Most true statements are not absolutely true. They may be true enough for all practical purposes; true in some sense; officially true, but effectively meaningless; true, other things being equal; true, as far as it goes; or true in theory, but not in practice.
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Unfortunately, formal logic does not generally preserve sort-of truth. Sometimes it does: if “All ravens are black” is pretty much true, inasmuch as they are all very dark gray, then “Huginn is black” will also be pretty much true. But if “all ravens are black” is pretty much true inasmuch as most ravens are absolutely black but a few are magenta, then “Huginn is black” might be entirely false. Sort-of truths don’t follow the standard rules of logical inference.
Could some other, more complicated logical rules work effectively with sort-of truths? The previous chapter contemplated adding the new truth value “sort of” to logic. This works formally, but doesn’t do much in practice. You can’t infer anything useful. As we saw, if you know that “all ravens are black” is sort-of true, you can’t conclude anything about specific ravens. And if “Huginn is black” is sort-of-true, it is also sort-of-false. You’d want to know in what sense is it true, and in what sense false.
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Unlike logicism, probabilism doesn’t require an absolute belief about what the truth of a statement is. However, it does require that any statement actually is either absolutely true or absolutely false. Suppose you want to know if there is any water in the refrigerator. To eliminate uncertainty, you look inside, and there appears to be only an eggplant. Now, is there water in the refrigerator? Well, with probability nearly 1.0, it’s sort of true that there is (in the cells of the eggplant) And with probability nearly 1.0, it’s sort of false (you were thirsty and there’s nothing to drink). It’s a rock-bottom principle of the mathematics that the probability of a statement being true and the probability of it being false have to add up to 1.0. (This is a different way of stating the Law of the Excluded Middle.) Here the probabilities of sort-of truth and sort-of falsity add up to nearly 2.0, which is uninterpretable as a probability. The math doesn’t work for sort-of truths.
For most rationalisms, these difficulties are sufficient reason to reject sort-of truths. Meaningful statements must be absolutely true or false—universally, objectively, independent of circumstances, purposes, or judgements—even if we don’t know whether they are true or false. (Then there is only epistemic uncertainty, and no ontological nebulosity.) However, outside of mathematics and maybe fundamental physics, there are few truths like that. The world of eggplant-sized objects just doesn’t work that way.
I think the point the author is making is that these defined truths quickly become useless. What is a precise definition of black? Colour is quite complex and the wavelengths of light reflected by...
ALSO: If you are able to come up with a precise definition for "black" and "raven", then we could certainly evaluate "All ravens are black" for a discrete truth value.
I think the point the author is making is that these defined truths quickly become useless. What is a precise definition of black? Colour is quite complex and the wavelengths of light reflected by an object are not universal for a fixed observer. We quickly arrive at a discrete "truth" that is effectively meaningless.
It seems to me the author acknowledges that discrete truth is possible, just that it becomes meaningless quite quickly. All ravens are black in the colloquial sense is useful information. All...
Most true statements are not absolutely true. They may be true enough for all practical purposes; true in some sense; officially true, but effectively meaningless; true, other things being equal; true, as far as it goes; or true in theory, but not in practice.
It seems to me the author acknowledges that discrete truth is possible, just that it becomes meaningless quite quickly. All ravens are black in the colloquial sense is useful information. All ravens are at some distance X in a controlled lighting environment measure reflected wavelengths in set S with a tolerance of Y over period Z is pretty useless when in some scenarios parrots may also qualify as "black".
I think the idea is not that it's impossible to make formally true statements about our world -- just that it is near-impossible to also make them meaningful.
What is a shade? What about a "black" raven with a molecular-size white spot? A slightly larger white spot? Half-white? Etc. etc. The moment we are forced to define black the statement loses all...
Like it makes way more sense to just decide some kind of interval of possible shades that we're just going to call "black"
What is a shade? What about a "black" raven with a molecular-size white spot? A slightly larger white spot? Half-white? Etc. etc.
The moment we are forced to define black the statement loses all value outside of the binary truthiness for that specific definition. Informally, we understand the symbolic intent of the statement without requiring it to be literally true.
He’s using the word “absolute” to distinguish between “true” and “false” as used in ordinary conversations versus “true” and “false” used in logic. Most everyday usages of “true” and “false,” even...
He’s using the word “absolute” to distinguish between “true” and “false” as used in ordinary conversations versus “true” and “false” used in logic. Most everyday usages of “true” and “false,” even by scientists, are only about sort-of truths and they aren’t in the context of any formal system. They simply aren’t formal at all. We need to distinguish that from the kind of truth needed by (various kinds of) logic, so he uses the word “absolute” here, but don’t read too much into it.
