## Beyond the Law of Noncontradiction

What is the basis for reason? And mathematics?

Moderators: AMod, iMod

Hiroshi Satow
Posts: 14
Joined: Thu Jun 20, 2019 5:21 pm
Location: Japan

### Beyond the Law of Noncontradiction

Dear logicians!

I think I’ve come up with something beyond the Law of Noncontradiction. Unfortunately, I’m not a trained philosopher, let alone a logician. I’m not sure whether I’m right or wrong, or rather, how wrong I am and how I am wrong. Anyway, here is what I’ve been thinking about.

In Plato’s Republic Socrates says “It is obvious that the same thing will never or suffer opposites in the same respect in relation to the same thing and at the same time.”(Republic 4:436b) Aristotle writes, “The same attribute cannot at the same time belong and not belong to the same subject and in the same respect.”(Metaphysics G, 3, 1005b18-20)

These are thought of as advocating the law of noncontradiction. Admitting of course what they say, in my opinion, there can be another kind of contradiction: It is that you cannot do two things at the same time, be they contradictory or not to one another. The so-called law of noncontradiction is just one case of it. To be sure, it cannot be true that you can take a step forward with both the right and the left legs at the same time. If you are using the right leg, to take a step forward, then you are not using the left one, and vice versa. To simultaneously use them both is against the law of noncontradiction, which is why you never can make it.

However, it seems to me that it also cannot be the case that you can take a step forward with the right leg twice at the same time. This is because you can use your right leg only once at a time. To use the right leg does not necessarily contradict with the use of the right leg. On the contrary, they are completely the same thing. No inconsistency can be found between the use of the right leg and the use of the right leg. Regardless, on no account can you afford to do that.

So, at least in some cases, I think you can say that in the world there can be found two facts that cannot concur, happening simultaneously, which might be named the Law of Nonconcurrence or whatever, one of which you call the Law of Noncontradiction, and the other the law of Nonrecurrence or something like that.

Thinking along these lines, the Law of Noncontradiction is not the ultimate law but can be derived from the Law of Nonconcurrence, just as the Law of Nonrecurrence is.

Could any one of you be kind enough to tell or teach me how I am wrong and/or how wrong I am?
Skepdick
Posts: 5282
Joined: Fri Jun 14, 2019 11:16 am

### Re: Beyond the Law of Noncontradiction

You are not wrong and you should follow your intuition on this, but be warned it will lead you right to the bottom of the physics/metaphysics (if there is even a difference) rabbit hole. The question you are asking is at the intersection of physics (the problem of time), linguistics and computer science.

The LNC contains a fatal ambiguity in its own definition:
contradictory propositions cannot both be true in the same sense at the same time
That is precisely the ambiguity you have stumbled upon. What does the notion of "same time" even mean? Time is always moving forward - it never stops. Time is measured as a duration, not an instant.

The LNC is also formalised as follows: P ∧ ¬P ⇔ False.
Language flows left to right, time flows as language flows.

So what if P is true before the we reach the "∧" symbol and then P changes to "false", shortly after. What if P oscillates/alternates between true/false very very fast and under our noses?

If concurrency/parallelism is what you are interested in then the people to speak to are the computer scientists, not the logicians.

Logic (in its classical form) cannot say many coherent things about concurrency. In fact, the notion of concurrency didn't appear in our formal languages until the last 50 years. It couldn't appear in our formal languages because the notion of control flow was formalised.

You will find Djikstra's solution to the problem of mutual exclusion relevant to your idea of "nonconcurrency". Or more broadly, the problem of the Dining philosophers

And finally, two facts can indeed "concur" in the Quantum computational paradigm. A Qubit is both true and false at the same time. Until a measurement is taken.

I'll repeat for emphasis: follow your intuition and go over the theory/history. The questions you are asking are very very relevant in distributed computing today. In an over-simplified way: it's how Google works.
Last edited by Skepdick on Tue Aug 11, 2020 12:26 pm, edited 1 time in total.
Skepdick
Posts: 5282
Joined: Fri Jun 14, 2019 11:16 am

### Re: Beyond the Law of Noncontradiction

Hiroshi Satow wrote: Tue Aug 11, 2020 8:26 am However, it seems to me that it also cannot be the case that you can take a step forward with the right leg twice at the same time. This is because you can use your right leg only once at a time. To use the right leg does not necessarily contradict with the use of the right leg. On the contrary, they are completely the same thing. No inconsistency can be found between the use of the right leg and the use of the right leg. Regardless, on no account can you afford to do that.
What you have identified here is the notion of a constraint, or a finite resource. You can't drink two glasses of water if you only have one.

