Modal Dialetheism

[John Page]

The reason for my posting is that I think the basis of modal logic is silly (pythonesquely).

One the one hand modal logic seems to be an attempt to map out all possible worlds.

On the other hand it rules out worlds that do not involve contradiction. This follows from the rule "Anything that is logically impossible necessarily involves self-contradiction."

I can argue, though, as follows: "Certain known things are self-contradictory and thus certain known things are logically impossible."

Therefore, modal logic cannot be used to map all possible worlds. I would accept the counter argument that modal logic can be used to map worlds that are logically possible but this rather proves my point since the possibilism is constrained by the axioms of the system of logic adopted.

Perhaps what we really need is modal quantal logic, but that would be a random guess.... ;)

Thoughts, anyone?

Cheers, John

[heusdens]

What about dialectics?

[ex-xian]

Originally posted by heusdens
What about dialectics?
Hegel's dialectic, as the ultimate form progressing knowledge, is incoherent. If dialectic is the Absolute, then we're at the pinacle that the method strives for. If it is not, then it has an antithesis, which, when resolved by synthesis, is other-than-dialetic.

That's not to say it can't be a useful heuristic, only not the exalted one that Hegelians wish to appoint it to.

[ex-xian]

Originally posted by John Page
The reason for my posting is that I think the basis of modal logic is silly (pythonesquely).

One the one hand modal logic seems to be an attempt to map out all possible worlds.

On the other hand it rules out worlds that do not involve contradiction. This follows from the rule "Anything that is logically impossible necessarily involves self-contradiction."

I can argue, though, as follows: "Certain known things are self-contradictory and thus certain known things are logically impossible."

Therefore, modal logic cannot be used to map all possible worlds. I would accept the counter argument that modal logic can be used to map worlds that are logically possible but this rather proves my point since the possibilism is constrained by the axioms of the system of logic adopted.

Perhaps what we really need is modal quantal logic, but that would be a random guess.... ;)

Thoughts, anyone?

Cheers, John
Maybe I'm missing something, but doesn't "all possible worlds" implicity mean "all logically possible worlds?"

[John Page]

Originally posted by ex-xian
Maybe I'm missing something, but doesn't "all possible worlds" implicity mean "all logically possible worlds?"
No, I think it includes logically possible worlds by definition. I guess the crux of it is that I think it is possible for logically impossible worlds to exist, hence the thread title.....

[spacer1]

I guess the crux of it is that I think it is possible for logically impossible worlds to exist, hence the thread title.....
How does it rule out logically impossible worlds? I would assume that each world would have its own logic, and that each world is self-contained. So, while one possible world compared to another may be logically inconsistent, I don't understand how one possible world could be logically inconsistent by itself.

[ex-xian]

Originally posted by John Page
No, I think it includes logically possible worlds by definition. I guess the crux of it is that I think it is possible for logically impossible worlds to exist, hence the thread title.....
How can something that is logically impossible exist? Are you thinking, as spacer1 posted, that the logics would be different for each world?

If not, then I'm not sure I understand what you're saying at all.

[heusdens]

Originally posted by ex-xian
Hegel's dialectic, as the ultimate form progressing knowledge, is incoherent. If dialectic is the Absolute, then we're at the pinacle that the method strives for. If it is not, then it has an antithesis, which, when resolved by synthesis, is other-than-dialetic.

That's not to say it can't be a useful heuristic, only not the exalted one that Hegelians wish to appoint it to.

In the philosophy of Hegel the highest form of knowing is the Absolute Idea (http://www.marxists.org/reference/archive/hegel/works/hl/hlabsolu.htm).

Dialectics is it's own thesis->anti-thesis->synthesis, in which the synthesis is not "other-then-dialectics" but a higher form of dialectics.

[ex-xian]

Originally posted by heusdens
In the philosophy of Hegel the highest form of knowing is the Absolute Idea (http://www.marxists.org/reference/archive/hegel/works/hl/hlabsolu.htm).

Dialectics is it's own thesis->anti-thesis->synthesis, in which the synthesis is not "other-then-dialectics" but a higher form of dialectics.
If dialectic isn't the Absolute, why is it the only thing that is except from its own reasoning?

[heusdens]

Originally posted by ex-xian
If dialectic isn't the Absolute, why is it the only thing that is except from its own reasoning?

Absolute and Relative

Absolute and Relative are philosophical terms concerning the mutual interdependence of things, processes and knowledge. ‘Absolute’ means independent, permanent and not subject to qualification. ‘Relative’ means partial or transient, dependent on circumstances or point-of-view. For dialectics, the Absolute is only the whole movement through various relative stages of understanding, but the progress of knowledge never comes to an end, so the absolute is relative. However, even a relative truth may nevertheless contain some grain of the whole absolute truth, so there is an absolute within the relative. Perception is relative to the observer, but the existence of an objective world is absolute.

Hegel used the various ‘definitions of the Absolute’ to characterise the successive philosophical standpoints shown to be in fact relative in the development of the Absolute Idea (http://www.marxists.org/glossary/terms/a/b.htm#absolute-idea)

Further Reading: Hegel: "in Being everything is immediate, in Essence everything is relative" (http://www.marxists.org/reference/archive/hegel/works/sl/slbeing.htm#SL111n_1) and Absolute and Relative. (http://www.marxists.org/reference/archive/hegel/help/mean06.htm#04) Einstein: Special and General Theory of Relativity. (http://www.marxists.org/reference/archive/einstein/works/1910s/relative/index.htm)

Absolute Idea

The “Absolute Idea” is both the apex and foundation of the philosophical system of Hegel. It includes all the stages of the Logic leading up to it; it is the process of development with all its stages and transitions. The Absolute Idea, or “World Spirit”, plays the same kind of role for Hegel as a deity “History is the Idea clothing itself with the form of events” (Philosophy of Right, § 346), and Marx rejects the need for any such concept since history is the product of people, not the other way around. Like "Absolute truth" knowledge of the Absolute Idea is an unattainable ideal, representing the whole of Nature which has developed to the point where it is conscious of itself, or the concept of Nature developed to such a degree of concreteness that it has “returned to itself” - an absolutely comprehensive, practical and concrete concept of the world.

Hegel defines the Absolute Idea (http://www.marxists.org/reference/archive/hegel/help/mean07.htm#15) as the “unity of the Theoretical Idea (http://www.marxists.org/glossary/terms/t/h.htm#theoretical-idea) and the Practical Idea" (http://www.marxists.org/glossary/terms/p/r.htm#practical-idea). The Theoretical Idea is the completed Notion (http://www.marxists.org/glossary/terms/n/o.htm#notion) or concrete concept of the world or object; the Practical Idea is the activity expressing this concept (practice); the unity of the two means fully “conscious practice”, people acting in true accord with their own nature.

Further Reading: Hegel’s exposition in the Shorter Logic (http://www.marxists.org/reference/archive/hegel/works/sl/slidea.htm#SL236) or in the Science of Logic (http://www.marxists.org/reference/archive/hegel/works/hl/hlabsolu.htm), or Lenin’s annotations (http://www.marxists.org/archive/lenin/works/1914/cons-logic/ch03.htm#LCW38_219b) on the Science of Logic. See also the Philosophy of Right (http://www.marxists.org/reference/archive/hegel/works/pr/prstate.htm#PR341) and Marx’s comments on Absolute Knowledge in his Critique of Hegel’s Dialectic (http://www.marxists.org/archive/marx/works/1844/manuscripts/hegel.htm#44h1).


Source:
Encyclopedia of Marxism (http://www.marxists.org/glossary/terms/a/b.htm)

[John Page]

Originally posted by spacer1
How does it rule out logically impossible worlds?
Here:
Originally posted by ex-xian
Maybe I'm missing something, but doesn't "all possible worlds" implicity mean "all logically possible worlds?"
What do you suppose is the difference between the two? I would say it is possible worlds that are illogical. If you then object that illogical worlds are impossible, how do you account for different logics?
Originally posted by spacer1
I would assume that each world would have its own logic, and that each world is self-contained. So, while one possible world compared to another may be logically inconsistent, I don't understand how one possible world could be logically inconsistent by itself.
But modal logic attempts to describe all possible worlds - but you are necessarily stuck with the POV of the modal logic you have selected.

In summary, all possible worlds are all possible worlds, even if you think some of them illogical or impossible. Even for the madman, his world exists, however contradictory it may be for you or I.

Cheers, John

[heusdens]

.. and perhaps inspect this (http://www.marxists.org/reference/archive/hegel/help/mean06.htm) page.

The Meaning of Hegel's Logic

VI: The Notion in Hegel's Logic (http://www.marxists.org/reference/archive/hegel/help/mean06.htm)

[heusdens]

Originally posted by John Page
In summary, all possible worlds are all possible worlds, even if you think some of them illogical or impossible. Even for the madman, his world exists, however contradictory it may be for you or I.

An "impossible outlook " or interpretation of the world, is something different then an impossible world.
Are we talking here about the real world, or just about our ideas or interpretations of the world?
The world is still possible, whatever and however one interprets the world, and that by the only relevant fact that the world itself exists. If a world is said to be impossible, this could just mean that such a world does not exist, and because it does not exist, it can not even be called a world, but is just a fixation of mind.

[John Page]

Originally posted by spacer1
....I don't understand how one possible world could be logically inconsistent by itself.
I'm not saying that logics are internally inconsistent by themselves - the point I'm driving at is that for each system of logic there is necessarily a POV that is different.

