Poll: Is it possible to believe in a contradiction?

[careful]

Spoiler: Option 3

Believing is an action that occurs in grades, so a binary criteria is not an adequate system

It is certainly possible to construct or entertain simultaneously multiple propositions that are in logical conflict, say for example (I'll be using phenomena in language to exemplify my arguments):

P1: Animals exist

P2: Animals do not exist

Both of these cannot be true, because one is a negation of the other.
Interestingly enough, I think our ability to do this at least shows that what we are able to speak is not bounded to only truthful propositions (perhaps this is not the same state of affairs for animal communication) and also that we can articulate a proposition without asserting its truth. The fact that P and its negation could even be articulated, and furthermore that it is totally comprehensible, maybe be more an indication of the mechanical qualities of our language faculty (though what sort of linguistic/mathematical/logical qualities would be indicated I would not know), say for example that syntactically permissible sentences can be articulated independently of their whether or not they are true. Adding to this example, a further observed quality, is nicely suggested by the well known instance of a syntactically permissible sentence that has no meaningful interpretation (ie it is incomprehensible):

"Colorless green ideas sleep furiously" Chomsky [http://en.wikipedia.org/wiki/Colorless_green_ideas_sleep_furiously]

So we should assume that grammaticality in general is not a criteria employed in assessing truthfulness. Nor in the general case does a grammatical consideration make it any more feasible to derive meaning from a sentence.

With these ideas in mind, I think the sole agent responsible for our ability to form P1 and P2 may in principle be merely the syntactic flexibility of our language operating outside of the bounds of truth or comprehensibility. This is certainly a very mechanical aspect of language.

Having a plausible explanation for why we might be able to form grammatical and comprehensible propositions like P1 and P2 in the first place that conflict in logical terms we should now formulate a working definition of "believing". Let us assume belief to be a psychological state of mind and articulate its relation to the objective truth-hood of those entities that are the objects of believe. I need to propose the objectivity of truth values here, even though there may not be such a thing. Whether there is true objectivity, or what that even means, is not my concern here, so just think of this post more or less as an exploration of implications resulting from assuming there is objectivity in the truth or falsity of propositions. So that whether a given proposition is true or false is always predetermined independently of anyone individuals state of mind and specifically that truth-hood is not determined by unanimous agreement from collected individuals.

Taking the Wikipedia definition as a starting point:

• [li]Belief is the psychological state in which an individual holds a proposition or premise to be true.[/li]

With this definition, what an individual believes in is limited to what that individual holds as true. If a proposition is objectively true and an individual believes to be true, then everything seems consistently in accord with our definitions and assumptions. What needs explaining is the possibility of a situation where a proposition is objectively true but an individual believes it to be false (or vice-versa).

For the affirmative side of the argument (i.e. an individual can believe in a contradiction) let's make an expansion on that definition and assume that an individual can "belief" in false propositions, keeping in mind that we have objective and predetermined truth-values, so that consequently a system of "beliefs" is not defined as those propositions which are held to be true in the mind of an individual, but that the believed in propositions that an individual holds can include false ones as well. In this sense, our usage of the term "believing" is just being taken as synonymous with "holding" (as a cognitive action), and now the term "holding" has the burden of definition. Well at some eventual point of inquiry we will have no option but to invoke some set of axioms, ill stop the potential infinite regress now by taking the meaning of the term "holding" in a cognitive sense as axiomatic, and I will appeal to the reader?s intuition for justification. Although this discussion may be irrevocably hampered by not explicating what is meant by "holding" something in the mind, I still think we can get some interesting ideas out by moving on from this.
All this would certainly be at odds to Aristotle's way of thinking:

Spoiler: Aristotle's way of thinking

"One cannot say of something that it is and that it is not in the same respect and at the same time."

But in asserting a cognitive ability to hold both true and false propositions, how are we now to go about in trying to empirically refute or validate this? Could we draw efficacious data from social sciences, economics, or religion? I don't know. This is why I started this thread.

The negative side of the argument (i.e. an individual can't believe in a contradiction) seems to be merely an acceptance of Wikipedia's definition that the only propositions held in the mind are the truthful ones. This would be nice if it were readily the case, but remember that our language (which is an invention of the mind) is powerful enough to grant us with the ability to articulate in a grammatical way, and further to comprehend to an extent, propositions which are objective contradictions (at least by assumption of objectivity). Well grammar is a process in the mind and so somewhere in the mind is an agent which has generated a contradiction and in some realm of the mind this contradiction has a seat. If we are to functionally segregate the language faculty from the faculty of the mind that is responsible for beliefs and believing, this would yield an easy explanation by then saying that language can operate outside of an individual's held beliefs. In other words we are capable of articulating false propositions but not believing in them because not all language related events in the mind are codependent on the beliefs of the individual.

Well it's mid afternoon, so I have to get drunk and go visit the bank now. Post your thoughts.

 

[Rowan93]

People can believe contradictions because they compartmentalise. If you see something that proves a bunch of things you believe to be wrong, you don't tend to update all the beliefs. This is just what we get for running on software "designed" by a process that isn't even sapient, on equally broken hardware.

Or, in short, we need robot brains.

 

[DoPo]

Of course we can. Orwell named that double-thinking. Anyone can hold two contradictory opinions, and in fact most people do. The example that personally shocks me the most - people that believe that "democracy" is equal to "absolute freedom" in all aspects. Never mind that the word means something completely different, the same people have given up some of their freedoms. And the biggest paradox is, that it usually comes up when they are denied a relatively small freedom, such as being punished (in some way) for cursing, or something like that. Or even better yet, murder is bad but is punishable by...death (not always or anywhere but you get the idea).

