesis in these doctrines, but it seems like a reasonable idea.

PS. How do I subscribe to a thread? Since the changes I can't see how to do it. Is it automatic if I post a message?

You automatically subscribe when you post a message. If there is another way I don't know it.