My issue with a claim (maybe implicit) that modal logic encompasses all possible worlds. According to my relativist standpoint it will be impossible to attain such a goal. Of course one can acknowledge and try to embrace this objection through the addition of dialetheism principles to admit contradictions.

Cheers, John

[John Page]

Originally posted by heusdens
An "impossible outlook " or interpretation of the world, is something different then an impossible world.
Then you misunderstand "world" and "possible".
Originally posted by heusdens
Are we talking here about the real world, or just about our ideas or interpretations of the world?
Modal logic attempts to embrace the latter.
http://plato.stanford.edu/entries/logic-modal/

[heusdens]

Dialectical Materialism

Dialectical Materialism is a way of understanding reality; whether thoughts, emotions, or the material world. Simply stated, this methodology is the combination of Dialectics and Materialism. The materialist dialectic is the theoretical foundation of Marxism (while being communist is the practice of Marxism).

"It is an eternal cycle in which matter moves, a cycle that certainly only completes its orbit in periods of time for which our terrestrial year is no adequate measure, a cycle in which the time of highest development, the time of organic life and still more that of the life of being conscious of nature and of themselves, is just as narrowly restricted as the space in which life and self-consciousness come into operation. A cycle in which every finite mode of existence of matter, whether it be sun or nebular vapour, single animal or genus of animals, chemical combination or dissociation, is equally transient, and wherein nothing is eternal but eternally changing, eternally moving matter and the laws according to which it moves and changes.

Fredrick Engels
Dialectics of Nature
Introduction

"Motion is the mode of existence of matter. Never anywhere has there been matter without motion, or motion without matter, nor can there be."

"Change of form of motion is always a process that takes place between at least two bodies, of which one loses a definite quantity of motion of one quality (e.g. heat), while the other gains a corresponding quantity of motion of another quality (mechanical motion, electricity, chemical decomposition).

"Dialectics, so-called objective dialectics, prevails throughout nature, and so-called subjective dialectics (dialectical thought), is only the reflection of the motion through opposites which asserts itself everywhere in nature, and which by the continual conflict of the opposites and their final passage into one another, or into higher forms, determines the life of nature."

Fredrick Engels
Dialectics of Nature

But dialectical materialism insists on the approximate relative character of every scientific theory of the structure of matter and its properties; it insists on the absence of absolute boundaries in nature, on the transformation of moving matter from one state into another, that from our point of view [may be] apparently irreconcilable with it, and so forth.

Vladimir Lenin
Materialism and Empirio-criticism

With each epoch-making discovery even in the sphere of natural science, materialism has to change its form; and after history was also subjected to materialistic treatment, a new avenue of development has opened here, too. [Ch. 2, The End of Classical German Philosophy]

"For dialectical philosophy nothing is final, absolute, sacred. It reveals the transitory character of everything and in everything; nothing can endure before it except the uninterrupted process of becoming and of passing away, of endless ascendancy from the lower to the higher."

Fredrick Engels
The End of Classical German Philosophy

An example of dialectical materialism applied is the materialist conception of history .

'Dialectical Materialism' was coined by Karl Kautsky and popularised in the Second International after the death of Marx and Engels.

See also: dialectics, materialism, Historical Materialism and Political Economy.



Dialectics

Dialectics is the method of reasoning which aims to understand things concretely in all their movement, change and interconnection, with their opposite and contradictory sides in unity.

Dialectics is opposed to the formal, metaphysical mode of thought of ordinary understanding which begins with a fixed definition of a thing according to its various attributes. For example formal thought would explain: ‘a fish is something with no legs which lives in the water’.

Darwin however, considered fish dialectically: some of the animals living in the water were not fish, and some of the fish had legs, but it was the genesis of all the animals as part of a whole interconnected process which explained the nature of a fish: they came from something and are evolving into something else.

Darwin went behind the appearance of fish to get to their essence. For ordinary understanding there is no difference between the appearance of a thing and its essence, but for dialectics the form and content of something can be quite contradictory — parliamentary democracy being the prime example: democracy in form, but dictatorship in content!

And for dialectics, things can be contradictory not just in appearance, but in essence. For formal thinking, light must be either a wave or a particle; but the truth turned out to be dialectical — light is both wave and particle. (See the principle of excluded middle)

We are aware of countless ways of understanding the world; each of which makes the claim to be the absolute truth, which leads us to think that, after all, “It’s all relative!”. For dialectics the truth is the whole picture, of which each view make up more or less one-sided, partial aspects.

At times, people complain in frustration that they lack the Means to achieve their Ends, or alternatively, that they can justify their corrupt methods of work by the lofty aims they pursue. For dialectics, Means and Ends are a unity of opposites and in the final analysis, there can be no contradiction between means and ends — when the objective is rightly understood, "the material conditions [means] for its solution are already present or at least in the course of formation" (Marx, Preface of Contribution to a Political Economy)

One example of dialectics we can see in one of Lenin's call: “All Power to the Soviets” spoken when the Soviets were against the Bolsheviks. Lenin understood, however, that the impasse could only be resolved by workers’ power and since the Soviets were organs of workers’ power, a revolutionary initiative by the Bolsheviks would inevitably bring the Soviets to their side: the form of the Soviets during the time (lead by Mensheviks and SRs) were at odds with the content of the Soviets as Workers’, Peasants’ and Soldiers’ Councils.

Formal thinking often has trouble understanding the causes of events — something has to be a cause and something else the effect — and people are surprised when they irrigate land and 20 years later — due to salination of the land, silting of the waterways, etc — they have a desert! Dialectics on the other hand understands that cause and effect are just one and another side of a whole network of relations such as we have in an ecosystem, and one thing cannot be changed without changing the whole system.

These are different aspect of Dialectics, and there are many others, because dialectics is the method of thinking in which concepts are flexible and mobile, constrained only by the imperative of comprehending the movement of the object itself, however contradictory, however transient.

History: Dialectics has its origins in ancient society, both among the Chinese and the Greeks, where thinkers sought to understand Nature as a whole, and saw that everything is fluid, constantly changing, coming into being and passing away. It was only when the piecemeal method of observing Nature in bits and pieces, practiced in Western thinking in the 17th and 18th century, had accumulated enough positive knowledge for the interconnections, the transitions, the genesis of things to become comprehensible, that conditions became ripe for modern dialectics to make its appearance. It was Hegel who was able to sum up this picture of universal interconnection and mutability of things in a system of Logic which is the foundation of what we today call Dialectics.

As Engels put it:

“the whole world, natural, historical, intellectual, is represented as a process — i.e., as in constant motion, change, transformation, development; and the attempt is made to trace out the internal connection that makes a continuous whole of all this movement and development.” [Socialism: Utopian & Scientific]

It was in the decade after Hegel’s death — the 1840s — when Hegel’s popularity was at its peak in Germany, that Marx and Engels met and worked out the foundations of their critique of bourgeois society.

Hegel’s radical young followers had in their hands a powerful critical tool with which they ruthlessly criticised Christianity, the dominant doctrine of the day. However, one of these Young Hegelians, Ludwig Feuerbach, pointed out that Holy Family was after all only a Heavenly image of the Earthly family, and said that by criticising theology with philosophy, the Young Hegelians were only doing the same as the Christians — Hegel’s Absolute Idea was just another name for God! For Feuerbach, ideas were a reflection of the material world and he held it to be ridiculous that an Idea could determine the world. Feuerbach had declared himself a materialist.

Marx and Engels began as supporters of Feuerbach. However, very soon they took up an opposition to Feuerbach to restore the Hegelian dialectic which had been abandoned by Feuerbach, and to free it from the rigidity of the idealistic Hegelian system and place the method on a materialist basis:

“Hegel was an idealist. To him, the thoughts within his brain were not the more or less abstract pictures of actual things and processes, but, conversely, things and their evolution were only the realized pictures of the ‘Idea’, existing somewhere from eternity before the world was. This way of thinking turned everything upside down, and completely reversed the actual connection of things in the world. ” [Fredrick Engels, Socialism: Utopian and Scientific]

Thus, for Marx and Engels, thoughts were not passive and independent reflections of the material world, but products of human labour, and the contradictory nature of our thoughts had their origin in the contradictions within human society. This meant that Dialectics was not something imposed on to the world from outside which could be discovered by the activity of pure Reason, but was a product of human labour changing the world; its form was changed and developed by people, and could only be understood by the practical struggle to overcome these contradictions — not just in thought, but in practice.

Further Reading: [The Science of Dialectics], by Fredrick Engels, Dialectics of Nature, by Fredrick Engels, an example of dialectics in: The Metaphysics of Political Economy, by Karl Marx; The ABC of Materialist Dialectics, by Leon Trotsky; Lenin's Summary of Dialectics.

See also the Sampler for multiple definitions. For examples of Dialectics: references to Examples from History and Society and Examples from Personal Life in Hegel’s Logic; and see the definition on Taoism for a look at an ancient process of dialectics.

Source:
Encyclopedia of Marxism (http://www.marxists.org/glossary/terms/d/i.htm)

[John Page]

Originally posted by heusdens
......
Source:
Encyclopedia of Marxism (http://www.marxists.org/glossary/terms/d/i.htm)
What has this cut and paste job to do with this thread?