If you look into the logical fallacies, you will see that a significant portion of them are double-thinking. Just go somewhere where they play a lottery or something, get a couple of smart people that frequent there and try to explain probability to them. Let's assume they understand it, they wouldn't really stop playing then - after all what if the odds are stacked against them, somebody's going to win eventually, why miss their chance?

 

[careful]

If you look into the logical fallacies, you will see that a significant portion of them are double-thinking. Just go somewhere where they play a lottery or something, get a couple of smart people that frequent there and try to explain probability to them. Let's assume they understand it, they wouldn't really stop playing then - after all what if the odds are stacked against them, somebody's going to win eventually, why miss their chance?

Well on your point of engaging in risky behavior despite knowledge of low likelihoods, I don't think this is very epitomically hypocritical behavior in anyway, nor do I really think such behaviors are suggestive of logically incongruent beliefs. Since probabilities in these situations are not assumed to be 0 or 1, there is always a chance of success. So there is no irrefutable and conclusive evidence that outcomes will not be successful at least in the mind of the better. Hence the better does not hold a belief of the form:

If I purchase enough tickets, I will win

nor a belief of the form (even after discovery of the probabilistic information, because the probabilities are neither 0 nor 1):

No matter how many tickets I purchase, I will not win

So I don't see the logical fallacy you are alluding too.
You brought up a really good example with Orwell's double-think, which is all the more relevant because the double-think was also realized in propositions of language as well as numerical intuition. I believe that he said a constructable proposition in double-think is 1+1=3. A statement like this is much harder to embrace than a language-based contradiction because propositions about numbers do not contain the inherent ambiguity that language-based propositions do while the ambiguity inherent in language works in our favor by our being able to take advantage of the fact that the grammars of natural languages are not as well enumerated or explicated as other formal systems are and hence proving the contradictory aspect of the proposed proposition would be an easier task. It would be much much harder, I believe, to construct a contradiction in a non-language based system, such as numbers or imagery for example, that would likely be the candidate for demonstrating the contradiction-containing proposition, which is by principle a belief held by rational humans, that we are looking for.

 

[careful]

People can believe contradictions because they compartmentalise. If you see something that proves a bunch of things you believe to be wrong, you don't tend to update all the beliefs. This is just what we get for running on software "designed" by a process that isn't even sapient, on equally broken hardware.

Or, in short, we need robot brains.

Well, in the categorization of information it is possible that not every category is being subject to the same criteria for assessing truth values. Plus I am making a distinction between knowledge and belief, with the presumption that it is possible to hold knowledge of something while not committing to a belief of it. Take the memory of a song for example. If you can recall by memory the song, then that song is certainly part of your knowledge base. But it makes no sense to consider a "belief of the song". I take the two to be different, but I do claim that both knowledge and beliefs are categorized in the mind as you say, albeit not necessarily in a hierarchy with respect to each other. So I agree with you on the observable categorization ability, but I don't see how in principle this ability is necessarily contingent upon an ability to belief in a contradiction. In fact, to me it seems, that a belief in a contradiction would only complicate the categorization, and since a more simpler categorization methodology might in reality be much more likely to emerge in intelligent beings, the ability to belief in a contradiction might even be discouraged in favor of a more simple categorization system.

I think to validate your thesis, you would have to construct a logical/mathematical model of how humans categorize beliefs, which of course would have to be empirically justificated for ultimate acceptance, and then show that it logically follows through formal inference that this categorizing system is necessarily contingent upon the ability to belief in a contradiction, or in other words, to demonstrate that if humans were not able to belief in a contradiction then their observed method of categorizing beliefs would be logically impossible.

 

[Rowan93]

People can believe contradictions because they compartmentalise. If you see something that proves a bunch of things you believe to be wrong, you don't tend to update all the beliefs. This is just what we get for running on software "designed" by a process that isn't even sapient, on equally broken hardware.

Or, in short, we need robot brains.

Well, in the categorization of information it is possible that not every category is being subject to the same criteria for assessing truth values. Plus I am making a distinction between knowledge and belief, with the presumption that it is possible to hold knowledge of something while not committing to a belief of it. Take the memory of a song for example. If you can recall by memory the song, then that song is certainly part of your knowledge base. But it makes no sense to consider a "belief of the song". I take the two to be different, but I do claim that both knowledge and beliefs are categorized in the mind as you say, albeit not necessarily in a hierarchy with respect to each other. So I agree with you on the observable categorization ability, but I don't see how in principle this ability is necessarily contingent upon an ability to belief in a contradiction. In fact, to me it seems, that a belief in a contradiction would only complicate the categorization, and since a more simpler categorization methodology might in reality be much more likely to emerge in intelligent beings, the ability to belief in a contradiction might even be discouraged in favor of a more simple categorization system.

I think to validate your thesis, you would have to construct a logical/mathematical model of how humans categorize beliefs, which of course would have to be empirically justificated for ultimate acceptance, and then show that it logically follows through formal inference that this categorizing system is necessarily contingent upon the ability to belief in a contradiction, or in other words, to demonstrate that if humans were not able to belief in a contradiction then their observed method of categorizing beliefs would be logically impossible.

