Pragmatists from Pierce through the positivists to Rorty have agreed with you that the goal is to avoid wasting time on theories of truth and meaning and instead focus on finding practical tools; they've only spoken of theories of truth when they thought there was was no other way to make their points understandable to those too firmly entrenched in the philosophical mainstream (or, even more often, had such theories attributed to them by people who assumed that must be what they were up to despite their explicit disavowals). I'm not saying all of those people agreed with you about everything (the positivists, for example, thought the fact/value distinction was a useful tool, although of course they didn't think it represented any fundamental truth about reality), but I think you greatly exaggerate your originality here. Of course, one might reasonably insist that originality is not as important as whether the theories actually are useful, but while I tend to be in sympathy with the pragmatist tradition, the fact that it has been around for quite a while without seeming to have radically triumphed over all rivals does provide some reason for doubt about the extent of its world-beating potential.
I think you greatly exaggerate your originality here.
I thought it might come across that way, but didn't want to invest a bunch of time listing my intellectual debts (the post is long enough already). For the record, I'm aware that my ideas aren't entirely original, and I suspect that when I think they are I would be able to find similar ideas in others' writing independently.
the fact that it has been around for quite a while without seeming to have radically triumphed over all rivals does provide some reason for doubt about the extent of its world-beating potential.
I think that part of the problem here is that pragmatists didn't spend nearly as much energy on the details of applying their ideas as, say, Carnap and Popper did. They also tended to keep their discussion of pragmatism to philosophical circles, rather than engaging with scientific circles about their research. There's a lot of inertia to fight in order to shift scientific paradigms and the pragmatists didn't engage in the social and political organisation necessary to do so.
I think I've provided a fair summary of some of the benefits of wearing a pragmatic thinking cap. And I'll be outlining those and others in more detail later.
That it hasn't been radically triumphant isn't strong evidence towards its lack of world-beating potential though. Pragmatism is weird and confusing, perhaps it just hasn't been exposited or argued for clearly and convincingly enough. Perhaps it historically has been rejected for cultural reasons ("we're doing physicalism so nyah"). I think there is value on clearly presenting it to the LW/MIRI crowd. There are unresolved problems with a naturalistic philosophy that should be pointed out, and it seems that pragmatism solves them.
As for originality, I'm not sure how think about this. Pretty much everything has already been thought of, but it is hard to read all of the literature to be familiar with it. So how do you write? Acknowledge that there probably is some similar exposition, but we don't know where it is? What if you've come up with most of these ideas yourself? What if every fragment of your idea has been thought of, but it has never been put together in this particular way (which I suspect is going to be the case with us). The only reason for not appearing to be original is so not to seem arrogant to people like you who've read these arguments before.
Do you have direct, object-level criticisms of our version of pragmatism? Because that would be great. We've been having a hard time finding ones that we haven't already fixed, and it seems really unlikely that there aren't any. (I've been working on this with OP)
As I said, I'm sympathetic to pragmatism. But I guess I'd turn the question around, and ask what you think pragmatism will improve. Serious researchers are pretty good at rationalizing how procedures that work fit into their paradigm (or just not thinking about it and using the procedures that work regardless of any conflicting absolutist principles they might have). I'm sure removing the hypocrisy would be of some benefit, but given the history it would also likely be extremely difficult; in what cases do you think it is clear that this would be the best place to apply effort, and why?
Oh, and on reductionism (and to some extent truth absolutism generally), trying to give a unified account of everything requires thoroughly exploring the connections between different realms, and there are definitely tendencies to view realms as much more isolated than they are for purposes of simplification. To take what is admittedly a small scale reductionist project rather than a global reductionist project, there seems to be a strong tendency to sharply separate the physiological from the psychological when looking at behavior, in ways that seem to hinder understanding, not to mention the ability to deal with serious problems. For example, the pointless disputes about drugs for psychological therapy that focus on the bogus question of whether the psychological disorders have a biological base (how could they not, unless perhaps we're Cartesians?) rather than the much more pertinent questions of whether they work and how they compare to alternatives. While reductionist projects that try to fit everything into a single framework are sometimes guilty of ignoring phenomena that are too complicated or insufficiently well understood to fit into the framework, it is equally true that sharply separating projects into distinct categories can drastically underestimate how much influence there is from factors outside a particular narrowly defined sphere.
This is the best place to apply effort for my goals, because I think that there might be some problems underlying MIRI's epistemology and philosophy of math that is causing confusion in some of their papers.