[spacer1]

Originally posted by John Page:
What do you suppose is the difference between the two?["possible worlds" and "logically possible worlds"]
Nothing that I can see. I posited different logics for different possible worlds because, otherwise, I'm not sure that I understand your point. Is there a possible world where square circles exist?
I would say it is possible worlds that are illogical. If you then object that illogical worlds are impossible, how do you account for different logics?
Why are possible worlds illogical, and according to which (possible world's) system of logic?
But modal logic attempts to describe all possible worlds - but you are necessarily stuck with the POV of the modal logic you have selected.
"All possible worlds." How are we "stuck" with any particular point of view?
In summary, all possible worlds are all possible worlds, even if you think some of them illogical or impossible.
I believe that for a world to be logically impossible, it must break some tautological meaning of words, e.g. square circle. Therefore, it is our description of its being possible that is contradictory. If the description contradicts itself, merely by the meaning of the words, then it cannot be possible in reality either. Otherwise, we need new meanings for our words.
My issue with a claim (maybe implicit) that modal logic encompasses all possible worlds. According to my relativist standpoint it will be impossible to attain such a goal. Of course one can acknowledge and try to embrace this objection through the addition of dialetheism principles to admit contradictions.
This would seem to remove all value from any system of logic. Anything goes.

[heusdens]

Originally posted by spacer1
I believe that for a world to be logically impossible, it must break some tautological meaning of words, e.g. square circle. Therefore, it is our description of its being possible that is contradictory. If the description contradicts itself, merely by the meaning of the words, then it cannot be possible in reality either. Otherwise, we need new meanings for our words.


But the world does contain "square circles", that is, it contains entities or properties of things that are mutually exclusive.
For instance: particle - wave dualities.
Now this duality has partly gone, because we enhanced our models, but still our models indicate properties of nature that are intuitively and logically wrong. High energy physics shows a lot of such phenomena.

Again this shows that wether or not the world is posible, according to our logic and thinking, has nothing to do with the possibility (i.e. real existence) of the world itself.

That means: we have to change our approach and model of the real world, such that it encompasses such real existing phenomena. That is however not to say that "anything goes" as the arbiter in this case is nature itself.

[John Page]

Originally posted by spacer1
Nothing that I can see. I posited different logics for different possible worlds because, otherwise, I'm not sure that I understand your point. Is there a possible world where square circles exist?
Yes, why not?
Originally posted by spacer1
Why are possible worlds illogical, and according to which (possible world's) system of logic?
I am suggesting that a system of logic L applies to a limited domain and all worlds outside of that domain are illogical w.r.t. L.
Originally posted by spacer1
"All possible worlds." How are we "stuck" with any particular point of view?
Once you adopt a view you are automatically excluding other views. Even if you develop a view that encompasses other views (as modal logic attempts to) there will still be views that are contrary to such modal logic.
Originally posted by spacer1
I believe that for a world to be logically impossible, it must break some tautological meaning of words, e.g. square circle. Therefore, it is our description of its being possible that is contradictory. If the description contradicts itself, merely by the meaning of the words, then it cannot be possible in reality either. Otherwise, we need new meanings for our words.
But, in your example, aren't you just defining two types of shape as mutually exclusive? Can't they be viewed logically as extreme ends of a continuum of types of enclosed area? Tautologies are meant to be broken ;).
Originally posted by spacer1
This would seem to remove all value from any system of logic. Anything goes.
Perhaps "Nothing goes".

Cheers, John

[spacer1]

Originally posted by John Page:
Yes, why not?
Because, as you note, squares and circles are mutually exclusive shapes. Any description of a shape cannot (logically) be both.
I am suggesting that a system of logic L applies to a limited domain and all worlds outside of that domain are illogical w.r.t. L.
Unless we are communicating and understanding our concepts according to some other system of logic than L, I don't see why it should matter.
Once you adopt a view you are automatically excluding other views. Even if you develop a view that encompasses other views (as modal logic attempts to) there will still be views that are contrary to such modal logic.
It appears to me that any logic would be useless if it were otherwise.
But, in your example, aren't you just defining two types of shape as mutually exclusive? Can't they be viewed logically as extreme ends of a continuum of types of enclosed area?
Yes, they are mutually exclusive, and even if we consider them as extreme ends of a continuum, they will still be mutually exclusive. Red is not violet.
Perhaps "Nothing goes".
It does if you don't privilege any system of logic.

[John Page]

Originally posted by spacer1
Because, as you note, squares and circles are mutually exclusive shapes. Any description of a shape cannot (logically) be both.
....interesting that you put the qualifier "logic" in - and I don't disagree that applying conventional rules of logic to a world in which a circle is not a square, a circle will not be a square.

Three points.

1. Think of a continuum between a square whose sides start to bulge until its fully "inflated" to a circle. At what point do we slip from one mutually exclusive definition to the other? I know this is a bit of a Xeno approach but I'm preparing the ground for my other points.

2. Not all descriptions of shapes are mutually exclusive (a sqaure and an oblong are both rectangles).

3. The descriptions of shapes are held mentally. I think this point is significant and let me give an example. During childhood development, we learn to differentiate between different types of thing. Before we have knowledge of the commonly accepted notions (nothing to do with language) of "what a circle is" and "what a square is" we perceive just shapes. At some point in time I would suggest it highly probable that some children believe squares and circles as being the same in order to later refine their perception and conclude they are mutually exclusive.

So, what I'm trying to show here is that we must consider the case where a system tests what happens when an object can be both a square and circle in order to determine that this cannot happen in actuality. For things to be otherwise (I think) would require the existence of some Kantian pure reason that tells us what circles and squares are - my argument is that they are synthetic a priori notions.
Originally posted by spacer1
Unless we are communicating and understanding our concepts according to some other system of logic than L, I don't see why it should matter.
:confused: There are many systems of logic and it doesn't seem to me as though we have a logic that accurately describes the (generic) process of the human mind. In addition to this point, it appears that all humans are different and capable of thinking differently (to some degree). What I'm resisting is some notion of a universal logic L which might appear to be (through intersubjective agreement of truth/falsity) but does not, in fact, exist.
Originally posted by spacer1
It appears to me that any logic would be useless if it were otherwise.
Otherwise than what? I don't understand your reasoning.
Originally posted by spacer1
It does if you don't privilege any system of logic.
Apparently so - hence relativism.

Cheers, John

[ex-xian]

Originally posted by John Page
....interesting that you put the qualifier "logic" in - and I don't disagree that applying conventional rules of logic to a world in which a circle is not a square, a circle will not be a square.
But in any possible world, squares and circles, formally defined, would be such that one cannot be the other.


Three points.

1. Think of a continuum between a square whose sides start to bulge until its fully "inflated" to a circle. At what point do we slip from one mutually exclusive definition to the other? I know this is a bit of a Xeno approach but I'm preparing the ground for my other points.
As soon as the square's sides bulge, it ceases to be a square. And until every point on the object is equidistant from the center, it is not a circle. The slip occurs as soon as the object ceases to meet the definitions.

2. Not all descriptions of shapes are mutually exclusive (a sqaure and an oblong are both rectangles).
But circles and squares are.

3. The descriptions of shapes are held mentally. I think this point is significant and let me give an example. During childhood development, we learn to differentiate between different types of thing. Before we have knowledge of the commonly accepted notions (nothing to do with language) of "what a circle is" and "what a square is" we perceive just shapes. At some point in time I would suggest it highly probable that some children believe squares and circles as being the same in order to later refine their perception and conclude they are mutually exclusive.
Ok.

So, what I'm trying to show here is that we must consider the case where a system tests what happens when an object can be both a square and circle in order to determine that this cannot happen in actuality. For things to be otherwise (I think) would require the existence of some Kantian pure reason that tells us what circles and squares are - my argument is that they are synthetic a priori notions.
Again, Ok. But when the tests are finished, the definitions of square and cirlce are mutally exclusive.

:confused: There are many systems of logic and it doesn't seem to me as though we have a logic that accurately describes the (generic) process of the human mind. In addition to this point, it appears that all humans are different and capable of thinking differently (to some degree). What I'm resisting is some notion of a universal logic L which might appear to be (through intersubjective agreement of truth/falsity) but does not, in fact, exist.
I agree that any logic created by human minds can at best, be only an approximation. However, it seems that general principles can be formalized and be absolutely true. I can't define any of those truths, but the alternative is fraught with contradition.

[JohannGoodflag]

What do we mean by logic?

I would like to make a few propositions, and would be interested in your guys' opinion on them.


Logic is a way of dealing with some world (or perhaps more than one world) in an abstract way (not requiring that we actually fiddle with objects in the world to test propositions).
A body of ideas/methods can only be meaningfully described as being a system of logic if none of the events or relationships in the world(s) it is meant to model present a contradiction in that body of ideas/methods.

For instance, we seem to agree that there is no logic that is handed down from above. However, not all bodies of knowledge or systems of thought are systems of logic either. For instance, "my dog has fleas" is not a system of logic, nor is the recipe for pineapple upside-down cake. You can call them "systems of logic" just as easily as you can call them "my grandmother Sue", but it won't be useful to do so.

My personal concept of logic is that it is a system of thought such that the real world cannot produce events which are logically contradictory. If what I currently consider "logic" does present me with a contradictory statement which is true in the real world, it is evidence that I must reform my system of logic. (More likely, though, is that I have chosen bad axioms.)

Is there any way that the word "logic" can be meaningfully defined, if we suppose that for every system of logic, the real world will contain things which are necessarily contradictory in that system of logic? I wouldn't think so.

Some side notes:

Not even the early models of QM necessarily violated logic -- they were merely operating from poor assumptions, IMO, which is not at all the same.

Depending on what your definition of "possible world" is, there actually can be square circles without contradiction in a possible world, while keeping the definition of "circle" and "square" the same --- but changing the definition of "distance". (This is a purely mathematical idea, so whether the world is "reeely reeely possible" is a matter of metaphysics; but the world is logically coherent, and even easy to describe if anyone is interested.)

