Right, yeah I agree that we can evaluate empiricism on empirical grounds. That is a thing we can do. And yes, as you say, we can come to different conclusions about empiricism when we evaluate it on empirical grounds. Very interesting point re object-level and meta-level conclusions. But why would start with empiricism at all? Why should we begin with empiricism, and then conclude on such grounds either that empiricism is trustworthy or untrustworthy?
When I say “empiricism cannot justify empiricism”, I mean that empiricism cannot explain why we trust empiricism, because the decision to start with empiricism as the framework for evaluating empiricism is not itself accounted for by empiricism. And when I say “accounted for in a way that resolves doubt”, not merely argued for.
Maybe a clearer way to say it is that I actually agree with everything you’ve said, but I don’t think what you’ve said is yet sufficient to resolve the question of whether our reasoning is based on something trustworthy.
(Also, yes I do think the first enigma is close to or identical to Hume’s problem of induction.)
Maybe a clearer way to say it is that I actually agree with everything you’ve said, but I don’t think what you’ve said is yet sufficient to resolve the question of whether our reasoning is based on something trustworthy.
I get the impression that by the standards you have set, it is impossible to have a “trustworthy” justification:
For anything you believe, you should be able to ask for its justifications. Thus justifications form a graph, with an edge from A to B meaning that “A justifies B”.
Just from how graphs work, if you start from any node and repeatedly ask for its justifications, you must eventually reach (i) a node with no justifications (in-edges), or (ii) a cycle, or (iii) an infinite chain.
However, unjustified beliefs, cyclic reasoning, and infinite regress are all untrustworthy.
Do you simultaneously believe all three of these statements? I disbelieve 3.
I disbelieve 2 because it assumes that there are a finite number of nodes in the graph. (We don’t have to hold an infinite graph in our finite brains; we might instead have a finite algorithm for lazily expanding an infinite graph.)
(2) doesn’t require the graph to be finite. Infinite graphs also have the property that if you repeatedly follow in-edges, you must eventually reach (i) a node with no in-edges, or (ii) a cycle, or (iii) an infinite chain.
EDIT: Proof, since if we’re talking about epistemology I shouldn’t spout things without double checking them.
Let G be any directed graph with at most countably many nodes. Let P be the set of paths in G. At least one of the following must hold:
(i) Every path in P is finite and acyclic.
(ii) At least one path in P is cyclic.
(iii) At least one path in P is infinite.
Now we just have to show that (i) implies that there exists at least one node in G that has no in-edges. Since every path is finite and acyclic, every path has a (finite) length. Label the nodes of G with the length of the largest path that ends at that node. Pick any node N in G. Let n be its label. Strongly induct on n:
If n=0, we’re done: the maximum path length ending at this node is 0, so it has no in-edges. (A.k.a. it lacks justification.)
If n>0, then there is a non-empty path ending at N. Follow it back one edge to a node N’. N’ must be labeled at most n-1, because if its label was larger then N’s label would be larger too. By the inductive hypothesis, there exists a node in G with no in-edges.
Ah good point. OK yeah I believe that (2) doesn’t require the graph to be finite, and I also agree that it’s not tenable to believe all three of your statements.
If, hypothetically, we were to stop here, then you might look at our short dialog up to this point as, roughly, a path through a justification graph. But if we do stop, it seems that it will be because we reached some shared understanding, or ran out of energy, or moved on to other tasks. I guess that if we kept going, we would reach a node with no justifications, or a cycle, or an infinite chain as you say. Now:
A node with no justification would be quite a strange thing to experience. I would write something, and you would question me, and I would have literally nothing that I could say
A cycle would be quite a normal experience to go a few loops around—plenty of conversations go in loops for some finite time—but it would be strange for there to be absolutely no way out of the cycle. We would just go and go and go until we lost all energy, and neither of us would notice that we’re in a cycle?
An infinite chain would be perhaps the most “normal” of the three experiences. We would just have some length of conversation and then, what, give up? Since we have finite minds, there must be a finite program that generates the infinite graph, so wouldn’t we eventually notice that and say “huh, it looks like we are on a path with the following generator functions”. What then? Would we not go some place else in the justification graph other than the infinite chain we were previously on?
So it’s hard for me to imagine really experiencing any of the three possibilities you point out. Yet they would seem to be not just possible but actually guaranteed (in aggregate).
As you said, very often a justification-based conversation is looking to answer a question, and stops when it’s answered using knowledge and reasoning methods shared by the participants. For example, Alice wonders why a character in a movie did something, and then has a conversation with Bob about it. Bob shares some facts and character-motivations that Alice didn’t know, they figure out the character’s motivation together, and the conversation ends. This relied on a lot of shared knowledge (about the movie universe plus the real universe), but there’s no reason for them to question their shared knowledge. You get to shared ground, and then you stop.