I don't think we can give you favorable feedback, because you haven't claimed anything yet.
Truth is a terrible goal for epistemology. Nature gives us information, not access to truth. Many structuralist and post-modern critiques of meaning evaporate if you interpret the meaning of the sentence "The sky is blue" as refining the probability distribution describing the sky's color, rather than as being problematic because "blue" isn't clearly defined, or because the speaker hasn't been outside in ten minutes. A sentence's meaning is more like the odds ratio multipliers it provides for your priors than like a truth predication.
A sentence's meaning is more like the odds ratio multipliers it provides for your priors than like a truth predication.
And what do you mean by this? That the old truth model is less correct than the probabilistic model, or that the probabilistic model performs better in applications? Or maybe you're prone to say that the latter is more correct, but what you mean by that is that there's more use for it. That's the tension I am trying to bring out, those two different interpretations of epistemic claims. And my claim is that the second gets us farther than the first. For instance it permits us to use combinations of tools that most epistemologies would frown upon, like contradictory theories.
There's a shift in perspective that has to happen in the course of this discussion, from evaluating the intuitive correctness and reality-correspondence (even probabilistically) of theories as sets of claims about the world to evaluating the potential uses and practical strength of theories as tools to accomplish our goals. I'm supporting my approach epistemology in the second more pragmatic way rather than the first way, which is more epistemic.
If the relevant behavior of the brain is computable (which seems likely to me), isn't there then a computable algorithm that does everything that you can do, if not better? I understand if you're objecting to overly simplistic models, but the idea that there is no one single (meta-)model that is most correct seems wrong in principle if not in present-day practice.
I'm fine with agents being better at achieving their goals than I am, whether or not computational models of the brain succeed. We can model this phenomenon in several ways: algorithms, intelligence, resource availability, conditioning pressures, so on.
But "most correct" isn't something I feel comfortable applying as a blanket term across all models. If we're going to talk about the correctness (or maybe "accuracy," "efficiency," "utility," or whatever) of a model, I think we should use goals as a modulus. So we'd be talking about optimal models relative to this or that goal, and a most correct model would be a model that performs best relative to all goals. There isn't currently such a model, and even if we thought we had one it would only be best in the goals we applied it to. Under those circumstances there wouldn't be much reason to think that it would perform well under drastically different demands (i.e. that's something we should be very uncertain about).
The computable algorithm isn't a meta-model though. It's just you in a different substrate. It's not something the agent can run to figure out what to do because it necessarily take more computing power. And there is nothing preventing such a pragmatic agent from having a universe-model that is computable, considering finding a computable algorithm approximating itself, and copying that algorithm over and over.
I'll also give my pragmatism a slogan: "It's just a model."
In what aspect is your idea of pragmatism supposed to differ from general semantics with the slogan "The map is not the territory"? How about reading Science and Sanity and seeing whether that's the philosophy that you are looking for?
Instead I mean that I don't even think that the truth is a useful or coherent concept when stretched to accommodate what philosophers have tried to make it accommodate.
That's a claim about ontology not a claim about epistemology. When it comes to modern source I consider Barry Smith worth reading. He's doing practical ontology for bioinformatical problems.
In what aspect is your idea of pragmatism supposed to differ from general semantics with the slogan "The map is not the territory"?
I'm not requiring that "territory" be a coherent concept at all. Suppositions about territories are models that my epistemology evaluates rather than assumptions built into the epistemology.
That's a claim about ontology not a claim about epistemology. When it comes to modern source I consider Barry Smith worth reading. He's doing practical ontology for bioinformatical problems.
If you like, you can think of this as a an ontological critique of most epistemologies. I wouldn't like to phrase it that way, though.
I'm not requiring that "territory" be a coherent concept at all.
What do you mean with "coherent" concept inside pragmatism? In what sense does a pragmatist worry about whether or not something is coherent?
At the moment most of what you wrote seems like a bunch of catch phrase without a look at the deeper issues. General Semantics has in addition to it's nice slogan a bunch of thoughts about how to think.
I wouldn't like to phrase it that way, though.
Why? What wrong with the word ontology? I think you get into problems if you want to do ontology but refuse to think of yourself as doing ontology.
What do you mean with "coherent" concept inside pragmatism? In what sense does a pragmatist worry about whether or not something is coherent?