[John Page]

Originally posted by ex-xian
But in any possible world, squares and circles, formally defined, would be such that one cannot be the other.
This is the nub of the issue, I don't see on what authority you can state this as a certainty in "any possible world".
Originally posted by ex-xian
However, it seems that general principles can be formalized and be absolutely true. I can't define any of those truths, but the alternative is fraught with contradition.[.
Hence Modal Dialetheism (or Modal Multi-letheism)

[John Page]

Originally posted by JohannGoodflag
A body of ideas/methods can only be meaningfully described as being a system of logic if none of the events or relationships in the world(s) it is meant to model present a contradiction in that body of ideas/methods.
I think there is weight to the view that it is the contradiction (or possibility thereof) that gives rise to meaning. For example, True is False is a contradiction that defines what True is not.

[ex-xian]

Originally posted by JohannGoodflag
I would like to make a few propositions, and would be interested in your guys' opinion on them.

Logic is a way of dealing with some world (or perhaps more than one world) in an abstract way (not requiring that we actually fiddle with objects in the world to test propositions).

A body of ideas/methods can only be meaningfully described as being a system of logic if none of the events or relationships in the world(s) it is meant to model present a contradiction in that body of ideas/methods.
Without overcommitting myself, I'm pretty sure I would agree with these two points.

Is there any way that the word "logic" can be meaningfully defined, if we suppose that for every system of logic, the real world will contain things which are necessarily contradictory in that system of logic? I wouldn't think so.[/b][/quote]
Do you mean "logic" and in [a logic, that is, a formal system, or do just mean the word "logic" in general?

Depending on what your definition of "possible world" is, there actually can be square circles without contradiction in a possible world, while keeping the definition of "circle" and "square" the same --- but changing the definition of "distance". (This is a purely mathematical idea, so whether the world is "reeely reeely possible" is a matter of metaphysics; but the world is logically coherent, and even easy to describe if anyone is interested.)
I find this very interesting. Could you elaborate a bit?

Originally posted by John Page
This is the nub of the issue, I don't see on what authority you can state this as a certainty in "any possible world".
I can state it because of this: regardless of how the labels of "circle" and "square" are used in any possible world, the concepts behind them are carefully defined within the framework of mathematics...a rose by any other name.

In any world where the mathematical definitions that "square" and "cirlce" are used, the necessarily are mutally exclusive.


Hence Modal Dialetheism (or Modal Multi-letheism)
I guess I still don't understand what you mean by that term. By modal dialetheism, do you simply mean an affirmation of multivalent logic over bivalent.

[ex-xian]

Originally posted by John Page
I think there is weight to the view that it is the contradiction (or possibility thereof) that gives rise to meaning. For example, True is False is a contradiction that defines what True is not.
Maybe it would be better to say that negation defines things? That is, given x, x is everything that is ~~x.

[JohannGoodflag]

John Page
I think there is weight to the view that it is the contradiction (or possibility thereof) that gives rise to meaning. For example, True is False is a contradiction that defines what True is not. Define "possibility", as in the phrase "the possibility thereof". Do you mean "concievability", as in we can at least superficially come up with the idea of it happening?

I think that the ideas of true and false precede contradiction, both in a standard presentation of logic, and in terms of how people learn logic in practise. (I don't mean formal training in school: I mean in kindergarden and prior, when learning about lies, stories, etc.)

I would postulate that meaning is always a relational matter. Meaning is given to statements by virtue of what it says about relationships between things. In this sense, contradictions are not a necessary thing for meaning.

JohannGoodflag
Is there any way that the word "logic" can be meaningfully defined, if we suppose that for every system of logic, the real world will contain things which are necessarily contradictory in that system of logic? I wouldn't think so.

ex-xian
Do you mean "logic" and in a logic, that is, a formal system, or do just mean the word "logic" in general?
By logic, I mean some system of thought, so I suppose I mean "a" logic. However, without an idea to the contrary, I don't know that "a" logic would necessarily would have to be formal. Any system of thought which models propositional relationships for some world (and perhaps more general systems of thought than this) could concievably be a logic, whether formal or not.

JohannGoodflag
Depending on what your definition of "possible world" is, there actually can be square circles without contradiction in a possible world, while keeping the definition of "circle" and "square" the same --- but changing the definition of "distance". (This is a purely mathematical idea, so whether the world is "reeely reeely possible" is a matter of metaphysics; but the world is logically coherent, and even easy to describe if anyone is interested.)

ex-xian
I find this very interesting. Could you elaborate a bit?

Certainly.

As per usual, describe points on the plane by ordered paris of real numbers, (x,y). The point (0,0) is the origin, etc. Let p1 = (x1, y1) and p2 = (x2, y2) be two points on the plane. Our usual concept of distance is given by a metric function, d(p1,p2) which has some specific properties (http://mathworld.wolfram.com/Metric.html). The metric function we all know and love is essentially due to Pythagoras:

d(p1, p2) = sqrt((x1 - x2)^2 + (y1 - y2)^2)

However, this is not the only metric function: another favorite one (and sometimes practical to use!) is the so-called square metric:

D(p1, p2) = max( abs(x1 - x2), abs(y1 - y2) )

The reason why it's called the square metric will become apparent very quickly.

Now, how do we define circles and squares?

A square is a plane figure with four sides of the same length, and where the angle at each vertex 90 degrees.
A circle is a plane figure whose boundary points are all equidistant to some point (i.e. the center).

You'd have to specify how you were defining angles, I suppose: however, there is at least one way (using linear algebra) that one could define an angle of ninety degrees without making reference to distances. I'll assume that no-one wants to pick at it for now.

Under the usual metric, d, these two definitions are mutually exclusive, of course. However, under the square metric D, every circle will also be a square. For instance, the set of points on the unit circle using the metric D are the line segments {(1,y): -1 <= y <= 1}, {(x,1): -1 <= x <= 1}, {(-1,y): -1 <= y <= 1}, and {(x,-1): -1 <= x <= 1}, which is easy to verify. It's pretty clearly a square. Not all squares are circles, though: any square whose sides are not aligned with the x- and y-axes will not be a circle under the metric D either.

This topic is considered (very incidentally) when first discussing metric spaces in introductory topology, where the square metric D is "the second favorite" for talking about easy-to-picture metric spaces. No big deal is made out of the fact that the "balls around a point x" under the metric D are actually (hyper-)cubic in shape.

There are reasons for dismissing this as a possible world. For instance, the distance between two points in the square metric depends strongly on your choice of co-ordinate system. This is anathema to physics since Newton, at the very least. The situations where this metric is practical are in very constrained situations (such as navigating city blocks) or abstract ones (not relating to physical space).

[ex-xian]

Originally posted by JohannGoodflag
As per usual, describe points on the plane by ordered paris of real numbers, (x,y). The point (0,0) is the origin, etc. Let p1 = (x1, y1) and p2 = (x2, y2) be two points on the plane. Our usual concept of distance is given by a metric function, d(p1,p2) which has some specific properties (http://mathworld.wolfram.com/Metric.html). The metric function we all know and love is essentially due to Pythagoras:

d(p1, p2) = sqrt((x1 - x2)^2 + (y1 - y2)^2)

However, this is not the only metric function: another favorite one (and sometimes practical to use!) is the so-called square metric:

D(p1, p2) = max( abs(x1 - x2), abs(y1 - y2) )

The reason why it's called the square metric will become apparent very quickly.

Now, how do we define circles and squares?

A square is a plane figure with four sides of the same length, and where the angle at each vertex 90 degrees.
A circle is a plane figure whose boundary points are all equidistant to some point (i.e. the center).

You'd have to specify how you were defining angles, I suppose: however, there is at least one way (using linear algebra) that one could define an angle of ninety degrees without making reference to distances. I'll assume that no-one wants to pick at it for now.
Wait! I know this one! Orthogonalilty, right?


Under the usual metric, d, these two definitions are mutually exclusive, of course. However, under the square metric D, every circle will also be a square. For instance, the set of points on the unit circle using the metric D are the line segments {(1,y): -1 <= y <= 1}, {(x,1): -1 <= x <= 1}, {(-1,y): -1 <= y <= 1}, and {(x,-1): -1 <= x <= 1}, which is easy to verify. It's pretty clearly a square. Not all squares are circles, though: any square whose sides are not aligned with the x- and y-axes will not be a circle under the metric D either.

This topic is considered (very incidentally) when first discussing metric spaces in introductory topology: no big deal is made out of the fact that the "balls around a point x" are actually (hyper-)cubic in shape.
This is all I know about topology: a cube and a sphere are topologiclly equivalent, where a torus isn't. So are two shape TE if there exists a metric that can transform one into the other.

There are reasons for dismissing this as a possible world. For instance, the distance between two points in the square metric depends strongly on your choice of co-ordinate system. This is anathema to physics since Newton, at the very least. The situations where this metric is practical are in very constrained situations (such as navigating city blocks) or abstract ones (not relating to physical space).
I see... and thanks for the explanation. So we still say that squares and circles taken with a pythagorean metric are mutually exclusive (I'm not sure of the technical way to express this, but I guess you get my idea).

[John Page]

Originally posted by JohannGoodflag
Define "possibility", as in the phrase "the possibility thereof". Do you mean "concievability", as in we can at least superficially come up with the idea of it happening?
By possibility I meant possibility of its conception.
Originally posted by JohannGoodflag
I think that the ideas of true and false precede contradiction, both in a standard presentation of logic, and in terms of how people learn logic in practise. (I don't mean formal training in school: I mean in kindergarden and prior, when learning about lies, stories, etc.)