If you insist on questioning everything, you are liable to get to nodes without justification:
“The lawn’s wet.” / “Why?” / “It rained last night.” / “Why’d that make it wet?” / “Because rain is when water falls from the sky.” / “But why’d that make it wet?” / “Because water is wet.” / “Why?” / “Water’s just wet, sweetie.”. A sequence of is-questions, bottoming out at a definition. (Well, close to a definition: the parent could talk about the chemical properties of liquid water, but that probably wouldn’t be helpful for anyone involved. And they might not know why water is wet.)
“Aren’t you going to eat your ice cream? It’s starting to melt.” / “It sure is!” / “But melted ice cream is awful.” / “No, it’s the best.” / “Gah!”. This conversation comes to an end when the participants realize that they have fundamentally different preferences. There isn’t really a justification for “I dislike melted ice cream”. (There’s an is-ought distinction here, though it’s about preferences rather than morality.)
Ultimately, all ought-question-chains end at a node without justification. Suffering is just bad, period.
And I think if you dig too deep, you’ll get to unjustified-ish nodes in is-question-chains too. For example, direct experience, or the belief that the past informs the future, or that reasoning works. You can question these things, but you’re liable to end up on shakier ground than the thing you’re trying to justify, and to enter a cycle. So, IDK, you can not count those flimsy edges and get a dead end, or count them and get a cycle, whichever you prefer?
We would just go and go and go until we lost all energy, and neither of us would notice that we’re in a cycle?
There’s an important shift here: you’re not wondering how the justification graph is shaped, but rather how we would navigate it. I am confident that the proof applies to the shape of the justification graph. I’m less confident you can apply it to our navigation of that graph.
“huh, it looks like we are on a path with the following generator functions”
Not all infinite paths are so predictable / recognizable.
Yeah. Though you might be able to re-phrase the reasoning to turn it into one of the others?
EDIT: in more detail, it’s something like this. I have a whole bunch of ways of reasoning, and can use many of them to examine the others. And they all generally agree, so it seems fine. (Sean Carrol says this.) You can’t use completely broken reasoning to figure the world out. But if you start with partially broken reasoning, you can bootstrap your way to better and better reasoning. (Yudkowski says this.)
The main point is that I have been convinced by the reasoning in my previous comment and others that a search for an Ultimate Justification is fruitless, and have adjusted my expectations accordingly. When your intuitions don’t match reality, you need to update your intuitions.
have a whole bunch of ways of reasoning, and can use many of them to examine the others. And they all generally agree, so it seems fine. (Sean Carrol says this.) You can’t use completely broken reasoning to figure the world out. But if you start with partially broken reasoning, you can bootstrap your way to better and better reasoning. (Yudkowski says this.)
Indefinitely? I agree that you can generally do better, but that doesn’t mean you can hit Absolute Truth...
Right, yeah I agree that we can evaluate empiricism on empirical grounds. That is a thing we can do. And yes, as you say, we can come to different conclusions about empiricism when we evaluate it on empirical grounds. Very interesting point re object-level and meta-level conclusions. But why would start with empiricism at all? Why should we begin with empiricism, and then conclude on such grounds either that empiricism is trustworthy or untrustworthy?
When I say “empiricism cannot justify empiricism”, I mean that empiricism cannot explain why we trust empiricism, because the decision to start with empiricism as the framework for evaluating empiricism is not itself accounted for by empiricism. And when I say “accounted for in a way that resolves doubt”, not merely argued for.
Maybe a clearer way to say it is that I actually agree with everything you’ve said, but I don’t think what you’ve said is yet sufficient to resolve the question of whether our reasoning is based on something trustworthy.
(Also, yes I do think the first enigma is close to or identical to Hume’s problem of induction.)
I get the impression that by the standards you have set, it is impossible to have a “trustworthy” justification:
For anything you believe, you should be able to ask for its justifications. Thus justifications form a graph, with an edge from A to B meaning that “A justifies B”.
Just from how graphs work, if you start from any node and repeatedly ask for its justifications, you must eventually reach (i) a node with no justifications (in-edges), or (ii) a cycle, or (iii) an infinite chain.
However, unjustified beliefs, cyclic reasoning, and infinite regress are all untrustworthy.
Do you simultaneously believe all three of these statements? I disbelieve 3.
I disbelieve 2 because it assumes that there are a finite number of nodes in the graph. (We don’t have to hold an infinite graph in our finite brains; we might instead have a finite algorithm for lazily expanding an infinite graph.)
(2) doesn’t require the graph to be finite. Infinite graphs also have the property that if you repeatedly follow in-edges, you must eventually reach (i) a node with no in-edges, or (ii) a cycle, or (iii) an infinite chain.
EDIT: Proof, since if we’re talking about epistemology I shouldn’t spout things without double checking them.
Let G be any directed graph with at most countably many nodes. Let P be the set of paths in G. At least one of the following must hold:
(i) Every path in P is finite and acyclic. (ii) At least one path in P is cyclic. (iii) At least one path in P is infinite.
