Inconsistency is a general, powerful case of having reason to reject something. Inconsistency brings with it the guarantee of being wrong in at least one place.
I would agree if the laws of the universe or the system, political or material are also consistent and understood completely. I think history shows us clearly that there are few laws which, under enough scrutiny are consistent in their known form—hence exogenous variables and stochastic processes.
We don’t have to understand the universe completely to be very confident that it contains no contradictions. If the laws as we understand them are not self-consistent, then we have reason to reject them—we just might, until we have better alternatives, have stronger reason to keep them around.
It wouldn’t look like anything, doesn’t mean anything, and couldn’t be observed. You can’t speak counterfactually about universes with contradictions in them without being incoherent, because no possible world contains contradictions.
Yes, but given that we’re not logically omniscient, it seems like it would be awfully useful to also have a weaker concept of coherence for discussing practical affairs. Otherwise I fear we wouldn’t be allowed to talk about counterfactuals at all, for who among us is wise enough to prove that a purported possible world doesn’t contain any hidden contradictions?
‘Descriptions’ that claim to describe possible worlds can contain contradictions. But such descriptions don’t describe anything, they’re just words.
Maybe they don’t describe anything, but that doesn’t make them “just words.” To be concrete, QED is, to the best of my ability to wrest information from physicists, inconsistent; yet it remains “the most accurate physical theory.”
You don’t have to go as exotic as QED to derive inconsistencies from the assumption of the continuum. When physicists encounter these inconsistencies, I suspect the continuum (or another source of infinity) is behind them. Singularities, for example, can be handled using discrete cut-offs.
Indeed, there is something about the phrase that doesn’t mean anything. Perhaps because contradiction exactly means ‘not possible’ (thus ‘not contained’). So that if there ever was a ‘contradiction’ actually realized in reality, then we would just need to look to reality to see how the ‘contradiction’ was possible after all.
A contradiction comes about when you have a list of things that are true (A=B, B=C, …) and somewhere in the list you find something (A~=C) that reduces to B=~B for some B.
Can a universe be possible where B and ~B are both true for some B?
Sometimes I feel like this is the universe we live in already, for exactly the kinds of things where “true” doesn’t mean anything. The ‘contradictions are impossible’ rule doesn’t apply to them. So, circularly, that’s why true doesn’t mean anything for them. So we might deduce something along the lines of truth and logic have meaning for a statement B IFF B and ~B are not simultaneously true/possible.
“Things” in reality aren’t “true” or “false” outside the context of specific logical tools. In particular, consistency is a property of (some of the) logical systems, considered as a good heuristic for developing ones that are interesting (formally, consistency alone doesn’t make a system “good”: indeed, a consistent system may even prove false formulas!). For logical systems, it does make sense to talk about which ones are consistent and which ones are not.
We don’t have to understand the universe completely to be very confident that it contains no contradictions.
Where is the proof of concept for this?
I have severalresources which point to extreme inconsistency with the current and past behaviors of particle and astro physics. Beyond natural sciences, there are inconsistencies in the way that political systems are organized and interacted with even on a local level—yet most find them acceptable enough to continue to work with.
You argue that inconsistency alone is enough to reject a theory. The point I make is that understanding that a process may work differently under different circumstances is not necessarily inconsistent and does not “guarantee” it being wrong. That is the point behind chaotic modeling.
There can still be valuable achievements that come from better understanding how the seemingly inconsistent theories work and I argue would not be wholly acceptable as a sole reason for rejection as you seem to advocate.
I still am not convinced that all systems must be consistent to exist—however that is a much different discussion.
“Inconsistencies” in the enactment of politics aren’t real contradictions. If this is the kind of example you find relevant, I must have no idea at all what you’re talking about.
It wouldn’t mean anything for the universe to contain contradictions, really, because this isn’t the kind of thing that might be. If we had square circles or if it were the case that both P and ~P, then we’d have contradictions, but this is the sort of thing that can be said and not imagined.
I don’t we disagree but I think we can make this point more strongly. It isn’t just that the universe never could have contradiction or that we can’t imagine a contradictory universe. Rather, universes just aren’t the sorts of things that are contradictory or not contradictory. Its like saying that most coffee cups hate Nietzsche. A piece of language can be contradictory because the semantic content of one part of the piece doesn’t constrain the semantic content of another part. But the universe doesn’t have any semantic content at all.
So contradictory theories aren’t wrong because the universe is consistent and (therefore) “inconsistency brings with it the guarantee of being wrong in at least one place”. Rather they are bad because a self-contradictory theory can be made to show anything. There is nothing it can’t predict or explain. Thus, we can reject them on purely formal, analytic grounds. Contradictions don’t say anything at all because they say everything.
Those two books look excellent … but I don’t see how they are relevant to this philosophical question. Both appear to discuss the problem of justifying inconsistent theories, not justifying an inconsistent universe. I think it is perfectly obvious that a superior and consistent theory would still be preferred by either of these philosophers.