Yes, synthetic a priori (to possible conceptual knowledge thereof).
Originally posted by JohannGoodflag
I would postulate that meaning is always a relational matter. Meaning is given to statements by virtue of what it says about relationships between things. In this sense, contradictions are not a necessary thing for meaning. Yes, a mere difference is not necessarily a (literal) contradiction.

Cheers, John

[John Page]

Originally posted by ex-xian
So we still say that squares and circles taken with a pythagorean metric are mutually exclusive
So, with Johann's help, do you agree that the pythagorean metric is not a universal/absolute truth?

[ex-xian]

Originally posted by John Page
So, with Johann's help, do you agree that the pythagorean metric is not a universal/absolute truth?
No! Quite the opposite. The pythagorean metric is the defining characteristic of mutually exclusive squares and cirlces.

edited to add:
I would still like to know what is meant by "modal dialetheism." My study of logic has been only propositional and bivalent. I've only recently began exploring the other possibilites.

[John Page]

Originally posted by ex-xian
The pythagorean metric is the defining characteristic of mutually exclusive squares and cirlces.
So only applies to possible world for which the pythagorean metric is an axiom.
Originally posted by ex-xian
I would still like to know what is meant by "modal dialetheism." My study of logic has been only propositional and bivalent. I've only recently began exploring the other possibilites.
I made it up because the breeds of modal logic I have read about seem fundamentally flawed to me. I highly recommend Stanford's Plato pages on modal logic (http://plato.stanford.edu/entries/logic-modal/) and dialetheism (http://plato.stanford.edu/entries/dialetheism/) .

Cheers, John

[ex-xian]

Originally posted by John Page
So only applies to possible world for which the pythagorean metric is an axiom.
Actually, the PT is a theorem, not an axiom. At any rate, I don't see how this changes anything. Before I was arguing that squareness and cirleness are mutally exclusive based upon their definitions within the formal system of mathematics. Now I assert the squareness and circleness are mutally exclusive within the formal system of mathematics where distance is measured via the PT.

I made it up because the breeds of modal logic I have read about seem fundamentally flawed to me. I highly recommend Stanford's Plato pages on modal logic (http://plato.stanford.edu/entries/logic-modal/) and dialetheism (http://plato.stanford.edu/entries/dialetheism/) .

Cheers, John
I've read the bit about modal logic, but not the bit abou dialetheism. I let you know what I think.

[John Page]

Originally posted by ex-xian
Actually, the PT is a theorem, not an axiom. At any rate, I don't see how this changes anything. Before I was arguing that squareness and cirleness are mutally exclusive based upon their definitions within the formal system of mathematics.
Driving it this way, your view looks like "The formal system of mathematics is axiomatic for all possible worlds within system E."

Cheers, John

[ex-xian]

Originally posted by John Page
Driving it this way, your view looks like "The formal system of mathematics is axiomatic for all possible worlds within system E."

Cheers, John
What's wrong with that?

[John Page]

Originally posted by ex-xian
What's wrong with that?
Oh, there's nothing "wrong" with it. Except that I don't see the universe as being constrained by it. And contradictions do exist. And there are multiple formal systems mathematics.

[ex-xian]

Originally posted by John Page
Oh, there's nothing "wrong" with it. Except that I don't see the universe as being constrained by it. And contradictions do exist. And there are multiple formal systems mathematics.
I'm not saying that the universe conforms to mathematics. Einstien said "So far as mathematics refer to reality, they are not certain. As far as they are certain they do not refer to reality."

But mathematics would be axiomatic in all possible worlds, just as any axiomatic system would be. I only think the universe is constrained by consistency.

And any mathematical system is certain within its own system. Any contradictions are resolved by changing or adding to the axioms. Set theory is the perfect example.

[John Page]

Originally posted by ex-xian
And any mathematical system is certain within its own system. Any contradictions are resolved by changing or adding to the axioms. Set theory is the perfect example.
Broadly, yes, but I'm not sure about your use of the word "within". Arguably the axioms are not "within" they are "given". In this sense, discovered contradictions are not "resolved" by inventing new, given, axioms - more "explained away". Now the validity of the explanation, including the new axiom, is fair game. Godel had something to say about this ;).

Cheers, John

[JohannGoodflag]

John Page
Oh, there's nothing "wrong" with it. Except that I don't see the universe as being constrained by it. And contradictions do exist. And there are multiple formal systems mathematics. By "contradictions do exist", do you mean in mathematics, or reality? Could you please clarify, and perhaps give an example or two?

JohannGoodflag
I would postulate that meaning is always a relational matter. Meaning is given to statements by virtue of what it says about relationships between things. In this sense, contradictions are not a necessary thing for meaning.

John Page
Yes, a mere difference is not necessarily a (literal) contradiction.

I'm a little confused by your response. Contrast it with: "I think there is weight to the view that it is the contradiction (or possibility thereof) that gives rise to meaning." It is that comment which I was responding to, in the quotation above: and then you say something about differences, which I find difficult to relate to your comment on how contradictions may be the "source of meaning" (implying, all meaning).


* * *

Notes on circular squares and the Pythagorean Theorem:

ex-xian
Orthogonalilty, right?
At the time I had been thinking of something more complicated, but yes, that also makes (much more) sense. :)

ex-xian
This is all I know about topology: a cube and a sphere are topologiclly equivalent, where a torus isn't. So are two shape TE if there exists a metric that can transform one into the other.

The metric doesn't transform one to the other... the situation is slightly more complicated than that. The particular metric function defines the concepts of square, circle for a given metric space. A homotopy function describes how one particular shape can be deformed to another (and is generally not unique).

So we still say that squares and circles taken with a pythagorean metric are mutually exclusive (I'm not sure of the technical way to express this, but I guess you get my idea).

I think this is the right way to say it.

John Page
So, with Johann's help, do you agree that the pythagorean metric is not a universal/absolute truth? [... it] only applies to possible world for which the pythagorean metric is an axiom.

ex-xian
Actually, the PT is a theorem, not an axiom. At any rate, I don't see how this changes anything. Before I was arguing that squareness and cirleness are mutally exclusive based upon their definitions within the formal system of mathematics.

I suspect the PT can only be proven if one presupposes the usual definition of distance: in this sense, it is an 'axiom'. In mathematics, we just talk about metric spaces, where we declare up front which metric (way of measuring distance) we consider meaningful. The fact that the 'Pythagorean' metric is useful in reality can be considered a part of physics, really.

There is a sort of "reason why" it is useful, though: if I'm not mistaken, it's the only metric which does not depend on what co-ordinate system you choose, which jives with the principle of relativity (which was known since at least the time of Galileo, although most famously used by Einstein). The principle of relativity is pretty solid as far as axioms about reality go, so as far as we're concerned, the PT works marvelously --- even though we cannot prove it to be true of the real world.

Taking up John's question above for myself, I would agree with you (and with Einstein) that nothing in math is absolute, insofar as it is used to refer to things in reality. Math is a lens, not a crystal ball.

[John Page]

Originally posted by JohannGoodflag
By "contradictions do exist", do you mean in mathematics, or reality? Could you please clarify, and perhaps give an example or two?
Reality. Example: Classical logic when applied to Liar Paradox.
Originally posted by JohannGoodflag
I'm a little confused by your response. Contrast it with: "I think there is weight to the view that it is the contradiction (or possibility thereof) that gives rise to meaning." It is that comment which I was responding to, in the quotation above: and then you say something about differences, which I find difficult to relate to your comment on how contradictions may be the "source of meaning" (implying, all meaning).

I think a difference in meaning gives rise to a contradiction and, as ex-xian has observed, ascribing mutually exclusive properties to the same entity seems to do the trick (for a single observer). e.g. Men are women. This makes no sense unless we requalify the relationship between women e.g. Men are women to the extent that they normally have two arms, two legs and a head.

[JohannGoodflag]

JohannGoodflag
By "contradictions do exist", do you mean in mathematics, or reality? Could you please clarify, and perhaps give an example or two?

Johan Page
Reality. Example: Classical logic when applied to Liar Paradox.

"This sentence is false" does not refer to something in reality: it refers to an abstract (the sentence itself), rather than an object or relationship between objects. The fact that 'this sentence' is understood to refer to the sentence itself (rather than being a free variable, something not yet specified by missing context) is also purely a matter of convention, and slightly sloppy from a linguistic point of view: self-referential logic puzzles are the only place where we see such shenanigans, and probably they exist for the sole purpose of making such puzzles possible. Also, for possibly independent reasons, the sentence does not necessarily have any meaning, depending on which logician you talk to. So, a tenable (but, of course, not universally accepted) position is that it is not a contradiction because it lacks any meaning.

Do you have any stronger examples?

I think a difference in meaning gives rise to a contradiction and, as ex-xian has observed, ascribing mutually exclusive properties to the same entity seems to do the trick (for a single observer). e.g. Men are women.
It seems to me that you are saying that ascribing to a single object different (and in particular, incompatible) meanings is what you consider to give rise to a contradiction.

This seems reasonable --- but then, you are supposing the existence of meaning before you recognise the presence of a contradiction. This does not support your statement that contradictions may be the source of meaning. Perhaps, what you are trying to say is that contradictions are what give the concept of meaning itself a meaning?