No, I'm not talking about a categorization system that makes sense, with hierarchies and such, you only get that with a sane, competent, sapient being writing the code. Evolution is, at its absolute best, only one out of three of those. Nothing is properly categorized, it all exists in a sort of mess, but there are wuzzy lines separating some beliefs from other beliefs that keep things from being properly set out. Or something else equally stupid, I don't know any actual neuroscience - the main thing I'm trying to say is that human brains aren't "well-designed" enough to be incapable of believing a contradiction.

 

[Zen Toombs]

Long story short, yes a person can, either through compartmentalization or by not thinking their beliefs through.

 

[CrystalShadow]

People can believe contradictions because they compartmentalise. If you see something that proves a bunch of things you believe to be wrong, you don't tend to update all the beliefs. This is just what we get for running on software "designed" by a process that isn't even sapient, on equally broken hardware.

Or, in short, we need robot brains.

Well, in the categorization of information it is possible that not every category is being subject to the same criteria for assessing truth values. Plus I am making a distinction between knowledge and belief, with the presumption that it is possible to hold knowledge of something while not committing to a belief of it. Take the memory of a song for example. If you can recall by memory the song, then that song is certainly part of your knowledge base. But it makes no sense to consider a "belief of the song". I take the two to be different, but I do claim that both knowledge and beliefs are categorized in the mind as you say, albeit not necessarily in a hierarchy with respect to each other. So I agree with you on the observable categorization ability, but I don't see how in principle this ability is necessarily contingent upon an ability to belief in a contradiction. In fact, to me it seems, that a belief in a contradiction would only complicate the categorization, and since a more simpler categorization methodology might in reality be much more likely to emerge in intelligent beings, the ability to belief in a contradiction might even be discouraged in favor of a more simple categorization system.

I think to validate your thesis, you would have to construct a logical/mathematical model of how humans categorize beliefs, which of course would have to be empirically justificated for ultimate acceptance, and then show that it logically follows through formal inference that this categorizing system is necessarily contingent upon the ability to belief in a contradiction, or in other words, to demonstrate that if humans were not able to belief in a contradiction then their observed method of categorizing beliefs would be logically impossible.

No, I'm not talking about a categorization system that makes sense, with hierarchies and such, you only get that with a sane, competent, sapient being writing the code. Evolution is, at its absolute best, only one out of three of those. Nothing is properly categorized, it all exists in a sort of mess, but there are wuzzy lines separating some beliefs from other beliefs that keep things from being properly set out. Or something else equally stupid, I don't know any actual neuroscience - the main thing I'm trying to say is that human brains aren't "well-designed" enough to be incapable of believing a contradiction.

Yes, but as an AI researcher will readily admit, many problems the human mind is very good at, depend on things being fuzzy.

Take trying to work out what is, and is not a car?

What defines for instance, the difference between a car, a truck, and a train?

How about a car with an extra set of wheels that allows it to run on railway track? Is that still a car, or is it a train?

If you try and force hard dividing lines into situations like this you always end up with things that are impossible to categorise.

In fact, it's quite easy to argue that binary either/or states are almost non-existent in the environment we usually have to deal with.

most things are fuzzy. There is no clear dividing line between life and death either for instance. A 'dead' body often still contains many living cells.
At what point is something 'dead' or alive then? 50%? 25% 99%?

To believe there is in fact only an either/or (it's either dead, or it's alive) relationship is a gross oversimplification of reality in almost all cases.

Few things are clearly in one category or another.

A processing system which insists that they are will struggle with any but the most contrived of scenarios.

Or to put it differently, in absolutes, something is either true, or it is false.
(That's a tree, or it isn't.)

But the actual environment we are dealing with most of the time is quite different.
(There's a 95% probability it's a tree. But it could also be a bush, or a flower. Or perhaps even a rock. Or a painting... Or... - Well, you get the idea.)

And it gets worse, in that not only is there uncertainty in classification because of imperfect information, but there is also a case to be made that in many situations the actual thing you are trying to classify isn't neatly in one category or another.

Is A shade somewhere between Yellow and green, in fact, a shade of green, or a shade of yellow?

At what concentration of ingredients does my fruit juice become just plain water?

When does paper become cardboard?

At what point can you say you have jet fuel, compared to say, kerosene?

Very few things have a clear, true or false, either/or answer to them.

Any data processing device that cannot cope with ambiguity would be fundamentally broken if it had to deal with an environment which contains them.

 

[Yopaz]

Christians believe god is love. Christians believe that god killed the population of Sodom and Gomorrah, killed all humans in a flood, that god made people sacrifice their children and that he made a bet (which is not allowed) with the devil (which is double bad) where he killed a man's family, made him sick and then actually appeared before and fought, just to prove a point.

We believe contradictions all the time. Our minds aren't perfect. If you ask the same question using different words and points of view then you are bound to get contradictions.

My example. Is it OK to steal? Is it OK to steal from the rich? Is it OK to steal as a last resort to save your family? Is it OK to kill someone? Is it OK to kill someone who has done murder himself? Is it ethically right to have the death penalty? Is it OK to kill to save your own life or those near to you?

When asked like that you might get consistent answers, bu if you make a form with various ethical questions and jumble all of those questions within several others you will get contradictions. They can even look at the results and when you point out the contradictions they will disagree that they are contradictions.

 

[Redingold]

Humans are very good at doublethink. There's nothing impossible about believing contradictory things, unless you want to also be correct.

 

[Rowan93]

No, I'm not talking about a categorization system that makes sense, with hierarchies and such, you only get that with a sane, competent, sapient being writing the code. Evolution is, at its absolute best, only one out of three of those. Nothing is properly categorized, it all exists in a sort of mess, but there are wuzzy lines separating some beliefs from other beliefs that keep things from being properly set out. Or something else equally stupid, I don't know any actual neuroscience - the main thing I'm trying to say is that human brains aren't "well-designed" enough to be incapable of believing a contradiction.