In computer science the general concept of critical section deals with such scenarios where two (or more) agents need to access shared resources.

Classical logic doesn't allow you to express this notion in any useful way. The resource interpretation of linear logic allows for expressing such formalisms.
Eodnhoj7
Posts: 6324
Joined: Mon Mar 13, 2017 3:18 am

### Re: Beyond the Law of Noncontradiction

Hiroshi Satow wrote: Tue Aug 11, 2020 8:26 am Dear logicians!

I think I’ve come up with something beyond the Law of Noncontradiction. Unfortunately, I’m not a trained philosopher, let alone a logician. I’m not sure whether I’m right or wrong, or rather, how wrong I am and how I am wrong. Anyway, here is what I’ve been thinking about.

In Plato’s Republic Socrates says “It is obvious that the same thing will never or suffer opposites in the same respect in relation to the same thing and at the same time.”(Republic 4:436b) Aristotle writes, “The same attribute cannot at the same time belong and not belong to the same subject and in the same respect.”(Metaphysics G, 3, 1005b18-20)

These are thought of as advocating the law of noncontradiction. Admitting of course what they say, in my opinion, there can be another kind of contradiction: It is that you cannot do two things at the same time, be they contradictory or not to one another. The so-called law of noncontradiction is just one case of it. To be sure, it cannot be true that you can take a step forward with both the right and the left legs at the same time. If you are using the right leg, to take a step forward, then you are not using the left one, and vice versa. To simultaneously use them both is against the law of noncontradiction, which is why you never can make it.

However, it seems to me that it also cannot be the case that you can take a step forward with the right leg twice at the same time. This is because you can use your right leg only once at a time. To use the right leg does not necessarily contradict with the use of the right leg. On the contrary, they are completely the same thing. No inconsistency can be found between the use of the right leg and the use of the right leg. Regardless, on no account can you afford to do that.

So, at least in some cases, I think you can say that in the world there can be found two facts that cannot concur, happening simultaneously, which might be named the Law of Nonconcurrence or whatever, one of which you call the Law of Noncontradiction, and the other the law of Nonrecurrence or something like that.

Thinking along these lines, the Law of Noncontradiction is not the ultimate law but can be derived from the Law of Nonconcurrence, just as the Law of Nonrecurrence is.

Could any one of you be kind enough to tell or teach me how I am wrong and/or how wrong I am?
(P=P) v (P =/= -P) observes the law of excluded middle applied to the laws of logic. Either the law of identity is false in which case P=-P or the law of non contradiction is false in which case P=-P. Either way P=-P and P=/=-P simultaneously. The same can be observed where 1=1 but 1 may equal a horse or a jet. 1=1 and 1=/=1 simultaneously.
Eodnhoj7
Posts: 6324
Joined: Mon Mar 13, 2017 3:18 am

### Re: Beyond the Law of Noncontradiction

Hiroshi Satow wrote: Tue Aug 11, 2020 8:26 am Dear logicians!

I think I’ve come up with something beyond the Law of Noncontradiction. Unfortunately, I’m not a trained philosopher, let alone a logician. I’m not sure whether I’m right or wrong, or rather, how wrong I am and how I am wrong. Anyway, here is what I’ve been thinking about.

In Plato’s Republic Socrates says “It is obvious that the same thing will never or suffer opposites in the same respect in relation to the same thing and at the same time.”(Republic 4:436b) Aristotle writes, “The same attribute cannot at the same time belong and not belong to the same subject and in the same respect.”(Metaphysics G, 3, 1005b18-20)

These are thought of as advocating the law of noncontradiction. Admitting of course what they say, in my opinion, there can be another kind of contradiction: It is that you cannot do two things at the same time, be they contradictory or not to one another. The so-called law of noncontradiction is just one case of it. To be sure, it cannot be true that you can take a step forward with both the right and the left legs at the same time. If you are using the right leg, to take a step forward, then you are not using the left one, and vice versa. To simultaneously use them both is against the law of noncontradiction, which is why you never can make it.

However, it seems to me that it also cannot be the case that you can take a step forward with the right leg twice at the same time. This is because you can use your right leg only once at a time. To use the right leg does not necessarily contradict with the use of the right leg. On the contrary, they are completely the same thing. No inconsistency can be found between the use of the right leg and the use of the right leg. Regardless, on no account can you afford to do that.

So, at least in some cases, I think you can say that in the world there can be found two facts that cannot concur, happening simultaneously, which might be named the Law of Nonconcurrence or whatever, one of which you call the Law of Noncontradiction, and the other the law of Nonrecurrence or something like that.