Now we just have to show that (i) implies that there exists at least one node in G that has no in-edges. Since every path is finite and acyclic, every path has a (finite) length. Label the nodes of G with the length of the largest path that ends at that node. Pick any node N in G. Let n be its label. Strongly induct on n:
If n=0, we’re done: the maximum path length ending at this node is 0, so it has no in-edges. (A.k.a. it lacks justification.)
If n>0, then there is a non-empty path ending at N. Follow it back one edge to a node N’. N’ must be labeled at most n-1, because if its label was larger then N’s label would be larger too. By the inductive hypothesis, there exists a node in G with no in-edges.
Ah good point. OK yeah I believe that (2) doesn’t require the graph to be finite, and I also agree that it’s not tenable to believe all three of your statements.
If, hypothetically, we were to stop here, then you might look at our short dialog up to this point as, roughly, a path through a justification graph. But if we do stop, it seems that it will be because we reached some shared understanding, or ran out of energy, or moved on to other tasks. I guess that if we kept going, we would reach a node with no justifications, or a cycle, or an infinite chain as you say. Now:
A node with no justification would be quite a strange thing to experience. I would write something, and you would question me, and I would have literally nothing that I could say
A cycle would be quite a normal experience to go a few loops around—plenty of conversations go in loops for some finite time—but it would be strange for there to be absolutely no way out of the cycle. We would just go and go and go until we lost all energy, and neither of us would notice that we’re in a cycle?
An infinite chain would be perhaps the most “normal” of the three experiences. We would just have some length of conversation and then, what, give up? Since we have finite minds, there must be a finite program that generates the infinite graph, so wouldn’t we eventually notice that and say “huh, it looks like we are on a path with the following generator functions”. What then? Would we not go some place else in the justification graph other than the infinite chain we were previously on?
So it’s hard for me to imagine really experiencing any of the three possibilities you point out. Yet they would seem to be not just possible but actually guaranteed (in aggregate).
Interested in what you make of this.
As you said, very often a justification-based conversation is looking to answer a question, and stops when it’s answered using knowledge and reasoning methods shared by the participants. For example, Alice wonders why a character in a movie did something, and then has a conversation with Bob about it. Bob shares some facts and character-motivations that Alice didn’t know, they figure out the character’s motivation together, and the conversation ends. This relied on a lot of shared knowledge (about the movie universe plus the real universe), but there’s no reason for them to question their shared knowledge. You get to shared ground, and then you stop.
If you insist on questioning everything, you are liable to get to nodes without justification:
“The lawn’s wet.” / “Why?” / “It rained last night.” / “Why’d that make it wet?” / “Because rain is when water falls from the sky.” / “But why’d that make it wet?” / “Because water is wet.” / “Why?” / “Water’s just wet, sweetie.”. A sequence of is-questions, bottoming out at a definition. (Well, close to a definition: the parent could talk about the chemical properties of liquid water, but that probably wouldn’t be helpful for anyone involved. And they might not know why water is wet.)
“Aren’t you going to eat your ice cream? It’s starting to melt.” / “It sure is!” / “But melted ice cream is awful.” / “No, it’s the best.” / “Gah!”. This conversation comes to an end when the participants realize that they have fundamentally different preferences. There isn’t really a justification for “I dislike melted ice cream”. (There’s an is-ought distinction here, though it’s about preferences rather than morality.)
Ultimately, all ought-question-chains end at a node without justification. Suffering is just bad, period.
And I think if you dig too deep, you’ll get to unjustified-ish nodes in is-question-chains too. For example, direct experience, or the belief that the past informs the future, or that reasoning works. You can question these things, but you’re liable to end up on shakier ground than the thing you’re trying to justify, and to enter a cycle. So, IDK, you can not count those flimsy edges and get a dead end, or count them and get a cycle, whichever you prefer?
There’s an important shift here: you’re not wondering how the justification graph is shaped, but rather how we would navigate it. I am confident that the proof applies to the shape of the justification graph. I’m less confident you can apply it to our navigation of that graph.
Not all infinite paths are so predictable / recognizable.
Which is the trustworthy one? I’m guessing circular reasoning.
Yeah. Though you might be able to re-phrase the reasoning to turn it into one of the others?
EDIT: in more detail, it’s something like this. I have a whole bunch of ways of reasoning, and can use many of them to examine the others. And they all generally agree, so it seems fine. (Sean Carrol says this.) You can’t use completely broken reasoning to figure the world out. But if you start with partially broken reasoning, you can bootstrap your way to better and better reasoning. (Yudkowski says this.)
The main point is that I have been convinced by the reasoning in my previous comment and others that a search for an Ultimate Justification is fruitless, and have adjusted my expectations accordingly. When your intuitions don’t match reality, you need to update your intuitions.
Indefinitely? I agree that you can generally do better, but that doesn’t mean you can hit Absolute Truth...