Yes, but as an AI researcher will readily admit, many problems the human mind is very good at, depend on things being fuzzy.

Take trying to work out what is, and is not a car?

What defines for instance, the difference between a car, a truck, and a train?

How about a car with an extra set of wheels that allows it to run on railway track? Is that still a car, or is it a train?

If you try and force hard dividing lines into situations like this you always end up with things that are impossible to categorise.

In fact, it's quite easy to argue that binary either/or states are almost non-existent in the environment we usually have to deal with.

most things are fuzzy. There is no clear dividing line between life and death either for instance. A 'dead' body often still contains many living cells.
At what point is something 'dead' or alive then? 50%? 25% 99%?

To believe there is in fact only an either/or (it's either dead, or it's alive) relationship is a gross oversimplification of reality in almost all cases.

Few things are clearly in one category or another.

A processing system which insists that they are will struggle with any but the most contrived of scenarios.

Or to put it differently, in absolutes, something is either true, or it is false.
(That's a tree, or it isn't.)

But the actual environment we are dealing with most of the time is quite different.
(There's a 95% probability it's a tree. But it could also be a bush, or a flower. Or perhaps even a rock. Or a painting... Or... - Well, you get the idea.)

And it gets worse, in that not only is there uncertainty in classification because of imperfect information, but there is also a case to be made that in many situations the actual thing you are trying to classify isn't neatly in one category or another.

Is A shade somewhere between Yellow and green, in fact, a shade of green, or a shade of yellow?

At what concentration of ingredients does my fruit juice become just plain water?

When does paper become cardboard?

At what point can you say you have jet fuel, compared to say, kerosene?

Very few things have a clear, true or false, either/or answer to them.

Any data processing device that cannot cope with ambiguity would be fundamentally broken if it had to deal with an environment which contains them.

I'm not sure if you could have actual contradictions there, except for, say, a belief that X is jet fuel and X is not jet fuel.

It's not really possible, in a practical sense at least, to think of the substance that just went into a plane as not jet fuel, even while the jet is using it as fuel (sure, you might have a different definition, but if you definition of "jet fuel" is not "something that can/does fuel a jet", you're either using it figuratively and don't really believe it, or you have a wrong definition).
But that sort of thing can get a little more complex, and if something like that fits into a larger framework of beliefs, then a belief two or three steps further away might not get updated. And if it doesn't, then the framework of beliefs you have is contradictory. And human brains tend to do that, and that's what I was meant to begin with, finally have an example coming to mind that isn't religion-based.

 

[CrystalShadow]

No, I'm not talking about a categorization system that makes sense, with hierarchies and such, you only get that with a sane, competent, sapient being writing the code. Evolution is, at its absolute best, only one out of three of those. Nothing is properly categorized, it all exists in a sort of mess, but there are wuzzy lines separating some beliefs from other beliefs that keep things from being properly set out. Or something else equally stupid, I don't know any actual neuroscience - the main thing I'm trying to say is that human brains aren't "well-designed" enough to be incapable of believing a contradiction.

Yes, but as an AI researcher will readily admit, many problems the human mind is very good at, depend on things being fuzzy.

Take trying to work out what is, and is not a car?

What defines for instance, the difference between a car, a truck, and a train?

How about a car with an extra set of wheels that allows it to run on railway track? Is that still a car, or is it a train?

If you try and force hard dividing lines into situations like this you always end up with things that are impossible to categorise.

In fact, it's quite easy to argue that binary either/or states are almost non-existent in the environment we usually have to deal with.

most things are fuzzy. There is no clear dividing line between life and death either for instance. A 'dead' body often still contains many living cells.
At what point is something 'dead' or alive then? 50%? 25% 99%?

To believe there is in fact only an either/or (it's either dead, or it's alive) relationship is a gross oversimplification of reality in almost all cases.

Few things are clearly in one category or another.

A processing system which insists that they are will struggle with any but the most contrived of scenarios.

Or to put it differently, in absolutes, something is either true, or it is false.
(That's a tree, or it isn't.)

But the actual environment we are dealing with most of the time is quite different.
(There's a 95% probability it's a tree. But it could also be a bush, or a flower. Or perhaps even a rock. Or a painting... Or... - Well, you get the idea.)

And it gets worse, in that not only is there uncertainty in classification because of imperfect information, but there is also a case to be made that in many situations the actual thing you are trying to classify isn't neatly in one category or another.

Is A shade somewhere between Yellow and green, in fact, a shade of green, or a shade of yellow?

At what concentration of ingredients does my fruit juice become just plain water?

When does paper become cardboard?

At what point can you say you have jet fuel, compared to say, kerosene?

Very few things have a clear, true or false, either/or answer to them.

Any data processing device that cannot cope with ambiguity would be fundamentally broken if it had to deal with an environment which contains them.

I'm not sure if you could have actual contradictions there, except for, say, a belief that X is jet fuel and X is not jet fuel.

It's not really possible, in a practical sense at least, to think of the substance that just went into a plane as not jet fuel, even while the jet is using it as fuel (sure, you might have a different definition, but if you definition of "jet fuel" is not "something that can/does fuel a jet", you're either using it figuratively and don't really believe it, or you have a wrong definition).
But that sort of thing can get a little more complex, and if something like that fits into a larger framework of beliefs, then a belief two or three steps further away might not get updated. And if it doesn't, then the framework of beliefs you have is contradictory. And human brains tend to do that, and that's what I was meant to begin with, finally have an example coming to mind that isn't religion-based.