"Coherent" is a stand-in for some worries I have: Does having our epistemology underpinned by a model-reality relationship skew our motivations for creating models? Does it close certain fruitful paths by making us believe they are epistemically nonsensical or questionable? Does it have significant limitations in where it can be fruitfully applied and how? I think the answer to each is yes, which motivates me to get rid of the model-reality relationship from my core epistemology. Although of course I consider it perfectly legitimate to use that relationship as a heuristic in the context of a pragmatic background epistemology.
Why? What wrong with the word ontology? I think you get into problems if you want to do ontology but refuse to think of yourself as doing ontology.
It's not that I refuse. I just don't put much stock in the distinction between epistemology and ontology. I think they're entangled, and that pretending they aren't leads to confusion (see the p-zombie debate, for example).
I didn't really bring out the ontological elements of what I was doing in this post, and I recognised that afterward. I'll fix that oversight later.
Does it close certain fruitful paths by making us believe they are epistemically nonsensical or questionable?
Thinking that there is a reality out there that's separate from you model means that you can't do magic "Law of attraction" stuff where you change the territory by changing your model. You reject a whole bunch of mysticism that presupposes that model and territory are the same.
Do you think that some of that mysticism is a fruitful path that get's wrongly rejected?
Does having our epistemology underpinned by a model-reality relationship skew our motivations for creating models?
Different people have quite different motivations for creating models. There are logical positivists who think that the only goal of a model is to represent reality as accurately as possible. That doesn't mean that everyone who considers map and territory separate holds that extremist position.
If I look at the public transportation map of Berlin then the distances between places aren't very accurate. The map isn't designed for that purpose. That doesn't make it a bad map and I can still mentally distinguish the territory of Berlin from the map.
Do you think that some of that mysticism is a fruitful path that get's wrongly rejected?
No, but that's because I've seen it in action and noted that I don't have much use for it, and not because I've constructed an epistemology that proscribes it altogether.
I don't see the point of barring paths as inherently epistemically irrational. I would rather let anyone judge for themselves which tools would be appropriate or inappropriate, and model the success or failures in whichever way helps them choose tools more effectively later.
For example there's a commonly held belief that we shouldn't believe two mutually contradictory models since they can't both describe reality and at least one of them will lead us astray. In other words it isn't epistemically rational to believe both. I want to scrap judgements like that from the underpinnings of our epistemology, because that really does close fruitful paths. During revolutions in physics, after one theory gains a slight advantage the competitors all die out. I would like to see more of a plurality, so that we can have multiple tools in our arsenal with different potential uses. Rather than deciding that I can believe only one, I'll say that I can use any to the extent that they work, and I will hold beliefs about where and how I can apply them.
If I look at the public transportation map of Berlin then the distances between places aren't very accurate. The map isn't designed for that purpose. That doesn't make it a bad map and I can still mentally distinguish the territory of Berlin from the map.
You're right, of course, motivations vary. Transit maps are not trying to model distances, just the order of stops on various lines. But motivations in some areas, like logic and physics, are much more heavily influenced by the positivists than transit maps. I think we should be paying more attention to the specific uses we have in mind when constructing any model, including logics and theories of physics, whereas model-reality epistemologies make us think only of mirroring reality once we get to things considered more fundamental.
Of course some people are doing what I'm suggesting in "fundamental" areas. Constructivists in the foundations of math are constructing their foundations explicitly so that all math can be computable and subject to automated proof checking and theorem proving. Usually they don't fret about whether a constructive foundation will give us the real, true picture of math. Like I've said, I think we should adopt that mentality everywhere.
For example there's a commonly held belief that we shouldn't believe two mutually contradictory models since they can't both describe reality and at least one of them will lead us astray.
Maybe commonly held by positivists.
Not among people who really follow the "the map is not the territory". There are many maps of the city of Berlin. I will use a different map when I want to navigate Berlin via the public transport system than when I want to drive via bike.
At the same time if my goal is staying remaining sane, it's useful to not forget that neither of those maps are the territory of the city of Berlin. In the case of the city of Berlin few people will make the mistake of confusing the two. In other domains people do get into issues because things get complicated and they forget that their maps aren't the territory.
But motivations in some areas, like logic and physics, are much more heavily influenced by the positivists than transit maps.
For physics that true. For biology for example it isn't. It's not like the positivists are the only people around.
In not sure whether you position is: "I don't like positivism, let's do something different" or "I don't like positivism, let's do X". If it's the second I'm not sure what X is. If it's the first, I think that reading Science and Sanity would be helpful.