The strategy you describe of making statements more precise is described in more detail later in the same chapter and in other parts of the book, and Chapman doesn’t think it works either, in general:
Encountering a sort-of truth, rationalists often say “there must be an absolute truth somewhere in the vicinity; we should find and use that instead.” I’ll describe four strategies for converting sort-of truths into absolute ones: here briefly, and in detail in later chapters.
Each of the four methods works in some cases. Indeed, these moves are all meta-rational: they are methods of ontological remodeling, intended to make rationality work better. Unfortunately for rationalism, they provide no general solution, either individually or in combination. Commonly, none of them can generate absolute truths that are usable in practice.
(Note that Chapman isn’t talking about Rationalists, the people in the social movement we’ve had discussions about recently.)
Again, I think you're taking "absolute" to mean more than intended. Yes, even mathematical theorems are relative to axioms and systems of reasoning, but they can still be considered "absolute" in...
Again, I think you're taking "absolute" to mean more than intended. Yes, even mathematical theorems are relative to axioms and systems of reasoning, but they can still be considered "absolute" in that they follow from the assumptions, and you can formally say what the assumptions are. They are true independent of space and time and who is stating them.
Everyday use of language is considerably more context-sensitive than that. Often, you can't even enumerate all the hidden assumptions.
Ironically, even saying whether something is an "absolute truth" or not is a relative statement.
I don't think this is really getting at how math works. Mathematicians rarely write fully formal proofs because it's tedious. However, the idea is that any mathematical proof could be turned into...
I don't think this is really getting at how math works. Mathematicians rarely write fully formal proofs because it's tedious. However, the idea is that any mathematical proof could be turned into a formal proof, if someone did the work. (There are computerized proof systems that have gotten fairly far proving a lot of theorems.) If that's not possible then the proof must be somehow wrong.
So proofs really are either correct or incorrect, and that's why logic works for math. And while a lot of math is entirely theoretical and useless so far, some of it is very useful for building practical things.
The things we say in everyday language aren't like that, though. They couldn't be turned into something like a mathematical proof, even in principle. Logic doesn't really work for them, at least not in a way so that you'd trust logic over actually trying it and seeing what happens.
Okay, this sounds like saying that all mathematical truths are conditional? I guess I can go along with that. I think we've lost touch with the philosophical issues that Chapman was writing about,...
Okay, this sounds like saying that all mathematical truths are conditional? I guess I can go along with that. I think we've lost touch with the philosophical issues that Chapman was writing about, though.
You seem to be claiming that all disagreements about truth are semantic disagreements. Is this what you intend to say? Do you have any caveats about that?
You seem to be claiming that all disagreements about truth are semantic disagreements. Is this what you intend to say? Do you have any caveats about that?
How would you assert the statement "(as long as everyone is correctly following the rules of inference)" in your theory, since inference itself doesn't make sense without a notion of truth or what...
How would you assert the statement "(as long as everyone is correctly following the rules of inference)" in your theory, since inference itself doesn't make sense without a notion of truth or what a proposition is?
Your concluding statement seems to acknowledge this.
this is not really any different from asserting "As long as everyone is on the same page with regards to what words mean, and everyone plays by the same rules, everyone should be able to reach the same conclusions"
and this is equivalent to saying that locally deterministic systems are determined by their initial states :)
This original argument bugged me so I tried a little singular switcheroo. With a wink and a nod towards univalent logics, one-valued logic would have proposition values all be some *. It's...
I'd say yes, truth is singular: there are no degrees of truth. For two reasons, I think that every proposition has exactly one truth value. (1) I'm not aware of any problem in logic or philosophy whose solution really does require positing fewer or more than one truth-value. (2) To my knowledge, every system of logic or semantics that accommodates other than one truth-value has consequences that are deeply implausible. These systems include two-or-three-valued logics, infinite-valued logic, supervaluation semantics, and others. In light of (1), I see no reason to flirt with those implausible consequences. When solving a problem seems to require other than one truth-value, the real trouble lies somewhere else. Or so it seems to me.
This original argument bugged me so I tried a little singular switcheroo. With a wink and a nod towards univalent logics, one-valued logic would have proposition values all be some *. It's consistent but kinda trivial at that level.
Sorry it was quite ambiguous. My general point was to contest the author's dismissal of non-binary logical systems. I'm suggesting that the initial argument by which they do so could also dismiss...