Thinking along these lines, the Law of Noncontradiction is not the ultimate law but can be derived from the Law of Nonconcurrence, just as the Law of Nonrecurrence is.

Could any one of you be kind enough to tell or teach me how I am wrong and/or how wrong I am?
A lemon can be both yellow and non yellow as a grade of yellow.

One can step using the right leg twice simply by stepping with the right and dragging the left.
PeteJ
Posts: 426
Joined: Fri Oct 16, 2015 1:15 pm

### Re: Beyond the Law of Noncontradiction

The LNC applies only to legitimate dialectical contradictory pairs. For a legitimate pair one member is true and one is false. Clearly, then, there cannot be a violation of the LNC. Where it seems to be violated it is being misapplied. This point is utterly basic and widely misunderstood in philosophy and physics.
Scott Mayers
Posts: 1872
Joined: Wed Jul 08, 2015 1:53 am

### Re: Beyond the Law of Noncontradiction

Skepdick wrote: Tue Aug 11, 2020 8:58 am
If concurrency/parallelism is what you are interested in then the people to speak to are the computer scientists, not the logicians.

Logic (in its classical form) cannot say many coherent things about concurrency. In fact, the notion of concurrency didn't appear in our formal languages until the last 50 years. It couldn't appear in our formal languages because the notion of control flow was formalised.

You will find Djikstra's solution to the problem of mutual exclusion relevant to your idea of "nonconcurrency". Or more broadly, the problem of the Dining philosophers

And finally, two facts can indeed "concur" in the Quantum computational paradigm. A Qubit is both true and false at the same time. Until a measurement is taken.

I'll repeat for emphasis: follow your intuition and go over the theory/history. The questions you are asking are very very relevant in distributed computing today. In an over-simplified way: it's how Google works.
Computer Science is just an extension of logic, not separate from it. Other areas that are also 'logic' is Information theory, mathematics, critical thinking, and decision making. The fact that people can make up any course with a label doesn't assure it isn't related to other areas. The general topic is still under the banner of 'logic'. Science is just a logic that emphasizes observation as its means to assign the initial premises, including axioms of the system itself, of logical argument. I agree with including all these other related areas that help with this issue but it still reduces to 'logic'.

Qubits are artificially three-valued logics, not actual representations of what the theorists necessarily refer to. So this cannot be used as though it is evidence of the capacity to overthrow some law regarding contradiction.

"Intuition" is not defined and is ambivalent to suggest without it.
Scott Mayers
Posts: 1872
Joined: Wed Jul 08, 2015 1:53 am

### Re: Beyond the Law of Noncontradiction

Hiroshi Satow wrote: Tue Aug 11, 2020 8:26 am Dear logicians!

I think I’ve come up with something beyond the Law of Noncontradiction. Unfortunately, I’m not a trained philosopher, let alone a logician. I’m not sure whether I’m right or wrong, or rather, how wrong I am and how I am wrong. Anyway, here is what I’ve been thinking about.

In Plato’s Republic Socrates says “It is obvious that the same thing will never or suffer opposites in the same respect in relation to the same thing and at the same time.”(Republic 4:436b) Aristotle writes, “The same attribute cannot at the same time belong and not belong to the same subject and in the same respect.”(Metaphysics G, 3, 1005b18-20)

These are thought of as advocating the law of noncontradiction. Admitting of course what they say, in my opinion, there can be another kind of contradiction: It is that you cannot do two things at the same time, be they contradictory or not to one another. The so-called law of noncontradiction is just one case of it. To be sure, it cannot be true that you can take a step forward with both the right and the left legs at the same time. If you are using the right leg, to take a step forward, then you are not using the left one, and vice versa. To simultaneously use them both is against the law of noncontradiction, which is why you never can make it.

However, it seems to me that it also cannot be the case that you can take a step forward with the right leg twice at the same time. This is because you can use your right leg only once at a time. To use the right leg does not necessarily contradict with the use of the right leg. On the contrary, they are completely the same thing. No inconsistency can be found between the use of the right leg and the use of the right leg. Regardless, on no account can you afford to do that.

So, at least in some cases, I think you can say that in the world there can be found two facts that cannot concur, happening simultaneously, which might be named the Law of Nonconcurrence or whatever, one of which you call the Law of Noncontradiction, and the other the law of Nonrecurrence or something like that.

Thinking along these lines, the Law of Noncontradiction is not the ultimate law but can be derived from the Law of Nonconcurrence, just as the Law of Nonrecurrence is.