Well, you get into a question of what defines the classification of something.

Jet fuel, obviously, can be classified as fuel that powers a jet engine.

However, it can also be classified as a liquid fuel with a specific composition of various different molecules.

If you take the first classification, then yes, something either is jet fuel, or it isn't.
(Although, since you can put diesel (or even vodka) in a petrol car and probably get it to run, at the risk of ruining the engine, the mere fact that you are using a particular kind of fuel to power your car doesn't automatically make it petrol.)

But if you take the second, you soon realise that if jet fuel is supposed to consist of a certain number of different molecules, in specific proportions, what do you have if the proportions are off?

Also, since it's composition, while being very complex, is nonetheless quite close to that of several other types of petroleum derived fuels, at what point, exactly does something stop being jet fuel, and start being something else?

The nature of the only two options being It IS jet fuel Or it IS NOT jet fuel, require that there be a specific, well-defined cutoff point where it goes from being one thing, to being something else.

If this were not the case, then there would be a range of possible compositions where there is no definitive answer as to whether this is jet fuel or not.
(And at the end of the day, such ambiguity is far more common in the real world than there being such a hard limit that precisely separates two things from each-other.)

Absolutes aren't real. A mathematically perfect circle is impossible to construct outside of the level of abstraction.

Truth is a trickier matter, because it implies something more than just what something is...

Classification on the other hand, is merely the act of grouping similar things together.
That no two examples of anything are ever 100% identical though, implies that no classification scheme is ever accurate.
Because, by stating that two different things are the same, you are inevitably making a statement that is false in an absolute sense.

Truth therefore, could be argued not to exist to begin with, unless you acknowledge the uncertainty inherent in any statement that does not describe an entirely unique thing unlike any other. (But any such description would be meaningless as a form of communication.)

Can a person hold contradictory beliefs? Very likely. Because it doesn't seem like we actually work out problems based on an underlying idea of what's going on, but rather on the far more flexible idea of how closely two things are related.

We don't group things by this is X, that is not X, but we compare things to other things we are already familiar with, then lump them together in whatever comes closest. We only try to create new groups if things currently lumped together in our minds are causing us problems due to their differences.

So, in a way, contradictions are what prompt us to make new groups of things in the first place.

If A = fish. B = NOT fish.
But C is sort of fish, but not really...

Then it either forces you to say that C is B, or C is A... But alternately, you could just say C is C, since it doesn's seem to be a fish, nor is it NOI a fish.

This works fine in a world where actual mutually exclusive things are very rare.

Black and white? Well what's grey then?
Night & Day? what about sunrise & sunset? Which are those?

To ask if you can believe in a contradiction, you first have to establish something which is in fact a contradiction, and not merely the result of over-simplifying reality.

Can a circle be a triangle? No... But is a hexagon closer to being a circle, or a triangle?

Can something be both small and large at the same time? Not really. But something can certainly be inbetween.

So... Is the mind really holding a contradiction, or is it trying to reduce a contradiction down to something else which actually makes sense?

 

[Rowan93]

I'm not sure if you could have actual contradictions there, except for, say, a belief that X is jet fuel and X is not jet fuel.

It's not really possible, in a practical sense at least, to think of the substance that just went into a plane as not jet fuel, even while the jet is using it as fuel (sure, you might have a different definition, but if you definition of "jet fuel" is not "something that can/does fuel a jet", you're either using it figuratively and don't really believe it, or you have a wrong definition).
But that sort of thing can get a little more complex, and if something like that fits into a larger framework of beliefs, then a belief two or three steps further away might not get updated. And if it doesn't, then the framework of beliefs you have is contradictory. And human brains tend to do that, and that's what I was meant to begin with, finally have an example coming to mind that isn't religion-based.

Well, you get into a question of what defines the classification of something.

Jet fuel, obviously, can be classified as fuel that powers a jet engine.

However, it can also be classified as a liquid fuel with a specific composition of various different molecules.

If you take the first classification, then yes, something either is jet fuel, or it isn't.
(Although, since you can put diesel (or even vodka) in a petrol car and probably get it to run, at the risk of ruining the engine, the mere fact that you are using a particular kind of fuel to power your car doesn't automatically make it petrol.)

But if you take the second, you soon realise that if jet fuel is supposed to consist of a certain number of different molecules, in specific proportions, what do you have if the proportions are off?

Also, since it's composition, while being very complex, is nonetheless quite close to that of several other types of petroleum derived fuels, at what point, exactly does something stop being jet fuel, and start being something else?

The nature of the only two options being It IS jet fuel Or it IS NOT jet fuel, require that there be a specific, well-defined cutoff point where it goes from being one thing, to being something else.

If this were not the case, then there would be a range of possible compositions where there is no definitive answer as to whether this is jet fuel or not.
(And at the end of the day, such ambiguity is far more common in the real world than there being such a hard limit that precisely separates two things from each-other.)

Absolutes aren't real. A mathematically perfect circle is impossible to construct outside of the level of abstraction.

Truth is a trickier matter, because it implies something more than just what something is...

Classification on the other hand, is merely the act of grouping similar things together.
That no two examples of anything are ever 100% identical though, implies that no classification scheme is ever accurate.
Because, by stating that two different things are the same, you are inevitably making a statement that is false in an absolute sense.

Truth therefore, could be argued not to exist to begin with, unless you acknowledge the uncertainty inherent in any statement that does not describe an entirely unique thing unlike any other. (But any such description would be meaningless as a form of communication.)