Not among people who really follow the "the map is not the territory". There are many maps of the city of Berlin. I will use a different map when I want to navigate Berlin via the public transport system than when I want to drive via bike.
At the same time if my goal is staying remaining sane, it's useful to not forget that neither of those maps are the territory of the city of Berlin. In the case of the city of Berlin few people will make the mistake of confusing the two. In other domains people do get into issues because things get complicated and they forget that their maps aren't the territory.
In not sure whether you position is: "I don't like positivism, let's do something different" or "I don't like positivism, let's do X".
I don't think you need a "real Berlin" for that usage of maps to make sense: instead of saying that a transit map models some aspect of the real Berlin, we can say that the transit map is functional for navigating Berlin.
I'd rather this phrasing because having the concept of a real Berlin can lead to confusions when we apply the idea of by analogy to other things, like theories of arithmetic, the universe. or "the self." That's why I want it removed from our base epistemology. Of course I'll be very happy to use the map and territory epistemology as a heuristic if I find it easier to think with in certain situations, but because of its shortcomings elsewhere I will not claim that it is the correct epistemology.
Hopefully that brief explanation helps answer what I am trying to do to some extent. In any case I'm thankful for both the discussion (which I'd be happy to continue, of course) and the reading suggestion.
I'd rather this phrasing because having the concept of a real Berlin can lead to confusions when we apply the idea of by analogy to other things, like theories of arithmetic, the universe.
I do think that there a real universe in the same sense that there a real Berlin. map(berlin) is not the same object as berlin just as map(universe) is not the same object as universe. Positivists want to have a state of affair where there's no difference between map(universe) and universe. That goal doesn't seem in reach and might even be theoretically impossible. That doesn't mean that it's helpful to just tell the positivists to pretend that map(universe) and universe are the same and the issue is solved.
In theory in bioinformatics different models of a phenomena have different sensitivity and specificity for a real phenomena. Depending on what you want to do you might use a model with high sensitivity or a model with high specificity. Neither of those models is more true and both aren't the same as the real phenomena. But to have the discussion about which models is more useful to describe a certain phenomena it's useful to have a notion of the phenomena.
In bioinformatics someone who wants to simulate 100 neurons is going to use a different model of neurons as someone who wants to simulate 10,000,000 neurons. At the same time it's important to understand that the models are not the reality. The Blue Brain Project claims to simulate a brain. If you want to know how much computational power is needed for "human uploading" you can't just take the amount of computational power that the Blue Brain project uses for a single neuron. Forgetting that they are investigating a model of a neuron and not a real neuron screws you.
If we take about whether or not there's more autism than there was 30 years ago it's very useful to be mentally aware of what you mean with the term autism. It could be that more people are diagnosed because they changed the diagnosis criteria. It could be that more people are diagnosed because there more awareness about autism in the general public and therefore fewer cases of autism stay undiagnosed.
Of course autism doesn't exist in the same ontological sense that a carbon atom exists. Positivism therefore doesn't really know what to do with it. You find positivist say silly things like that thing that exist in the same sense that autism exist aren't "real". The positivist doesn't want to talk about the ontology, that you need to talk about to speak meaningfully about how autism exists.
Because few people actual deal with practical ontology we have the DSM-V that defines mental illnesses in a really awful way. The committee that draw up the DSM-V didn't go and optimized their definitions for sensitivity and specificity so that two doctors will make the same diagnosis.
I'm going to drop discussion about the universe in particular for now. Explaining why I think that the map-territory epistemology runs into problems there would require a lot of exposition on points I haven't made yet, so it's better suited for a post than a comment.
I've realised that there's a lot more inferential distance than I thought between some of the things I said in this post and the content of other posts on LW. I'm thinking of strategies to bridge that now.
That doesn't mean that it's helpful to just tell the positivists to pretend that map(universe) and universe are the same and the issue is solved.
Hm, if you're attributing that to me then I think I haven't been nearly clear enough.
Earlier I said that I had ontological considerations but didn't go into them in my post explicitly. I'll outline them for you now (although I'll be talking about them in a post in the near future, over the next couple days if I kick myself into gear properly).
In the end I'm not going to be picky about what different models claim to be real so long as they work, but in the epistemology I use to consider all of those models I'm only going to make reference to agents and their perceptual interfaces. If we consider maps and models as tools that we use to achieve goals, then we're using them to navigate/manipulate some aspect of our experience.
