Paradox vs Contradiction: Are We Confusing Two Distinct Logical Tools?

[olwenboniface]

In many philosophical debates, I have found that the concepts of paradox and contradiction are often used interchangeably, even interchangeably. However, when examined closely, they seem to represent two completely different forms of ideological conflict.

• Contradiction: A contradiction is a situation in which two propositions cannot both be true. If “A is true,” then “A is not true” must be false. This creates an absolute logical boundary.

• Paradox: A paradox is more complex. It may appear to be a contradiction, but it opens up the possibility of a deeper truth or reveals a limit in our system of thinking. For example, “Less is more” sounds absurd but can be true in certain contexts.

What I am wondering is:

• Can we consider a paradox as just an “unresolved contradiction”? Or do they really belong to two different levels of logic and philosophy?

• When we encounter a paradox, should we treat it as a thinking error, or should we see it as an opportunity to explore the limits of our current conceptual system?

• In the history of philosophy, many important ideas (from Zeno to Kant) have originated from paradox. Is paradox a “philosophical motive” rather than a logical error?

I would like to hear your views:

• Do you have examples of cases where paradoxes actually lead to new truths?

• Are we being too easygoing in calling everything that is difficult to understand a “paradox”, instead of analyzing whether it is really a logical contradiction?

I look forward to receiving feedback to clarify this distinction, and perhaps find new approaches in analyzing modern philosophical problems.

[Eodnhoj7]

In many philosophical debates, I have found that the concepts of paradox and contradiction are often used interchangeably, even interchangeably. However, when examined closely, they seem to represent two completely different forms of ideological conflict.

• Contradiction: A contradiction is a situation in which two propositions cannot both be true. If “A is true,” then “A is not true” must be false. This creates an absolute logical boundary.

• Paradox: A paradox is more complex. It may appear to be a contradiction, but it opens up the possibility of a deeper truth or reveals a limit in our system of thinking. For example, “Less is more” sounds absurd but can be true in certain contexts.

What I am wondering is:

• Can we consider a paradox as just an “unresolved contradiction”? Or do they really belong to two different levels of logic and philosophy?

• When we encounter a paradox, should we treat it as a thinking error, or should we see it as an opportunity to explore the limits of our current conceptual system?

• In the history of philosophy, many important ideas (from Zeno to Kant) have originated from paradox. Is paradox a “philosophical motive” rather than a logical error?

I would like to hear your views:

• Do you have examples of cases where paradoxes actually lead to new truths?

• Are we being too easygoing in calling everything that is difficult to understand a “paradox”, instead of analyzing whether it is really a logical contradiction?

I look forward to receiving feedback to clarify this distinction, and perhaps find new approaches in analyzing modern philosophical problems.

Your beginning point is accurate, in general language they are used interchangeably.

What I am aware of is that at a more precise level of definition:

1. Contradiction implies opposition of distinct assertions, a seperation by conflict.

2. Paradox implies connection of distinct assertions, a unity of differences.

Now as to the rest:


A paradox can be viewed as such (this is copy and pasted from another thread in the math/logic section that is similar):

Yes a gradient approach can occur.

The statement of "I am a liar" observes that the person in question both tells the truth and lies. So how does that occur?

Within a given framework of identity, lets say the time and space of a week or several years, that identity has multiple expressions within the given space. Sometimes it is a liar. Sometimes it is a truthteller.

Within the given framework these things occur simultaneously and in grades, sometimes more truth than lies are told or vice versa. These can be observes at meta-identities, identities within identities. So where an identity in the time and space of a week may be "x and y", within the meta identity "x" may only occur in one time and space and "y" within another, all of which are part of the larger time and space of a week.

So identity as grades can be akin to a meta-identity, and identity within an identity.

Now on the other hand all dualisms result in gradation by degree of the dualism itself. Take for example the following dualistic symbolic chain (if you want this in normal language just ask):

1. T
2. F
3. (T,F)
4. T(T,F)
5. F(T,F)
6. (T,F)(T,F)
7. T((T,F)(T,F))
8. F((T,F)(T,F))
9. (T,F)((T,F)(T,F))
10. Unto infinity.