[Men are women] makes no sense unless we requalify the relationship between women e.g. Men are women to the extent that they normally have two arms, two legs and a head.
(To illustrate a point I made further above: note which word I replaced with the square brackets. Under what conditions would you suppose 'this' referred to the sentence quoted above, in the sentence quoted above?)

So, what you are saying is that "men are women" makes no sense unless we (arbitrarily) define "men" and "women" in such a manner that the sentence is no longer a contradiction. Fair enough: but how does this illustrate how contradictions can provide meaning? It seems to me that the insistence on meaning is exactly what would force us to either reject the sentence or redefine the terms. The contradiction does not provide meaning, it rather seems to be a wilful disregard of the purpose (or less absolutely, the usefulness) of meaning.

[John Page]

Originally posted by JohannGoodflag
"This sentence is false" does not refer to something in reality: it refers to an abstract (the sentence itself), rather than an object or relationship between objects.
:confused: The sentence is real enough, it is a mental object.
Originally posted by JohannGoodflag
self-referential logic puzzles are the only place where we see such shenanigans, and probably they exist for the sole purpose of making such puzzles possible.
:D I doubt it! Self-reference issues highlight how meaning appears to be as opposed to how meaning actually occurs (IMHO). References are always indirect, they are from one thing to another. If you think that the liar paradox sentence actually refers to itself then this is the source of the contradiction.
Originally posted by JohannGoodflag
Also, for possibly independent reasons, the sentence does not necessarily have any meaning, depending on which logician you talk to.
If it doesn't have any meaning then its not a sentence - another contradiction, methinks.
Originally posted by JohannGoodflag
B]Do you have any stronger examples?[/B]
Stronger? You haven't busted this one, yet.
Originally posted by JohannGoodflag
This seems reasonable --- but then, you are supposing the existence of meaning before you recognise the presence of a contradiction. This does not support your statement that contradictions may be the source of meaning. Perhaps, what you are trying to say is that contradictions are what give the concept of meaning itself a meaning?
Yes, I'm saying they go hand in hand.
Originally posted by JohannGoodflag
(To illustrate a point I made further above: note which word I replaced with the square brackets. Under what conditions would you suppose 'this' referred to the sentence quoted above, in the sentence quoted above?)

This? The concept of men being women.
Originally posted by JohannGoodflag
Fair enough: but how does this illustrate how contradictions can provide meaning?
It was an illustration of my position that differences are different than contradictions but can give rise to a contradiction if used in opposition. Men are women to some extent - think of a Venn diagram with two circles, one representing the scope of meaning of the term "men" and the other "women". Contradiction can occur by claiming that the non-intersecting meanings are similar through their association with the union.

Interesting - I await your comments.

Cheers, john

[JohannGoodflag]

John Page
The sentence is real enough, it is a mental object.
I should have clarified. A sentence is not an object in the real world, in the conventional sense. This is my basis for rejecting it as a contradiction about the real world.

A sentence exists as a physical phenomenon only as a pattern of electrons in a wire (internet transmission), magnetic fields on a hard drive (computer storage), vibrations in a compression wave through air (vocalization), spatial configuration of light absorption/reflection/emission (printed text), or any number of other media.

Furthermore, these patterns represent a sentence only because we have decided by linguistic convention (through the development of English thousands of years ago, and language itself possibly millions of years ago) and technical conventions (the ASCII code, UNICODE, HTML, not to mention recognition of phenomena such as Ohm's Law, etc.)

So, any sentence is not a physical object: it is a pattern in physical media, which we recognise as being sentences only by established conventions. It isn't even clear if the sentence is stored in any recognisable way in the brain, except by the individual brain's idiosyncratic means of memory retrieval --- more conventions, this time evolved through biology.

A sentence, like meaning in general, only exists as a consipracy between the medium which contains a pattern, and the interpreter of that pattern. And then, it isn't clear exactly where the sentence "really exists". So, I do not believe that a sentence is an object in the real world. It isn't even a relationship between objects in the real world, although such a relationship is required for the sentence to be recognized. A sentence may talk about the real world, but the sentence qua sentence is neither an object not a relation in the real world, IMO.

If it doesn't have any meaning then its not a sentence - another contradiction, methinks.

Some linguists will disagree with you. The sentence, "More people have been to Russia than I have", is syntactically flawless in English --- and purely meaningless. Unless you have stronger requirements for "sentencehood" than sytnactical correctness, it would seem that natural languages are able to produce sentences with no meaning.

JohannGoodflag
[...] you are supposing the existence of meaning before you recognise the presence of a contradiction. This does not support your statement that contradictions may be the source of meaning. Perhaps, what you are trying to say is that contradictions are what give the concept of meaning itself a meaning?

John Page
Yes, I'm saying they go hand in hand.

I'm confused. Your reply has the form of an affirmation, but it isn't clear what you are affirming. Are you saying that "the meaning of meaning" and contradictions are what go hand-in-hand? Or is it just meaning in general which goes hand-in-hand with contradictions?

JohannGoodflag
(To illustrate a point I made further above: note which word I replaced with the square brackets. Under what conditions would you suppose 'this' referred to the sentence quoted above, in the sentence quoted above?)

John Page
This? The concept of men being women.

That wasn't what I was asking. I was asking: Under what circumstances would you suppose 'this' in that sentence referred to the sentence itself?

It was an illustration of my position that differences are different than contradictions but can give rise to a contradiction if used in opposition. Men are women to some extent - think of a Venn diagram with two circles, one representing the scope of meaning of the term "men" and the other "women". Contradiction can occur by claiming that the non-intersecting meanings are similar through their association with the union.

I would say that the concepts of "man" and "woman" is fuzzy, and that it is up to the individual to judge where the boundaries lie. As such, they need not intersect at all.

For instance, I would tend to define 'man' and 'woman' such that there is no intersection. Ignoring the age issue for a moment, there would be a number of categories: the ones that come to mind are 'male', 'female', 'androgyne' (no gender traits), 'hermaphrodite' (traits of multiple genders).

Although one could vaguely describe a hermaphrodite as having a certain 'maleness' and 'femaleness' at the same time, it nonetheless remains that it is not 'both a man and a woman'; it is a hermaphrodite. (For an analogy, it is not true that the American flag is red, the american flag is white, and the american flag is blue; rather, it is red-white-and-blue, which is shorthand for saying that all three colours have a presence on the flag, and not the same as the logical conjunction.)

So, given this classification of gender-types (and there could be more, but let's consider just these four for now), I would say that there are fuzzy boundaries between all of them; but there is a meaningful way to define these categories so that 'male' and 'female' do not share a fuzzy border. If they do not share a fuzzy border, they need not have any intersection. They might both intersect a third gender (hermaphrodite, for instance), but that is different.

As far as "mean are women" being possibly true because they share traits in common (e.g. usually having two arms, two eyes, etc.) I would not agree with this at all. The fact that they share traits is a consequence of both being a subset of the larger set, humans. Birds also have two eyes, two legs, care for their young, and are warm blooded: many are also pretty intelligent. Does that mean I am in any meaningful way a bird? I would say not. If I have any "membership amplitude" in the set of birds, it is so abysmally low as to be completely negligeable. Or at least, it is by my determination of fuzziness.

However, you may claim that I resolve these so-called "paradoxes" by using my perogative to define things neatly and tidily so that there is no conflict. I do try to define things neatly and tidily, so to maximize the usefulness of words. However, I would claim that as soon as you allow the set of "men" and the set of "women" to intersect at all, the statement "some men are women" is no longer a contradiction: it is a true statement according to the definitions you provide. Of course, the more general "(all) men are women" will be essentially false unless all men have the qualities you ascribe to women. In that case, your definitions of "man" and "woman" are probably so limp-wristed as to be useless, and I would not be willing to entertain them anyway.

Edited to correct accidental butchering of John's name on my part, and to add clarifying remarks

[John Page]

Originally posted by JohannGoodflag
I should have clarified. A sentence is not an object in the real world, in the conventional sense. This is my basis for rejecting it as a contradiction about the real world.

A sentence exists as a physical phenomenon only as a pattern of electrons in a wire (internet transmission), magnetic fields on a hard drive (computer storage), vibrations in a compression wave through air (vocalization), spatial configuration of light absorption/reflection/emission (printed text), or any number of other media.

Furthermore, these patterns represent a sentence only because we have decided by linguistic convention (through the development of English thousands of years ago, and language itself possibly millions of years ago) and technical conventions (the ASCII code, UNICODE, HTML, not to mention recognition of phenomena such as Ohm's Law, etc.)

So, any sentence is not a physical object: it is a pattern in physical media, which we recognise as being sentences only by established conventions. It isn't even clear if the sentence is stored in any recognisable way in the brain, except by the individual brain's idiosyncratic means of memory retrieval --- more conventions, this time evolved through biology.

A sentence, like meaning in general, only exists as a consipracy between the medium which contains a pattern, and the interpreter of that pattern. And then, it isn't clear exactly where the sentence "really exists". So, I do not believe that a sentence is an object in the real world. It isn't even a relationship between objects in the real world, although such a relationship is required for the sentence to be recognized. A sentence may talk about the real world, but the sentence qua sentence is neither an object not a relation in the real world, IMO.

Johann:

Your response, I believe, contains the very contradiction we are talking about. Are you claiming that physicality is the only type of thing in the "real" world? It is clear to me that the word "sentence" is used to refer to (the concept of) a group of words that conforms to the syntactic rules for sentences which, in turn, form part of language exchanged between us. So, the object-type "sentence" has a particular form by which we come to know instances of sentences. I argue that we must experience an instance of the sentence in order to know it (is a sentence) - hence the (instance of a) sentence exist within the mind/brain which is part of reality.