Can a person hold contradictory beliefs? Very likely. Because it doesn't seem like we actually work out problems based on an underlying idea of what's going on, but rather on the far more flexible idea of how closely two things are related.

We don't group things by this is X, that is not X, but we compare things to other things we are already familiar with, then lump them together in whatever comes closest. We only try to create new groups if things currently lumped together in our minds are causing us problems due to their differences.

So, in a way, contradictions are what prompt us to make new groups of things in the first place.

If A = fish. B = NOT fish.
But C is sort of fish, but not really...

Then it either forces you to say that C is B, or C is A... But alternately, you could just say C is C, since it doesn's seem to be a fish, nor is it NOI a fish.

This works fine in a world where actual mutually exclusive things are very rare.

Black and white? Well what's grey then?
Night & Day? what about sunrise & sunset? Which are those?

To ask if you can believe in a contradiction, you first have to establish something which is in fact a contradiction, and not merely the result of over-simplifying reality.

Can a circle be a triangle? No... But is a hexagon closer to being a circle, or a triangle?

Can something be both small and large at the same time? Not really. But something can certainly be inbetween.

So... Is the mind really holding a contradiction, or is it trying to reduce a contradiction down to something else which actually makes sense?

I thought I'd pre-empted that, by basically saying that if you posit a definition of jet fuel that isn't "fuel for jets", you are positing a wrong definition.

And if you're correctly going about the business of defining things, then as soon as you say "jet fuel" if you do mean something other than "fuel for jets", you already have the possibly-arbitrary cut-off point between them in mind. If not, you shouldn't be using the word, because you don't know what it means.

This barely seems to have anything to do with what I've been saying, this is like re-reading what you said in the last post. Have I been communicating poorly?

 

[Womplord]

I BELIEVE THAT YOU CAN BELIEVE IN A CONTRADICTION!
I ALSO BELIEVE THAT YOU CANNOT BELIEVE A CONTRADICTION!

But seriously, you can definitely believe in two things that contradict each other. If you look closely at the beliefs and behavior of Christians, you can see how common this is. I started noticing it when I observed Christians. It's actually quite scary how easy it seems to make people believe contradictory things. Usually there's a belief based on emotion that someone won't give up, and also a belief based on reason which someone won't give up either. So yeah, they live their lives believing both.

 

[CrystalShadow]

Spoiler: Hidden for extreme length

I'm not sure if you could have actual contradictions there, except for, say, a belief that X is jet fuel and X is not jet fuel.

It's not really possible, in a practical sense at least, to think of the substance that just went into a plane as not jet fuel, even while the jet is using it as fuel (sure, you might have a different definition, but if you definition of "jet fuel" is not "something that can/does fuel a jet", you're either using it figuratively and don't really believe it, or you have a wrong definition).
But that sort of thing can get a little more complex, and if something like that fits into a larger framework of beliefs, then a belief two or three steps further away might not get updated. And if it doesn't, then the framework of beliefs you have is contradictory. And human brains tend to do that, and that's what I was meant to begin with, finally have an example coming to mind that isn't religion-based.

Well, you get into a question of what defines the classification of something.

Jet fuel, obviously, can be classified as fuel that powers a jet engine.

However, it can also be classified as a liquid fuel with a specific composition of various different molecules.

If you take the first classification, then yes, something either is jet fuel, or it isn't.
(Although, since you can put diesel (or even vodka) in a petrol car and probably get it to run, at the risk of ruining the engine, the mere fact that you are using a particular kind of fuel to power your car doesn't automatically make it petrol.)

But if you take the second, you soon realise that if jet fuel is supposed to consist of a certain number of different molecules, in specific proportions, what do you have if the proportions are off?

Also, since it's composition, while being very complex, is nonetheless quite close to that of several other types of petroleum derived fuels, at what point, exactly does something stop being jet fuel, and start being something else?

The nature of the only two options being It IS jet fuel Or it IS NOT jet fuel, require that there be a specific, well-defined cutoff point where it goes from being one thing, to being something else.

If this were not the case, then there would be a range of possible compositions where there is no definitive answer as to whether this is jet fuel or not.
(And at the end of the day, such ambiguity is far more common in the real world than there being such a hard limit that precisely separates two things from each-other.)

Absolutes aren't real. A mathematically perfect circle is impossible to construct outside of the level of abstraction.

Truth is a trickier matter, because it implies something more than just what something is...

Classification on the other hand, is merely the act of grouping similar things together.
That no two examples of anything are ever 100% identical though, implies that no classification scheme is ever accurate.
Because, by stating that two different things are the same, you are inevitably making a statement that is false in an absolute sense.

Truth therefore, could be argued not to exist to begin with, unless you acknowledge the uncertainty inherent in any statement that does not describe an entirely unique thing unlike any other. (But any such description would be meaningless as a form of communication.)

Can a person hold contradictory beliefs? Very likely. Because it doesn't seem like we actually work out problems based on an underlying idea of what's going on, but rather on the far more flexible idea of how closely two things are related.

We don't group things by this is X, that is not X, but we compare things to other things we are already familiar with, then lump them together in whatever comes closest. We only try to create new groups if things currently lumped together in our minds are causing us problems due to their differences.

So, in a way, contradictions are what prompt us to make new groups of things in the first place.

If A = fish. B = NOT fish.
But C is sort of fish, but not really...

Then it either forces you to say that C is B, or C is A... But alternately, you could just say C is C, since it doesn's seem to be a fish, nor is it NOI a fish.