Any dualism, and paradox requires a dualism by degree of differing but isomorphic expressions, results in infinite gradation of said dualism.

So the liars paradox results in different grades of true and false. This can be evidenced by true may be more than false on one set of days, vice versa, or all truths are partial truths and all lies are partial lies.


There is also another complementary way of viewing paradox:

Two opposing or various states existing at once in quantum mechanics is called superpositioning. These states existing at once are effectively indistinct potentiality. When the superposition states are observed one of the potential states is localized according to the state of the observer.

Now a paradox is similar. It is multiple values at once. The paradox is indistinct in its present state. Now when the paradox is observed one or more of the following things happens:

1. The observer chooses one of the several potential values and makes distinctions from there. You will see this in everyday life where a paradox of "this is that" is observed and people naturally takes sides. The paradox becomes a mirror of the observer in this scenario.

2. The observer adds context to the paradox. Now in a general paradox there is no context but the paradox itself and this leads to multiple states coexisting at once. Now if a paradox is given further context, by the observer(s), then a distinct value occurs.

For example the paradox of "I am a liar" had multiple values coexisting that results in the indistinct state of the paradox itself.

Now if the context of "on wednesdays" so we have "I am a liar on wednesdays" then the paradox ceases and we have a clearer and more defined assertion.

3. If opposites cancel eachother out then the paradox becomes pure logical potentiality, a logical space by which values can be projected or assigned. In these respects the paradox is empty of meaning and yet this emptiness becomes of mirror to the observer. As such it is a point by which the observers attention is transformed. You will find this method quite frequently in zen Buddhism where two opposing points, under the paradox, are observed and the cancelation causes a space of potentiality by which the observer is looking into a metaphorical mirror.

4. ****The fourth context is that the paradox becomes a dialectical synthesis where opposites merge to produce a new context. Aspects of an antithesis refine a thesis into a new truth, aspects of a these refine an antithesis into a new truth.

The key to all of this is context.

Context determines how the paradox unfolds to the observer.

Under one context the paradox can lead to gradation, another superpositioned logical states subject to context application, another a mirror to the observer by nature of being empty....so on and so forth.



What I am about to say is heresy in western philosophy:

Paradoxes are both rational and necessary.

View a paradox as "superpositioned assertions" from a perspective of quantum mechanics.

[Age]

In many philosophical debates, I have found that the concepts of paradox and contradiction are often used interchangeably, even interchangeably. However, when examined closely, they seem to represent two completely different forms of ideological conflict.

The whole purpose of 'debate', itself, is to create and cause 'conflict', itself, between two 'parties'.

• Contradiction: A contradiction is a situation in which two propositions cannot both be true. If “A is true,” then “A is not true” must be false. This creates an absolute logical boundary.

• Paradox: A paradox is more complex. It may appear to be a contradiction, but it opens up the possibility of a deeper truth or reveals a limit in our system of thinking. For example, “Less is more” sounds absurd but can be true in certain contexts.

But, are the words, 'less is more', alone, a 'paradox'. Sure, if within 'a head' there are concepts arising of when the words, 'less is more', although appearing contradictory and/or absurd can express 'a truth', like for example, when in relation to words, themselves, when sometimes 'less words', said, can 'say more, or even 'mean more'. However, the words, 'less is more', alone, (without any conceptual thinking nor context), appears to be an oxymoron and/or contradiction, itself. Do they not, to you?

What I am wondering is:

• Can we consider a paradox as just an “unresolved contradiction”?

you are absolutely free to 'consider' absolutely any thing. How, by definition, 'paradoxes' can and do express 'truths' or 'the truth', but only with a 'deeper inspection/reflection' and at a 'deeper level'. Like, for example, 'human beings do not need money to live'. In the days when this is being written, most adult human beings would consider 'that claim and/or proposition' to be absurd and/or contradictory. However, if and when one is to take a so-called 'deeper look', that claim and proposition exposes the actual Truth, which most of those adult human beings had never previously even considered, let alone realized.

Or do they really belong to two different levels of logic and philosophy?