Accordingly, I totally reject the description of a sentence given in the second part of the quote above. Moving to your third paragraph, it is your mind/brain that contains the linguistic conventions - are you arguing they are not part of the real world?

Originally posted by JohannGoodflag
I'm confused. Your reply has the form of an affirmation, but it isn't clear what you are affirming. Are you saying that "the meaning of meaning" and contradictions are what go hand-in-hand? Or is it just meaning in general which goes hand-in-hand with contradictions?
:confused: Differences and contradictions go hand in hand. Differences in meanings permit contradiction.
Originally posted by JohannGoodflag
That wasn't what I was asking. I was asking: Under what circumstances would you suppose 'this' in that sentence referred to the sentence itself?[/SIZE]
Depends upon either the intent of the author or the reading of reader. I presume what you are driving at is the case that in the sentence "This sentence refers to itself", "This" refers to the sentence "This sentence refers to itself". Am I correct?
Originally posted by JohannGoodflag
For instance, I would tend to define 'man' and 'woman' such that there is no intersection.
In which case "This man is a woman" is a contradiction, but, as you pointed out, this is not necessarily true in all possible worlds.

Cheers, John

[JohannGoodflag]

John Page
Are you claiming that physicality is the only type of thing in the "real" world?
Depends on what you mean by "physicality". I maintain that if there's anything other than physical interactions between (what we might call) material objects, then it is so difficult to even detect that for all practical purposes, we may neglect it's existence. Under this sort of interpretation of "physicality", my answer would be "yes".

It is clear to me that the word "sentence" is used to refer to (the concept of) a group of words that conforms to the syntactic rules for sentences which, in turn, form part of language exchanged between us. So, the object-type "sentence" has a particular form by which we come to know instances of sentences. I argue that we must experience an instance of the sentence in order to know it (is a sentence) - hence the (instance of a) sentence exist within the mind/brain which is part of reality.
[...]
Moving to your third paragraph, it is your mind/brain that contains the linguistic conventions - are you arguing they are not part of the real world?

The brain is a physical object. The patterns in the brain that allow us to understand language is a physical structure. But are these patterns the same in any human brain? Consider the patterns in my brain for understanding English. If you re-create the same patterns out of spaghetti or play-doh, do they have any meaning? For that matter, if you chopped the relevant bits out of my brain and put them in a perti dish, would they have any meaning? Would they any longer represent any linguistic faculty, other than by the historical accident that it once performed that function?

The human brain records language, by whatever means, into itself, and it interprets those patterns by yet another means. But do the patterns somehow explicitly represent the language? No! The only reason why we suppose the patterns have any relevance at all is beacause they play a role in determining our behaviour. The structural patterns of the brain have meaning in their physical relation and interaction with the rest of the body, and through it with the world at large.

Where do sentences fall into this mess? Sentences are part of the simplest model for guessing what people will do. When they make sounds of varying tone and intensity, moderated by the oral cavity, they make rich patterns. These patterns are perceived by the ears of others, which influences the patterns in the brains of those others, and in so doing influences their future behaviour. Trying to model this from the physical level would be a nightmare to wake up any physicist screaming. But if we build a model of what these sounds are for --- if we add a semantic description of some sort of inherent intent and purpose of the sounds (which need not exist but is useful for description), then we can understand these sounds as language, a medium for communicating very high-level brain states.

Language is a semantic model for our communication. It is not fundamental: it is the explanation for what actually is going on, the way of thinking about it so that it all makes sense. Under this interpretation, sentences are no more physical objects than the number three is.

It is possible to argue that all this requires that I assume that language plays the role of a theory in the first place: after all, a theory is also entertained in the brain, and therefore (by some undisclosed means) may have a "physical reality". I will concede that this "language-as-theory" theory is not clearly derivable from no premises --- but then, what is? It seems internally consistent, and therefore a tenable position.

I will concede that I may not be correct (whatever that means when digging up foundations of semantics and logic). I am not a neurologist, and I'm not entirely sure it would matter if I were. But this is the simplest explanation for my understanding of the world. If nothing is absolute in physics, then the same must also be true of social studies. Thus, I still say that sentences are not real objects: they are elements of a theory.

And thus, the Liar's paradox is a theoretical statement about an element of the theory itself. It is irrelevant that brains are physical: language may be considered a theory of one element of human interaction, and beacuse theory is not reality, the Liar's paradox is not a physical object.

Differences and contradictions go hand in hand. Differences in meanings permit contradiction.
Never mind. I asked you about how contradictions could be the source of meaning if meaning precedes contradictions, and you seem to keep changing the subject. Perhaps I'm being thickskulled, but for some time on this part of the thread, I have repeatedly failed to see the connections between my questions and your answers, so there you go.

JohannGoodflag
That wasn't what I was asking. I was asking: Under what circumstances would you suppose 'this' in that sentence referred to the sentence itself?

John Page
Depends upon either the intent of the author or the reading of reader. I presume what you are driving at is the case that in the sentence "This sentence refers to itself", "This" refers to the sentence "This sentence refers to itself". Am I correct?

Again, never mind. If you're interested in continuing with me this facet of the conversation, please track which sentence I was actually referring to (a sentence in one of your posts which was not actually self referential at all). I've certainly been trying to keep the context clear.

JohannGoodflag
For instance, I would tend to define 'man' and 'woman' such that there is no intersection.

John Page
In which case "This man is a woman" is a contradiction, but, as you pointed out, this is not necessarily true in all possible worlds.

No, "This man is a woman" would simply be false. Are you using "contradiction" in the sense of "is always false", or "antinomy"?

JohannGoodflag

Edited to remove a question addressing something which may not be a part of the miscommunications John and I are experiencing

[John Page]

Originally posted by JohannGoodflag
Under this sort of interpretation of "physicality", my answer would be "yes".
OK, good, that eliminates Dualism.
Originally posted by JohannGoodflag
The brain is a physical object. The patterns in the brain that allow us to understand language is a physical structure. But are these patterns the same in any human brain? Consider the patterns in my brain for understanding English. If you re-create the same patterns out of spaghetti or play-doh, do they have any meaning?
No, but how is this relevant?
1. Patterns may not be the same physcially but have functional equivalence. Relocation of motor functions through learning after a stroke indicates that there is at least one layer of indirection/plasticity involved.
2. The spaghetti or play-doh would likely not embody the processes of mind required to give those patterns meaning.
Originally posted by JohannGoodflag
The human brain records language, by whatever means, into itself, and it interprets those patterns by yet another means. But do the patterns somehow explicitly represent the language? No! The only reason why we suppose the patterns have any relevance at all is beacause they play a role in determining our behaviour. The structural patterns of the brain have meaning in their physical relation and interaction with the rest of the body, and through it with the world at large.
Again, I con't see how this is relevant. Language is expressed on paper but implemented in a mind - be it human or otherwise. The patterns in the brain are the results of analysis of other patterns in the brain and there are numerous studies showing how parts of the brain handle specialized language functions. All I can think of right now is to try considering the notion of a language as being separate from its implementation
Originally posted by JohannGoodflag
Under this sort of interpretation of "physicality", my answer would be "yes".
Gotta go - will finish later...

[John Page]

Originally posted by JohannGoodflag
Thus, I still say that sentences are not real objects: they are elements of a theory.

And thus, the Liar's paradox is a theoretical statement about an element of the theory itself. It is irrelevant that brains are physical: language may be considered a theory of one element of human interaction, and beacuse theory is not reality, the Liar's paradox is not a physical object.
Sorry, Johann, but I can't sqaure this away with some of your previous comments. If sentences do not participate in the real world how do they refer to anything in it? Sentences are at some level of abstraction from the directly physically tangible, but they are part of the real world nevertheless.

On your comments regarding the Liar Paradox, why do theories not participate in the real world. Here I'm refering to the actual notion, the theory itself, not what the theory proposes. Would you agree that if all humans understand PT, there is at least one instance of PT (stored, latent, abstracted, whatever) in each human's mind/brain?
Originally posted by JohannGoodflag
Never mind. I asked you about how contradictions could be the source of meaning if meaning precedes contradictions, and you seem to keep changing the subject.
I felt this was a kind of straw man, I'm not saying meaning precedes contradiction, I said they go hand in hand.
Originally posted by JohannGoodflag
Again, never mind. If you're interested in continuing with me this facet of the conversation, please track which sentence I was actually referring to (a sentence in one of your posts which was not actually self referential at all). I've certainly been trying to keep the context clear.
OK, I'm trying to understand. Here's the paragraph of mine containing that sentence:
I think a difference in meaning gives rise to a contradiction and, as ex-xian has observed, ascribing mutually exclusive properties to the same entity seems to do the trick (for a single observer). e.g. Men are women. This makes no sense unless we requalify the relationship between women e.g. Men are women to the extent that they normally have two arms, two legs and a head.
Following which there was the dialog:
Johann:
--------------------------------------------------------------------------------
[Men are women] makes no sense unless we requalify the relationship between women e.g. Men are women to the extent that they normally have two arms, two legs and a head.
--------------------------------------------------------------------------------
(To illustrate a point I made further above: note which word I replaced with the square brackets. Under what conditions would you suppose 'this' referred to the sentence quoted above, in the sentence quoted above?)
John : This? The concept of men being women.
Johann: That wasn't what I was asking. I was asking: Under what circumstances would you suppose 'this' in that sentence referred to the sentence itself?