Could any one of you be kind enough to tell or teach me how I am wrong and/or how wrong I am?
"Contradiction" literally comes from the etymological meaning, "with a third option asserted". ['con' with, 'tra' three, 'diction' stated thing] That something can be understood to be 'true and false' is this third of discrete possibilities. It doesn't mean that this cannot be a reality but rather that it requires doing more to convey what such a potential evaluation of something is with better clarity....if needed.

For instance, IF some X is deemed to be both true AND false correctly, then it just demands some presumed action, of which the usual is to agree to disallow this conclusion in some system of reasoning. But if the contradiction is required to be understood as literally real, this becomes a 'paradox'. Note that the "para-" in this term is also used in the word, 'parallel' and both mean that some ALTERNATE reality or perspective is needed to resolve the apparent confusion, even if we may not know it.

Here is an example of a 'contradiction' if initially interpreted by one limiting perspective: "I exist and do not exist." If one presents this as a riddle where we presume some actual sense can be made of this as a paradox, then it is assuming one might default to thinking that statement is referring to existance at some given point in time and space. The resolution to it would require determining if there isn't some other possible assumptions that permit this statement to be 'true' even though it appears contradictory. One might rationalize this non-contradictorily by adding a different unspoken premise, like that "the interval of time for 'existence' is two years before I was born and one year after." This then can make the statement only conditionally contradictory.

This is the same kind of issue involved in discussing certain apparent paradoxes in nature. In science, the slit experiments appeared to demonstrate that reality was paradoxical as just such a contradiction that can also BE true via our perspective but represents a resolution that can separate the range of possibilities. The theory that I think that answers this is parallel worlds,....distinct places or 'universes' where both exist in a larger universe but are exclusive domains such that things in one universe cannot be perceived of another on the SAME level of logical universes.

Does this help so far?
Skepdick
Posts: 5282
Joined: Fri Jun 14, 2019 11:16 am

### Re: Beyond the Law of Noncontradiction

Scott Mayers wrote: Thu Sep 03, 2020 2:48 pm Computer Science is just an extension of logic, not separate from it. Other areas that are also 'logic' is Information theory, mathematics, critical thinking, and decision making. The fact that people can make up any course with a label doesn't assure it isn't related to other areas. The general topic is still under the banner of 'logic'.
Let it be "under the banner of logic" - I still wouldn't speak to a logician about distributed systems, concurrency, parallelism, mutual exclusivity, race conditions, use-after-free etc.

I would speak to computer scientist.
Scott Mayers wrote: Thu Sep 03, 2020 2:48 pm "Intuition" is not defined and is ambivalent to suggest without it.
"Definition" is not defined either. Neither is "logic" or "mathematics" - it's not a problem, unless you make it one.
Scott Mayers
Posts: 1872
Joined: Wed Jul 08, 2015 1:53 am

### Re: Beyond the Law of Noncontradiction

Skepdick wrote: Thu Sep 03, 2020 4:25 pm
Scott Mayers wrote: Thu Sep 03, 2020 2:48 pm Computer Science is just an extension of logic, not separate from it. Other areas that are also 'logic' is Information theory, mathematics, critical thinking, and decision making. The fact that people can make up any course with a label doesn't assure it isn't related to other areas. The general topic is still under the banner of 'logic'.
Let it be "under the banner of logic" - I still wouldn't speak to a logician about distributed systems, concurrency and parallelism.

I would speak to computer scientist.
Scott Mayers wrote: Thu Sep 03, 2020 2:48 pm "Intuition" is not defined and is ambivalent to suggest without it.
"Definition" is not defined. Neither is "logic" or "mathematics" - it's not a problem, unless you make it one.
I'm a 'logician' and a 'computer scientist'. Computation is just an extension on logic and gets too deep than is relevant to this topic on a mere philosophical question that deals specifically WITH foundations of logic. Computer science deals with finding algorithms to solving problems in mechanized ways. You can USE computation to help understand logic complexity.

My point about definition is to your use of "intuition" when that word has contextual problems of interpretation. Most assume the mystical meaning versus the neutral one, especially new people to philosophy. So your use may appear to be asserting that the OP should just not bother inquiring and may be why he is not responding? I mean, if the solution is merely to look inside of your own automatic insight about what it is as though it speaks for itself, as most interpret 'intution' by default, your response is like saying, "you know it inside yourself without requiring intellectual inspection since intuition is ones' instinctive responses to something WITHOUT concern to logical inspection.
Skepdick
Posts: 5282
Joined: Fri Jun 14, 2019 11:16 am

### Re: Beyond the Law of Noncontradiction

Scott Mayers wrote: Thu Sep 03, 2020 4:41 pm I'm a 'logician' and a 'computer scientist'. Computation is just an extension on logic and gets too deep than is relevant to this topic on a mere philosophical question that deals specifically WITH foundations of logic.