We understand by trial and error that we don't have direct control over our experiences. Often we model this lack of control by saying that there's a real state of affairs that we don't have perfect access to. Like I said, I think this model has limitations in areas we consider more abstract, like math, so I don't want this included in my epistemology. Reality is a tool I can use to simplify my thinking in some situations, not something I want getting in the way in every epistemological problem I encounter.
Likewise, in your autism example, we have a model of possible failure modes that empirical research can have. This is an extremely useful tool, and a good application of the map-territory distinction, but that example still doesn't compel me to use either of those tools in my epistemology. The more tools I commit myself to, the less stable my epistemology is. (Keeping reservationism in the back of your mind would be helpful here.)
The difference is that saying there is a territory is also a model. The way I would rephrase map/territory into this language is "the model is not the data."
For the past three thousand years epistemology has been about the truth, the whole truth, and nothing but the truth. Philosophers and scientists have continuously attempted to pinpoint the nature of truth, to find general logico-syntactic criteria for generating justified inferences, and to discover the true nature of reality. I happen to think that truth is overrated. And by that I don't mean that I'm a stereotypical postmodernist, prepared to say that all views are on equal footing (because after all, who can really say what's true and what isn't?). Instead I mean that I don't even think that the truth is a useful or coherent concept when stretched to accommodate what philosophers have tried to make it accommodate. It's not a malleable enough concept to have the generality that philosophers are asking of it. We need something else in its place.
A view similar to this is reservationism, which was first introduced[1] by Moldbug in A Reservationist Epistemology. If you haven't read it, I suggest at least skimming it before reading the rest of this post, but the basic idea is that you can try to cram reason into an explicit General Theory of Reason for as long as you like, but at best it will always be a special case of "common sense." I have mixed feelings about Moldbug's post. On the one hand, it's delightfully witty and I agree with the general thrust of the argument. On the other hand, I think you can go a bit farther to explain his "common sense" notion than he lets on, and the abrasiveness and vagueness of his writing are likely to cloak some of the finer points. And despite giving (likely unintentional) hints about what we might replace "truth" with, he never does criticise the concept of truth, although he obviously criticises general theories of truth.
Since I do depart from Moldbug, I'll call myself a pragmatist rather than a reservationist. I'll also give my pragmatism a slogan: "It's just a model."[2] What's just a model? Bayesianism, falsificationism, positivism, naturalism, physicalism, panpsychism, quantum mechanics, operant conditioning, phlogistic chemistry, Catholicism, atheism, Hinduism, category theory, number theory, constructive analysis ... we could go all day with obvious examples. Here are some other examples: "Bayesian reasoners are optimal," "loop quantum gravity will give us a theory of everything," "a sentence is meaningful iff it, by itself or in conjunction with further premises, entails some observation statement not entailed by those other premises alone,"[3] and more mundane examples like "It's raining outside," "My mother is 52," "Common sense," and "It's just a model." Here's another, an example central to my position: models are conceptual tools that help us think about some aspect of our experience and achieve our goals. I italicised "conceptual tools" because I want to emphasise their role as tools rather than their role as theories or propositions, and I want to emphasise the utility of model-tools rather than their truth.
Lots of other models have been called pragmatism. Charles Peirce and William James came up with pragmatic "theories of truth." Richard Rorty and Ludwig Wittgenstein advanced pragmatic "theories of meaning." Instead of pragmatically explaining truth and related concepts, I'm giving it a rest. There are plenty of theories of truth already, and truth-focused epistemologies have their shortcomings. After all, what have the correspondence theory and Quinean naturalism given us in the philosophy of math except Platonism and confusion?[4] Of course, these shortcomings shouldn't come as a surprise under the models-as-tools theory. Tools are built and tested with specific domains of application in mind by agents with limited imagination, and when we try to apply the tools to other domains we run the risk that they could be utterly worthless.
Of course, to provide a working alternative I need to convince others that it's worth trying, so let me try. Under this paradigm, where we judge models by their utility, there is no need to fret over whether the continuum hypothesis is "true" or not, whatever that might mean: we just note that as far as we can tell it's neither here nor there and move on.[5] And suddenly the famous fact/value distinction looks very silly: of course facts[6] inform us about how we should act; "facts" are just another model-tool in our system of model-tools, and the whole point of building our model-tools is to use them. These benefits should be enough to get your attention, at the very least. Another is that we don't have to use awkward, gross-feeling terms like "common sense." Common sense, in Moldbug's usage, is just the process that leads us to justify using models. So instead of common sense being the standard, we have our goals and instrumental rationality. Model building and model use are special cases of tool building and tool use, and agent-like goal-directed behaviour in general.