I hope you see that I was responding by stating what "This" referred to, i.e. the concept of men being women. I don't think it reasonable to ask me to enumerate the circumstances under which it would refer internally to the sentence rather than the preceding concept. Best I can offer is a that for stand-alone statement beginning with "This", the word will refer to the stand-alone statement. Same as the use of "it", where in the case of doubt as to the subject of the sentence should default to the first subject. Is this different than your understadning of the conventions for English language?

Originally posted by JohannGoodflag
No, "This man is a woman" would simply be false. Are you using "contradiction" in the sense of "is always false", or "antinomy"?
Antinomy and Cleopatra. :)

Seriously, contradiction as in the sense of incompatible with sentential logic and false in accordance with the rules of that logic if the meanings of the words "men and women" are defined as XOR, rather than antinomy or paradox. This echoes back to my POV that difference and contradiction go hand in hand.

Hope this makes sense.

Cheers, john

[JohannGoodflag]

JohannGoodflag
Thus, I still say that sentences are not real objects: they are elements of a theory.

And thus, the Liar's paradox is a theoretical statement about an element of the theory itself. It is irrelevant that brains are physical: language may be considered a theory of one element of human interaction, and beacuse theory is not reality, the Liar's paradox is not a physical object.

John Page
Sorry, Johann, but I can't sqaure this away with some of your previous comments. If sentences do not participate in the real world how do they refer to anything in it? Sentences are at some level of abstraction from the directly physically tangible, but they are part of the real world nevertheless.

To paraphrase you, langauge may be written on paper, but it is interpreted by the brain. But where is language in the brain? Certain static and dynamic structures in the brain will be involved, but do these represent a physical presence of language? I would say not. They may be patterns which in some way embody language features, but they are no more "language itself" than three apples form "the number three itself".

Sentences don't "participate" in the real world any more than the number three participates in the real world. Even the concepts of sentences (and the number three) don't participate in the real world. However, there are patterns and structures in the human brain which interact with the rest of the human brain, and prompts what we might call "language-behaviour" --- talking, listening, reading, and writing --- which are best explained or understood in terms of a language theory.

In principle, unless you believe in dualism of some sort (and you seem not to), it seems inevitable to me that everything about humans can be explained through physical interactions between small particles. The fact that it would be impractical to try and model or solve such an immense physical system as a human from the sub-atomic level is irrelevant. If you grant that, then everything about humans is a feedback loop with a rich structure --- and with no actual need for a concept of "language" to explain our behaviour.

In particular, language-behaviour is the result of a cascade of causes and effects inside certain structures of the human brain which cause us to interact with the outside world (including other humans), and take in information from the outside world and filter it through these same brain centers. Because this is an unnecessarily elaborate model of human thought, we try and explain these behaviours in terms of a more flexible theory involving "language". The fact that we have come up with this theory ourselves, and that it too is somehow encoded in our brains, is irrelevant --- unless you presuppose that language is a fundamental part of reality (somehow) in the first place, the patterns representing that theory are just another part of the chemical cascades in our crania.

Language and its elements are another part of the human experience, and so, we tend to assume it has some deep importance: anthropocentrism saturates almost all of philosophy. But in the end, it's just a convenient way to explain our intricate language-behaviour, which can in principle be explained without the need to consider such a concept as 'language' at all.

If this is inconsistent with something I have said in the past, it may mean that my viewpoint is evolving with time, but I would still be interested in hearing where the conflict lies.

On your comments regarding the Liar Paradox, why do theories not participate in the real world. Here I'm refering to the actual notion, the theory itself, not what the theory proposes. Would you agree that if all humans understand PT, there is at least one instance of PT (stored, latent, abstracted, whatever) in each human's mind/brain?

The stored pattern of PT in my brain could just as easily be a recipe for blueberry pie, Beethoven's 5th Symphony, or a prescient vision of my own death. The meaning only exists in the relationships with the rest of the brain, and the way it causes the resulting human to behave. The PT exists only to explain part of my behaviour (and the behaviour of others) which we classify as "doing mathematics".


I felt this was a kind of straw man, I'm not saying meaning precedes contradiction, I said they go hand in hand.

( earlier this same thread: )
I think there is weight to the view that it is the contradiction (or possibility thereof) that gives rise to meaning. For example, True is False is a contradiction that defines what True is not.

This second quotation is what I'm asking about. Nevermind whatever hypothetical strawmen you think I'm attacking: I was just trying to understand these two sentences. Every communication I've made on this facet since your quotation has been an attempt to get you to explain how contradictions can give rise to meaning, under the assumption that you actually meant what you said above. It is now apparent that you did not, so never mind.

OK, I'm trying to understand. Here's the paragraph of mine containing that sentence: [...]
Let me start this facet from scratch, as we've tangled it irretrievably.

Consider the following sentence (the fact that you said it is really just a historical accident): "This makes no sense unless we requalify the relationship between women."

Now, this sentence existed in a larger context, but let's experiment with it a little. Under what counditions would you say that the sentence above is self-referential? That is, in what contexts could it be placed where you would it as a self-refertential sentence? In particular, how many ways can it be made to be self-referential without taking it as a quotation?

My contention is that the conditions under which it may be self-referential are exactly those conditions when the entire point of the discussion is to examine a self-referential sentence. It seems to me that the conventions which admit self-referential sentences in the first place do not exist outside of discussions of self-referential statements, or references to such discussions (e.g. in humour).

Seriously, contradiction as in the sense of incompatible with sentential logic and false in accordance with the rules of that logic if the meanings of the words "men and women" are defined as XOR, rather than antinomy or paradox. This echoes back to my POV that difference and contradiction go hand in hand.
Okay, so then your statement would then be that for any world, there exist statements which are always false. Given your idea that language somehow exists in itself in the real world, I can see how you go from there to "contradictions exist in any world". However, given what I have said above, I hope you can see why I would reject such a statement.

For me, we just have formal relationships which never obtain, and there's no magic or fanfare about it. By no means would I ever phrase such a thing "contradictions exist in any possible world", and I will still argue against any such phrasing, even if I correctly understand your reasons for putting it that way.

[John Page]

Originally posted by JohannGoodflag
Certain static and dynamic structures in the brain will be involved, but do these represent a physical presence of language? I would say not. They may be patterns which in some way embody language features, but they are no more "language itself" than three apples form "the number three itself".
1. I agree pretty much with your view on language aprt from the above. To me this is like saying that "Force is not in the internal combustion engine." There are instances of forces within the internal combustion engine (and we cannot see them but we can measure them) and ther are instances of language in the human mind/brain (and we cannot see them and we can measure them).
2. I agree the three apples to which you refer are are not the number three, it is the mind that ascribes to that compund object the property of "threeness" having quantified the like objects within the group.
Originally posted by JohannGoodflag
The stored pattern of PT in my brain could just as easily be a recipe for blueberry pie, Beethoven's 5th Symphony, or a prescient vision of my own death. The meaning only exists in the relationships with the rest of the brain, and the way it causes the resulting human to behave. The PT exists only to explain part of my behaviour (and the behaviour of others) which we classify as "doing mathematics".
I agree, people that understand PT have instances of PT stored or otherwise encoded into their mind/brain. I said this before. I'm not sure I agree that PT exists only to explain your behavior!
Originally posted by JohannGoodflag
This second quotation is what I'm asking about. Nevermind whatever hypothetical strawmen you think I'm attacking: I was just trying to understand these two sentences. Every communication I've made on this facet since your quotation has been an attempt to get you to explain how contradictions can give rise to meaning, under the assumption that you actually meant what you said above. It is now apparent that you did not, so never mind.
Here it is again. "True is false", when understood to be false gives rise to (an instance of) the meaning of false. i.e. I meant what I said.
Originally posted by JohannGoodflag
Consider the following sentence (the fact that you said it is really just a historical accident): "This makes no sense unless we requalify the relationship between women."

Now, this sentence existed in a larger context, but let's experiment with it a little. Under what counditions would you say that the sentence above is self-referential?
:confused: If you insert "sentence" after "This".
Originally posted by JohannGoodflag
In particular, how many ways can it be made to be self-referential without taking it as a quotation?

My contention is that the conditions under which it may be self-referential are exactly those conditions when the entire point of the discussion is to examine a self-referential sentence. It seems to me that the conventions which admit self-referential sentences in the first place do not exist outside of discussions of self-referential statements, or references to such discussions (e.g. in humour).
Very interesting. I'll ponder this some more. In the meantime, you may wish to consider that self-reference can only occur w.r.t. an observer so what we end up discussing is the sentence that is in your mind rather than the marks on paper. Perhaps you could give me an example of what you mean by "the conventions that admit self-referential statements".
Originally posted by JohannGoodflag
Okay, so then your statement would then be that for any world, there exist statements which are always false. Given your idea that language somehow exists in itself in the real world, I can see how you go from there to "contradictions exist in any world". However, given what I have said above, I hope you can see why I would reject such a statement.
Yes, I do, but I think your rejection premature. As I have stated before, I'm not saying "for any world", I'm not making a universal claim. I'm saying there are possible worlds in which certain statements that are always false - example, in the mental world of a devout believer it is always false that his/her god doesn't exist. I didn't say that contradictions exist in any possible world (use of the universal again) - what I tried to explain is why I think a world with contradictions can explain a world without, but not vice versa. If you think it valid to mentally construct a single possible world by combining one with contradictions and one without, IMO the combination would include contradictions.
Originally posted by JohannGoodflag
For me, we just have formal relationships which never obtain...
Is this support for relativism?

Cheers, John