The first page that comes up when I type "concurrency" in Google is this: https://en.wikipedia.org/wiki/Concurren ... r_science)

If you think logic/logicians have better understanding of "concurrency", then provide some bread crumbs.
Eodnhoj7
Posts: 6324
Joined: Mon Mar 13, 2017 3:18 am

### Re: Beyond the Law of Noncontradiction

PeteJ wrote: Thu Sep 03, 2020 10:52 am The LNC applies only to legitimate dialectical contradictory pairs. For a legitimate pair one member is true and one is false. Clearly, then, there cannot be a violation of the LNC. Where it seems to be violated it is being misapplied. This point is utterly basic and widely misunderstood in philosophy and physics.
Contradiction is grounded in opposing pairs. A phenomenon which exists through the dichotomy of "existence" or "non existence" or "true" or "false" is the grounding of contradiction.
Scott Mayers
Posts: 1872
Joined: Wed Jul 08, 2015 1:53 am

### Re: Beyond the Law of Noncontradiction

Skepdick wrote: Thu Sep 03, 2020 4:46 pm
Scott Mayers wrote: Thu Sep 03, 2020 4:41 pm I'm a 'logician' and a 'computer scientist'. Computation is just an extension on logic and gets too deep than is relevant to this topic on a mere philosophical question that deals specifically WITH foundations of logic.

The first page that comes up when I type "concurrency" in Google is this: https://en.wikipedia.org/wiki/Concurren ... r_science)

If you think logic/logicians have better understanding of "concurrency", then provide some bread crumbs.
That's irrelevant. The reason the foundations discussing logic don't speak of contradiction as merely time-related is due to my example above regarding how one can reinterpret one's perspective of a contradiction by extending domains regardless of whether the issue is time or not. The example about 'existence' I presented was to point out that there are unspoken assumptions that often get missed when something appears to be contradictory. Because logic is more universal than particular subsets or extensional topics, 'concurrent' events limit one to assuming contradictions are only about time. You can have contradictions without concerning time.

Also, 'contradiction' doesn't have to be understood as an 'error' or confusion regarding the foundations of logic, only the description of something understood to have discrete binary options to be treated as conflicting when you introduce a third option that denies the meaning of the exclusion. The 'laws' of logic foundationally are only a way to begin with clearly defined concepts, the least of which is whether something is or is not included in some universal class regardless of what that class is defined as.
Skepdick
Posts: 5282
Joined: Fri Jun 14, 2019 11:16 am

### Re: Beyond the Law of Noncontradiction

Scott Mayers wrote: Thu Sep 03, 2020 5:20 pm
Skepdick wrote: Thu Sep 03, 2020 4:46 pm
Scott Mayers wrote: Thu Sep 03, 2020 4:41 pm I'm a 'logician' and a 'computer scientist'. Computation is just an extension on logic and gets too deep than is relevant to this topic on a mere philosophical question that deals specifically WITH foundations of logic.

The first page that comes up when I type "concurrency" in Google is this: https://en.wikipedia.org/wiki/Concurren ... r_science)

If you think logic/logicians have better understanding of "concurrency", then provide some bread crumbs.
That's irrelevant. The reason the foundations discussing logic don't speak of contradiction as merely time-related is due to my example above regarding how one can reinterpret one's perspective of a contradiction by extending domains regardless of whether the issue is time or not. The example about 'existence' I presented was to point out that there are unspoken assumptions that often get missed when something appears to be contradictory. Because logic is more universal than particular subsets or extensional topics, 'concurrent' events limit one to assuming contradictions are only about time. You can have contradictions without concerning time.

Also, 'contradiction' doesn't have to be understood as an 'error' or confusion regarding the foundations of logic, only the description of something understood to have discrete binary options to be treated as conflicting when you introduce a third option that denies the meaning of the exclusion. The 'laws' of logic foundationally are only a way to begin with clearly defined concepts, the least of which is whether something is or is not included in some universal class regardless of what that class is defined as.
I am pointing him towards an empirical body of knowledge pertaining to “concurrency”. It has a small section on logic

One of those things is certainly “irrelevant”
Scott Mayers
Posts: 1872
Joined: Wed Jul 08, 2015 1:53 am

### Re: Beyond the Law of Noncontradiction

Skepdick wrote: Thu Sep 03, 2020 5:46 pm
Scott Mayers wrote: Thu Sep 03, 2020 5:20 pm
Skepdick wrote: Thu Sep 03, 2020 4:46 pm