My model is also compatible with the conception of rationality as winning. There is no holy reason juice in the universe[7] that stops us from picking a winning but decidedly not reason-juice-flavoured strategy[8]; the standard for picking a strategy is that it helps us achieve our goals, and strategies that make us sit in the corner don't pass. But my model is not compatible with the division between instrumental and epistemic rationality. Since the correspondence theory (and the map-territory metaphor) is just another tool in the toolbox, epistemic rationality is just a tool in the toolbox too, whereas instrumental rationality is the process we use to choose which tools we want to use and when (and why) we want to us them. In this model, instrumental rationality just is rationality, that "common sense" thing that Moldbug claimed subsumed everything else as a special case.
And before I'm accused of being a relativist, let me say that not all tools are created equal, and we do have reason to use some in certain situations as opposed to others; namely, we have reason to use tools in certain situations when they produce outcomes we like better relative to other tools at our disposal. So when it comes to a models of physics, we use Aristotelian physics for simple everyday situations[9], classical mechanics for many engineering projects and pedagogical functions, and quantum mechanics for many other engineering projects and current research.[10] Now, often people will read this transition through different models as evidence for their favourite epistemology, and I won't disappoint you there: this transition shows us that as people began encountering new problems, old tools often didn't cut it. Go figure. After all, they weren't built with those future problems in mind, and foreseeing every possible roadblock that a tool could face would require another very powerful tool!
Which brings me to the problem of induction. Traditionally the problem is to find a general justification for the truth of universal claims on the basis of particular cases. We can translate this into my pragmatic framework fairly easily: construct the one tool to rule them all, a tool so awesome that we can use to achieve any achievable goal and that has provisions for any pesky roadblocks. The traditional statement reads easily as "carry out a foundationalist programme like Descartes," or in other words create a bedrock of certainty. It's generally agreed that this is impossible. My reformulation can be reread in a similar way: "carry out a reductionist programme like a theory of everything." Since the problem of induction is unsolvable, I strongly doubt that a reductionist theory of everything is on the menu. And if such a theory is ever announced I suspect the pragmatic slogan will still apply: It's just a model. A model with a fancy name, sure, but nonetheless with a limited domain of applicability and its own set of weaknesses.
That all having been said, my views aren't as alien to the general LW memecluster as you might expect. My position assumes consequentalism, and it's Quinean in that it's continuous with science rather than "prior" to it. I think that the results of science are some of the best tools we've developed, that physicalism is a good model for conceptualising and solving many problems, and that the correspondence theory of truth is a good tool in certain contexts. My goal here is not really to be a contrarian, as fun as that is. Rather, one of my goals is to find a better way to conceptualise a broader class of epistemological and scientific problems than current frameworks comfortably allow.
If this post receives favourable feedback, I plan to write more posts expanding on these ideas. Specifically:
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[1] First introduced under that name, anyhow. For similar ideas, see Richard Rorty's Consequences of Pragmatism and Paul Feyerabend's Against Method.
[2] "My" is meant a bit loosely; I owe a lot to people I've discussed these ideas with, and to the reading material I've consumed. I'll elaborate on any of those contributions by request.
[3] This is a paraphrase of A. J. Ayer from Language, Truth and Logic, Dover ed. pp. 38-39.
[4] Quine gives us Platonism.
[5] It's been begrudgingly agreed that we can't decide on whether the continuum hypothesis is true since CH and its negation are independent of ZFC, but many people still argue about whether it is, ultimately, true or not. A pragmatic take on this debate is that since CH and ¬CH are both consistent with ZFC, we can strategically add either one of them as axioms for the purposes of making proofs easier if we like.
[6] I doubt the usefulness and coherence of "fact" as much as I do "truth," but conventional language is conventional language.
[7] "Universe" being another example of a model.
[8] Despite the arguments of champions of causal and evidential decision theories.
[9] See Induction by Holland, Holyoak, et al., pp. 203-9 and 224-5, and A Function for Thought Experiments by Thomas Kuhn.
[10] Obviously these are meant as examples of uses, not an exhaustive list.