Sorry it was quite ambiguous. My general point was to contest the author's dismissal of non-binary logical systems. I'm suggesting that the initial argument by which they do so could also dismiss binary systems if it's used from the perspective of somebody who's motivated to defend a hypothetical single-value logic.
Basically, it seems like the author is arguing "from my (binary logical) perspective, other perspectives seem implausible and unnecessary". Another perspective would be that we only ever arrive at the truths our system allowed for from the beginning - but then, as others have pointed out, maybe we're missing some?
I wonder what he would make of the Smullyan Two Envelope "Puzzle": Envelope 1: Of the sentences on the envelopes, at least one is false. Envelope 2: The prize is in envelope 1. Each of these...
I wonder what he would make of the Smullyan Two Envelope "Puzzle":
Envelope 1: Of the sentences on the envelopes, at least one is false.
Envelope 2: The prize is in envelope 1.
Each of these appears to be a proposition by his definition, and therefore each should be either true or false.
If the statement on Envelope 1 is false, then it states that at least one of the statements is false, and that's true, giving a contradiction. So the statement on Envelope 1 must be true.
In turn that means that one of the statements must be false, and it's not the statement on Envelope 1, so the statement on Envelope 2 must be false.
Thus the prize must be in Envelope 2.
But I can give you Envelopes with these statements, and put the prize in Envelope 1.
So the statements on the Envelopes, which are clearly propositions, cannot be binary in respect of their truth values. Makes me feel that the article is either wrong, or content-free.
The actual outcome of the China brain thought experiment is impossible to observe - that the 'machine' created is actually conscious rather than merely demonstrating the outcomes associated with...
Reminds me of the China Brain thought experiment, and how the argument seems to basically boil down to a person presupposing the results of an experiment that they won't actually do and using it as some kind of "evidence" to support their argument.
The actual outcome of the China brain thought experiment is impossible to observe - that the 'machine' created is actually conscious rather than merely demonstrating the outcomes associated with conscious beings can't be observed without begging the question. Actually performing the experiment wouldn't have any observables to measure its success - the hard problem of consciousness.
Unless you think there is a finite set of "rules" that can characterize all of mathematics, then it must be that any time you give me some set of axioms, I can find a (non-contradictory) statement that has no truth value with respect to your set of axioms
A charitable reading might be that the sentence is giving proposition as a defined term. The (classical) incompleteness theorems only apply to finite proofs and sets of axioms. (They can be generalized, but I don't know by how much.) So, class structures, and transfinite proofs could maybe circumvent them, which means that you can't quite say there is no metaphysics which circumvents them. I suppose any theory of philosophy expressible in the ZFC or in formal mathematics would suffer from that issue, but that isn't true of every theory. Consider a trivial theory which assigns a truth value to every formal statement consistent with first order logic - I don't believe there's a formal method to disprove this, though again, I could be wrong. You would lose Peano arithmetic, but it would be self-consistent and every statement would be true or false.
Maybe you do. It works for general audiences though. Additionally, I'd note that as a conclusion, it's arguable that rocks are conscious a la Boltzmann brains. I personally don't act as though...
Maybe you do. It works for general audiences though. Additionally, I'd note that as a conclusion, it's arguable that rocks are conscious a la Boltzmann brains. I personally don't act as though rocks are conscious, despite us not having any good arguments against it.
Here is a much better explanation from In the Cells of the Eggplant.
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I think the point the author is making is that these defined truths quickly become useless. What is a precise definition of black? Colour is quite complex and the wavelengths of light reflected by an object are not universal for a fixed observer. We quickly arrive at a discrete "truth" that is effectively meaningless.
It seems to me the author acknowledges that discrete truth is possible, just that it becomes meaningless quite quickly. All ravens are black in the colloquial sense is useful information. All ravens are at some distance X in a controlled lighting environment measure reflected wavelengths in set S with a tolerance of Y over period Z is pretty useless when in some scenarios parrots may also qualify as "black".
I think the idea is not that it's impossible to make formally true statements about our world -- just that it is near-impossible to also make them meaningful.
What is a shade? What about a "black" raven with a molecular-size white spot? A slightly larger white spot? Half-white? Etc. etc.
The moment we are forced to define black the statement loses all value outside of the binary truthiness for that specific definition. Informally, we understand the symbolic intent of the statement without requiring it to be literally true.
He’s using the word “absolute” to distinguish between “true” and “false” as used in ordinary conversations versus “true” and “false” used in logic. Most everyday usages of “true” and “false,” even by scientists, are only about sort-of truths and they aren’t in the context of any formal system. They simply aren’t formal at all. We need to distinguish that from the kind of truth needed by (various kinds of) logic, so he uses the word “absolute” here, but don’t read too much into it.