This works fine in a world where actual mutually exclusive things are very rare.

Black and white? Well what's grey then?
Night & Day? what about sunrise & sunset? Which are those?

To ask if you can believe in a contradiction, you first have to establish something which is in fact a contradiction, and not merely the result of over-simplifying reality.

Can a circle be a triangle? No... But is a hexagon closer to being a circle, or a triangle?

Can something be both small and large at the same time? Not really. But something can certainly be inbetween.

So... Is the mind really holding a contradiction, or is it trying to reduce a contradiction down to something else which actually makes sense?

I thought I'd pre-empted that, by basically saying that if you posit a definition of jet fuel that isn't "fuel for jets", you are positing a wrong definition.

And if you're correctly going about the business of defining things, then as soon as you say "jet fuel" if you do mean something other than "fuel for jets", you already have the possibly-arbitrary cut-off point between them in mind. If not, you shouldn't be using the word, because you don't know what it means.

This barely seems to have anything to do with what I've been saying, this is like re-reading what you said in the last post. Have I been communicating poorly?

I would say the problem is you're creating a definition that is unworkable, and hence implicitly wrong.

So to say "Fuel for jets" is the only valid definition, raises the problem that it is in fact, a non-definition.

It doesn't tell you anything about what you're dealing with. Therefore, as a practical definition it is entirely useless.

And a definition which is useless, cannot possibly be a correct definition.

 

[FalloutJack]

You're asking me to believe in a contradiction in terms...

You mean like...the ones that occur every day in the human mind because we are all insane people?

 

[Rowan93]

Spoiler: Hidden for extreme length

Well, you get into a question of what defines the classification of something.

Jet fuel, obviously, can be classified as fuel that powers a jet engine.

However, it can also be classified as a liquid fuel with a specific composition of various different molecules.

If you take the first classification, then yes, something either is jet fuel, or it isn't.
(Although, since you can put diesel (or even vodka) in a petrol car and probably get it to run, at the risk of ruining the engine, the mere fact that you are using a particular kind of fuel to power your car doesn't automatically make it petrol.)

But if you take the second, you soon realise that if jet fuel is supposed to consist of a certain number of different molecules, in specific proportions, what do you have if the proportions are off?

Also, since it's composition, while being very complex, is nonetheless quite close to that of several other types of petroleum derived fuels, at what point, exactly does something stop being jet fuel, and start being something else?

The nature of the only two options being It IS jet fuel Or it IS NOT jet fuel, require that there be a specific, well-defined cutoff point where it goes from being one thing, to being something else.

If this were not the case, then there would be a range of possible compositions where there is no definitive answer as to whether this is jet fuel or not.
(And at the end of the day, such ambiguity is far more common in the real world than there being such a hard limit that precisely separates two things from each-other.)

Absolutes aren't real. A mathematically perfect circle is impossible to construct outside of the level of abstraction.

Truth is a trickier matter, because it implies something more than just what something is...

Classification on the other hand, is merely the act of grouping similar things together.
That no two examples of anything are ever 100% identical though, implies that no classification scheme is ever accurate.
Because, by stating that two different things are the same, you are inevitably making a statement that is false in an absolute sense.

Truth therefore, could be argued not to exist to begin with, unless you acknowledge the uncertainty inherent in any statement that does not describe an entirely unique thing unlike any other. (But any such description would be meaningless as a form of communication.)

Can a person hold contradictory beliefs? Very likely. Because it doesn't seem like we actually work out problems based on an underlying idea of what's going on, but rather on the far more flexible idea of how closely two things are related.

We don't group things by this is X, that is not X, but we compare things to other things we are already familiar with, then lump them together in whatever comes closest. We only try to create new groups if things currently lumped together in our minds are causing us problems due to their differences.

So, in a way, contradictions are what prompt us to make new groups of things in the first place.

If A = fish. B = NOT fish.
But C is sort of fish, but not really...

Then it either forces you to say that C is B, or C is A... But alternately, you could just say C is C, since it doesn's seem to be a fish, nor is it NOI a fish.

This works fine in a world where actual mutually exclusive things are very rare.

Black and white? Well what's grey then?
Night & Day? what about sunrise & sunset? Which are those?

To ask if you can believe in a contradiction, you first have to establish something which is in fact a contradiction, and not merely the result of over-simplifying reality.

Can a circle be a triangle? No... But is a hexagon closer to being a circle, or a triangle?

Can something be both small and large at the same time? Not really. But something can certainly be inbetween.

So... Is the mind really holding a contradiction, or is it trying to reduce a contradiction down to something else which actually makes sense?

I thought I'd pre-empted that, by basically saying that if you posit a definition of jet fuel that isn't "fuel for jets", you are positing a wrong definition.

And if you're correctly going about the business of defining things, then as soon as you say "jet fuel" if you do mean something other than "fuel for jets", you already have the possibly-arbitrary cut-off point between them in mind. If not, you shouldn't be using the word, because you don't know what it means.

This barely seems to have anything to do with what I've been saying, this is like re-reading what you said in the last post. Have I been communicating poorly?

I would say the problem is you're creating a definition that is unworkable, and hence implicitly wrong.

So to say "Fuel for jets" is the only valid definition, raises the problem that it is in fact, a non-definition.

It doesn't tell you anything about what you're dealing with. Therefore, as a practical definition it is entirely useless.

And a definition which is useless, cannot possibly be a correct definition.