I would agree if the laws of the universe or the system, political or material are also consistent and understood completely. I think history shows us clearly that there are few laws which, under enough scrutiny are consistent in their known form—hence exogenous variables and stochastic processes.
We don’t have to understand the universe completely to be very confident that it contains no contradictions. If the laws as we understand them are not self-consistent, then we have reason to reject them—we just might, until we have better alternatives, have stronger reason to keep them around.
If the universe “contained contradictions”, what would it look like? What does this property mean, and how could it be observed?
It wouldn’t look like anything, doesn’t mean anything, and couldn’t be observed. You can’t speak counterfactually about universes with contradictions in them without being incoherent, because no possible world contains contradictions.
Yes, but given that we’re not logically omniscient, it seems like it would be awfully useful to also have a weaker concept of coherence for discussing practical affairs. Otherwise I fear we wouldn’t be allowed to talk about counterfactuals at all, for who among us is wise enough to prove that a purported possible world doesn’t contain any hidden contradictions?
‘Descriptions’ that claim to describe possible worlds can contain contradictions. But such descriptions don’t describe anything, they’re just words.
Maybe they don’t describe anything, but that doesn’t make them “just words.” To be concrete, QED is, to the best of my ability to wrest information from physicists, inconsistent; yet it remains “the most accurate physical theory.”
I don’t know enough to deal with the counter example. How does QED contradict itself?
In defense of the consistency of the universe...
You don’t have to go as exotic as QED to derive inconsistencies from the assumption of the continuum. When physicists encounter these inconsistencies, I suspect the continuum (or another source of infinity) is behind them. Singularities, for example, can be handled using discrete cut-offs.
(Later edit: Why down-voted?)
Here, again you say “contains contradictions”, as if it means anything.
Indeed, there is something about the phrase that doesn’t mean anything. Perhaps because contradiction exactly means ‘not possible’ (thus ‘not contained’). So that if there ever was a ‘contradiction’ actually realized in reality, then we would just need to look to reality to see how the ‘contradiction’ was possible after all.
A contradiction comes about when you have a list of things that are true (A=B, B=C, …) and somewhere in the list you find something (A~=C) that reduces to B=~B for some B.
Can a universe be possible where B and ~B are both true for some B?
Sometimes I feel like this is the universe we live in already, for exactly the kinds of things where “true” doesn’t mean anything. The ‘contradictions are impossible’ rule doesn’t apply to them. So, circularly, that’s why true doesn’t mean anything for them. So we might deduce something along the lines of truth and logic have meaning for a statement B IFF B and ~B are not simultaneously true/possible.
“Things” in reality aren’t “true” or “false” outside the context of specific logical tools. In particular, consistency is a property of (some of the) logical systems, considered as a good heuristic for developing ones that are interesting (formally, consistency alone doesn’t make a system “good”: indeed, a consistent system may even prove false formulas!). For logical systems, it does make sense to talk about which ones are consistent and which ones are not.
Where is the proof of concept for this?
I have several resources which point to extreme inconsistency with the current and past behaviors of particle and astro physics. Beyond natural sciences, there are inconsistencies in the way that political systems are organized and interacted with even on a local level—yet most find them acceptable enough to continue to work with.
You argue that inconsistency alone is enough to reject a theory. The point I make is that understanding that a process may work differently under different circumstances is not necessarily inconsistent and does not “guarantee” it being wrong. That is the point behind chaotic modeling.
There can still be valuable achievements that come from better understanding how the seemingly inconsistent theories work and I argue would not be wholly acceptable as a sole reason for rejection as you seem to advocate.
I still am not convinced that all systems must be consistent to exist—however that is a much different discussion.
“Inconsistencies” in the enactment of politics aren’t real contradictions. If this is the kind of example you find relevant, I must have no idea at all what you’re talking about.
I actually have no idea what it could possibly mean for the universe to contain contradictions. This looks like a category error.
It wouldn’t mean anything for the universe to contain contradictions, really, because this isn’t the kind of thing that might be. If we had square circles or if it were the case that both P and ~P, then we’d have contradictions, but this is the sort of thing that can be said and not imagined.
I don’t we disagree but I think we can make this point more strongly. It isn’t just that the universe never could have contradiction or that we can’t imagine a contradictory universe. Rather, universes just aren’t the sorts of things that are contradictory or not contradictory. Its like saying that most coffee cups hate Nietzsche. A piece of language can be contradictory because the semantic content of one part of the piece doesn’t constrain the semantic content of another part. But the universe doesn’t have any semantic content at all.
So contradictory theories aren’t wrong because the universe is consistent and (therefore) “inconsistency brings with it the guarantee of being wrong in at least one place”. Rather they are bad because a self-contradictory theory can be made to show anything. There is nothing it can’t predict or explain. Thus, we can reject them on purely formal, analytic grounds. Contradictions don’t say anything at all because they say everything.
Those two books look excellent … but I don’t see how they are relevant to this philosophical question. Both appear to discuss the problem of justifying inconsistent theories, not justifying an inconsistent universe. I think it is perfectly obvious that a superior and consistent theory would still be preferred by either of these philosophers.