The strategy you describe of making statements more precise is described in more detail later in the same chapter and in other parts of the book, and Chapman doesn’t think it works either, in general:
(Note that Chapman isn’t talking about Rationalists, the people in the social movement we’ve had discussions about recently.)
Again, I think you're taking "absolute" to mean more than intended. Yes, even mathematical theorems are relative to axioms and systems of reasoning, but they can still be considered "absolute" in that they follow from the assumptions, and you can formally say what the assumptions are. They are true independent of space and time and who is stating them.
Everyday use of language is considerably more context-sensitive than that. Often, you can't even enumerate all the hidden assumptions.
Ironically, even saying whether something is an "absolute truth" or not is a relative statement.
I don't think this is really getting at how math works. Mathematicians rarely write fully formal proofs because it's tedious. However, the idea is that any mathematical proof could be turned into a formal proof, if someone did the work. (There are computerized proof systems that have gotten fairly far proving a lot of theorems.) If that's not possible then the proof must be somehow wrong.
So proofs really are either correct or incorrect, and that's why logic works for math. And while a lot of math is entirely theoretical and useless so far, some of it is very useful for building practical things.
The things we say in everyday language aren't like that, though. They couldn't be turned into something like a mathematical proof, even in principle. Logic doesn't really work for them, at least not in a way so that you'd trust logic over actually trying it and seeing what happens.
Okay, this sounds like saying that all mathematical truths are conditional? I guess I can go along with that. I think we've lost touch with the philosophical issues that Chapman was writing about, though.
You seem to be claiming that all disagreements about truth are semantic disagreements. Is this what you intend to say? Do you have any caveats about that?
How would you assert the statement "(as long as everyone is correctly following the rules of inference)" in your theory, since inference itself doesn't make sense without a notion of truth or what a proposition is?
Your concluding statement seems to acknowledge this.
and this is equivalent to saying that locally deterministic systems are determined by their initial states :)
This original argument bugged me so I tried a little singular switcheroo. With a wink and a nod towards univalent logics, one-valued logic would have proposition values all be some *. It's consistent but kinda trivial at that level.
Care for a version for dummies? :)
Sorry it was quite ambiguous. My general point was to contest the author's dismissal of non-binary logical systems. I'm suggesting that the initial argument by which they do so could also dismiss binary systems if it's used from the perspective of somebody who's motivated to defend a hypothetical single-value logic.
Basically, it seems like the author is arguing "from my (binary logical) perspective, other perspectives seem implausible and unnecessary". Another perspective would be that we only ever arrive at the truths our system allowed for from the beginning - but then, as others have pointed out, maybe we're missing some?
I wonder what he would make of the Smullyan Two Envelope "Puzzle":
Each of these appears to be a proposition by his definition, and therefore each should be either true or false.
If the statement on Envelope 1 is false, then it states that at least one of the statements is false, and that's true, giving a contradiction. So the statement on Envelope 1 must be true.
In turn that means that one of the statements must be false, and it's not the statement on Envelope 1, so the statement on Envelope 2 must be false.
Thus the prize must be in Envelope 2.
But I can give you Envelopes with these statements, and put the prize in Envelope 1.
So the statements on the Envelopes, which are clearly propositions, cannot be binary in respect of their truth values. Makes me feel that the article is either wrong, or content-free.
one method is to restrict statements to being in first order logic, then you don't run into those issues
The actual outcome of the China brain thought experiment is impossible to observe - that the 'machine' created is actually conscious rather than merely demonstrating the outcomes associated with conscious beings can't be observed without begging the question. Actually performing the experiment wouldn't have any observables to measure its success - the hard problem of consciousness.
A charitable reading might be that the sentence is giving proposition as a defined term. The (classical) incompleteness theorems only apply to finite proofs and sets of axioms. (They can be generalized, but I don't know by how much.) So, class structures, and transfinite proofs could maybe circumvent them, which means that you can't quite say there is no metaphysics which circumvents them. I suppose any theory of philosophy expressible in the ZFC or in formal mathematics would suffer from that issue, but that isn't true of every theory. Consider a trivial theory which assigns a truth value to every formal statement consistent with first order logic - I don't believe there's a formal method to disprove this, though again, I could be wrong. You would lose Peano arithmetic, but it would be self-consistent and every statement would be true or false.
Maybe you do. It works for general audiences though. Additionally, I'd note that as a conclusion, it's arguable that rocks are conscious a la Boltzmann brains. I personally don't act as though rocks are conscious, despite us not having any good arguments against it.