It tells you exactly what you're dealing with. It tells you that if you use it to fill a tank that feeds into a jet engine which is otherwise functional, you will be able to use that jet engine.

 

[CrystalShadow]

Spoiler: Hidden for extreme length

Well, you get into a question of what defines the classification of something.

Jet fuel, obviously, can be classified as fuel that powers a jet engine.

However, it can also be classified as a liquid fuel with a specific composition of various different molecules.

If you take the first classification, then yes, something either is jet fuel, or it isn't.
(Although, since you can put diesel (or even vodka) in a petrol car and probably get it to run, at the risk of ruining the engine, the mere fact that you are using a particular kind of fuel to power your car doesn't automatically make it petrol.)

But if you take the second, you soon realise that if jet fuel is supposed to consist of a certain number of different molecules, in specific proportions, what do you have if the proportions are off?

Also, since it's composition, while being very complex, is nonetheless quite close to that of several other types of petroleum derived fuels, at what point, exactly does something stop being jet fuel, and start being something else?

The nature of the only two options being It IS jet fuel Or it IS NOT jet fuel, require that there be a specific, well-defined cutoff point where it goes from being one thing, to being something else.

If this were not the case, then there would be a range of possible compositions where there is no definitive answer as to whether this is jet fuel or not.
(And at the end of the day, such ambiguity is far more common in the real world than there being such a hard limit that precisely separates two things from each-other.)

Absolutes aren't real. A mathematically perfect circle is impossible to construct outside of the level of abstraction.

Truth is a trickier matter, because it implies something more than just what something is...

Classification on the other hand, is merely the act of grouping similar things together.
That no two examples of anything are ever 100% identical though, implies that no classification scheme is ever accurate.
Because, by stating that two different things are the same, you are inevitably making a statement that is false in an absolute sense.

Truth therefore, could be argued not to exist to begin with, unless you acknowledge the uncertainty inherent in any statement that does not describe an entirely unique thing unlike any other. (But any such description would be meaningless as a form of communication.)

Can a person hold contradictory beliefs? Very likely. Because it doesn't seem like we actually work out problems based on an underlying idea of what's going on, but rather on the far more flexible idea of how closely two things are related.

We don't group things by this is X, that is not X, but we compare things to other things we are already familiar with, then lump them together in whatever comes closest. We only try to create new groups if things currently lumped together in our minds are causing us problems due to their differences.

So, in a way, contradictions are what prompt us to make new groups of things in the first place.

If A = fish. B = NOT fish.
But C is sort of fish, but not really...

Then it either forces you to say that C is B, or C is A... But alternately, you could just say C is C, since it doesn's seem to be a fish, nor is it NOI a fish.

This works fine in a world where actual mutually exclusive things are very rare.

Black and white? Well what's grey then?
Night & Day? what about sunrise & sunset? Which are those?

To ask if you can believe in a contradiction, you first have to establish something which is in fact a contradiction, and not merely the result of over-simplifying reality.

Can a circle be a triangle? No... But is a hexagon closer to being a circle, or a triangle?

Can something be both small and large at the same time? Not really. But something can certainly be inbetween.

So... Is the mind really holding a contradiction, or is it trying to reduce a contradiction down to something else which actually makes sense?

I thought I'd pre-empted that, by basically saying that if you posit a definition of jet fuel that isn't "fuel for jets", you are positing a wrong definition.

And if you're correctly going about the business of defining things, then as soon as you say "jet fuel" if you do mean something other than "fuel for jets", you already have the possibly-arbitrary cut-off point between them in mind. If not, you shouldn't be using the word, because you don't know what it means.

This barely seems to have anything to do with what I've been saying, this is like re-reading what you said in the last post. Have I been communicating poorly?

I would say the problem is you're creating a definition that is unworkable, and hence implicitly wrong.

So to say "Fuel for jets" is the only valid definition, raises the problem that it is in fact, a non-definition.

It doesn't tell you anything about what you're dealing with. Therefore, as a practical definition it is entirely useless.

And a definition which is useless, cannot possibly be a correct definition.

It tells you exactly what you're dealing with. It tells you that if you use it to fill a tank that feeds into a jet engine which is otherwise functional, you will be able to use that jet engine.

No, it doesn't.

Consider I hand you a random cup of liquid. How would you be able to tell from the liquid alone, that this is jet fuel, and not, say... Dishwashing liquid?

It's not a very good idea to test this by putting the liquid in a jet engine, because if you use the wrong thing, the engine could be destroyed.

Thus, you need some way of determining, solely from the properties of the liquid itself, what it is.

Jet fuel, thanks to it's name confuses the issue.

Consider a diesel engine. You can run a diesel engine on certain blends of vegetable oils.

By you definition, vegetable oil would be diesel, because you can run a diesel engine with it.

Yet diesel and vegetable oil are not the same thing.

Also, consider cars in general.

You can have a car that runs on petrol, or a car that runs on diesel. They're both cars, the design of the engine is slightly different, but otherwise they're very similar.

What happens to a petrol powered car though if you pour diesel in it? (Hint: It's not a good idea to try it.)


Now, think about this for a moment:

Question: What is diesel?
Answer: It is the fuel used by diesel engines.

Question: What is a diesel engine?
Answer: It is an engine that runs on diesel.

So... If I give you an engine at random, will you be able to tell me if it's a diesel engine, or something else?

And... If I give you some fuel at random, how will you know if it's diesel or not?


Remember, a diesel engine can run on a variety of different fuels. The mere fact that it runs doesn't tell you what it is you've put into the engine...

You cannot define things that way without running into serious practical problems.