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.
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.