'That' will always remain 'up to you', depending on what definitions that you like to and want to use.

• When we encounter a paradox, should we treat it as a thinking error, or should we see it as an opportunity to explore the limits of our current conceptual system?

Would it not be best, or at least better, to always be considering one's 'current' 'conceptual system'?

• In the history of philosophy, many important ideas (from Zeno to Kant) have originated from paradox. Is paradox a “philosophical motive” rather than a logical error?

Again, every thing depends on one's own meanings, and definitions, that they are giving to words. For example, to some people, there is 'no history of philosophy' to even begin with, to then make decisions and/or answers upon.

I would like to hear your views:

Absolutely every thing is relative to the observer.

Would you like to hear 'the views' of others because you would like to 'debate', with them, to 'converse', with them, to just 'disagree', with them?

Or, would you like to have and 'argument', with them, or to have an 'argument', with them. And what I just did there was prove, irrefutably, that it always depends on what meaning, and/or definition, one places upon, and uses for, words.

• Do you have examples of cases where paradoxes actually lead to new truths?

Yes, many of them. Like, for example, the one above.

But, then again, what do you mean, exactly, by the word 'new', in 'new truths'?

• Are we being too easygoing in calling everything that is difficult to understand a “paradox”, instead of analyzing whether it is really a logical contradiction?

I, for One, would never call any thing that is, supposedly, difficult to understand a 'parodox', as, well to me anyway, a 'paradox' is what, literally, exposes or reveals an actual Truth.

And, all so-called 'paradoxes' that I have been exposed to, what the actual Truth within them is actually very simple to recognize and see. And, what might appear so-called 'difficult' to some of you, usually is, really, not at all.

I look forward to receiving feedback to clarify this distinction, and perhaps find new approaches in analyzing modern philosophical problems.

What are some of the so-called 'modern philosophical problems' that you see and/or have, exactly?

And, depending on 'the way' words are written and expressed if there is a 'logical contradiction', or not, or an actual 'paradox', or not, is very, very simple and easy to distinguish, and thus to determine, as well.

[Age]

In many philosophical debates, I have found that the concepts of paradox and contradiction are often used interchangeably, even interchangeably. However, when examined closely, they seem to represent two completely different forms of ideological conflict.

• Contradiction: A contradiction is a situation in which two propositions cannot both be true. If “A is true,” then “A is not true” must be false. This creates an absolute logical boundary.

• Paradox: A paradox is more complex. It may appear to be a contradiction, but it opens up the possibility of a deeper truth or reveals a limit in our system of thinking. For example, “Less is more” sounds absurd but can be true in certain contexts.

What I am wondering is:

• Can we consider a paradox as just an “unresolved contradiction”? Or do they really belong to two different levels of logic and philosophy?

• When we encounter a paradox, should we treat it as a thinking error, or should we see it as an opportunity to explore the limits of our current conceptual system?

• In the history of philosophy, many important ideas (from Zeno to Kant) have originated from paradox. Is paradox a “philosophical motive” rather than a logical error?

I would like to hear your views:

• Do you have examples of cases where paradoxes actually lead to new truths?

• Are we being too easygoing in calling everything that is difficult to understand a “paradox”, instead of analyzing whether it is really a logical contradiction?

I look forward to receiving feedback to clarify this distinction, and perhaps find new approaches in analyzing modern philosophical problems.

Your beginning point is accurate, in general language they are used interchangeably.

What I am aware of is that at a more precise level of definition:

1. Contradiction implies opposition of distinct assertions, a seperation by conflict.

2. Paradox implies connection of distinct assertions, a unity of differences.

Now as to the rest:


A paradox can be viewed as such (this is copy and pasted from another thread in the math/logic section that is similar):

Yes a gradient approach can occur.

The statement of "I am a liar" observes that the person in question both tells the truth and lies. So how does that occur?

But, the 'person', itself, is not telling both 'the truth' and 'lies'. So, why do you believe and claim that 'it' is?

Within a given framework of identity, lets say the time and space of a week or several years, that identity has multiple expressions within the given space. Sometimes it is a liar. Sometimes it is a truthteller.

What?

The identity of a 'person' remains 'the exact same', always.

Unless, of course, you, or another, just want to 'change the identity', whenever you want to. But, a 'person' will always remain 'just a person', all the time.

Within the given framework these things occur simultaneously and in grades, sometimes more truth than lies are told or vice versa. These can be observes at meta-identities, identities within identities. So where an identity in the time and space of a week may be "x and y", within the meta identity "x" may only occur in one time and space and "y" within another, all of which are part of the larger time and space of a week.

So identity as grades can be akin to a meta-identity, and identity within an identity.

And, 'a person' can tell 'a lie' at one moment, and in the next second tell 'a truth'. But, so what? Doing either never means that 'that person' is one of them, nor even what 'the body' is doing. A 'person' will always be 'a person', only.

Now on the other hand all dualisms result in gradation by degree of the dualism itself. Take for example the following dualistic symbolic chain (if you want this in normal language just ask):

1. T
2. F
3. (T,F)
4. T(T,F)
5. F(T,F)
6. (T,F)(T,F)
7. T((T,F)(T,F))
8. F((T,F)(T,F))
9. (T,F)((T,F)(T,F))
10. Unto infinity.

Any dualism, and paradox requires a dualism by degree of differing but isomorphic expressions, results in infinite gradation of said dualism.

So the liars paradox results in different grades of true and false.

Once more, the so-called, 'liar's paradox' is not even an actual 'paradox' at all. All 'that thing', essentially, is just the use of words in a Truly nonsensical, non logical, absurd, and/or irrational way.

But, and again, you are absolutely free to believe whatever you like "eodnhoj7" and to find and use whatever words you like and choose to, to 'try' your very hardest to back up and support 'your beliefs'. No matter how Truly irrational and illogical they really are.

This can be evidenced by true may be more than false on one set of days, vice versa, or all truths are partial truths and all lies are partial lies.

Do you, really, believe that you adult human beings go from 'telling lies' to 'telling truths' on a 'daily basis?

LOL you adult human beings tell an untold number of lies each and every day. And, with some of those lies not even being recognized by 'the one' telling them.

There is also another complementary way of viewing paradox:

Two opposing or various states existing at once in quantum mechanics is called superpositioning. These states existing at once are effectively indistinct potentiality. When the superposition states are observed one of the potential states is localized according to the state of the observer.

Now a paradox is similar. It is multiple values at once. The paradox is indistinct in its present state. Now when the paradox is observed one or more of the following things happens:

1. The observer chooses one of the several potential values and makes distinctions from there. You will see this in everyday life where a paradox of "this is that" is observed and people naturally takes sides. The paradox becomes a mirror of the observer in this scenario.

2. The observer adds context to the paradox. Now in a general paradox there is no context but the paradox itself and this leads to multiple states coexisting at once. Now if a paradox is given further context, by the observer(s), then a distinct value occurs.

For example the paradox of "I am a liar" had multiple values coexisting that results in the indistinct state of the paradox itself.

Now if the context of "on wednesdays" so we have "I am a liar on wednesdays" then the paradox ceases and we have a clearer and more defined assertion.

3. If opposites cancel eachother out then the paradox becomes pure logical potentiality, a logical space by which values can be projected or assigned. In these respects the paradox is empty of meaning and yet this emptiness becomes of mirror to the observer. As such it is a point by which the observers attention is transformed. You will find this method quite frequently in zen Buddhism where two opposing points, under the paradox, are observed and the cancelation causes a space of potentiality by which the observer is looking into a metaphorical mirror.

4. ****The fourth context is that the paradox becomes a dialectical synthesis where opposites merge to produce a new context. Aspects of an antithesis refine a thesis into a new truth, aspects of a these refine an antithesis into a new truth.

The key to all of this is context.

Context determines how the paradox unfolds to the observer.

Under one context the paradox can lead to gradation, another superpositioned logical states subject to context application, another a mirror to the observer by nature of being empty....so on and so forth.



What I am about to say is heresy in western philosophy:

Paradoxes are both rational and necessary.

View a paradox as "superpositioned assertions" from a perspective of quantum mechanics.