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Truth, Knowledge, and Belief: An Exploration

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I made mention of formal truth in a previous post, and said that I think it is a type of epistemic truth. I'd like to return to this idea now and be a bit more clear about what I mean by this.

 

Formal truth is generally taken to refer to logical or mathematical truth. These truths can be shown to follow directly, via deduction, from a well-defined set of axioms. That is to say, formal truths are actually provable. On standard arithmetic, that 2+5=7 is a formal truth. That the angles in a triangle add up to 180 degrees is a formal truth on Euclidean geometry. Other examples can be given, but I want to look at these two for now.

 

I want to explain why I think of formal truth as a type of epistemic truth, and not a type of ontological truth. It's very tempting to say 2+5=7, for example, is just a brute fact, that it's true irrespective of what we think, and is therefore an ontological truth, but I think this is incorrect. The reason why I think that this is incorrect is that "2", "5", and "7" are not material objects. They are ideas. Moreover, the rules of arithmetic are a human construction, and they don't have to be as they are. On addition modulo 6, for example, 2+5=1. It's possible to do this type of addition over a field which doesn't contain 7 at all (ie, a field in which 7 is not a thing). For the record, this is something that mathematicians actually do, and it does have real applications. So it does not have to be the case that 2+5=7. It is the case because of our conception of the numbers involved, and our definition of the rules of arithmetic. But this is how epistemic truth works.

 

The triangle example also breaks down as a matter of ontological truth. Ideal Euclidean triangles do not exist in the real world. All real-world triangles are approximations. Moreover, triangles which are drawn on the surface of the Earth violate this rule altogether, because the surface of the Earth is not flat. The axioms of Euclidean geometry, like the rules of arithmetic, are a human construction. They can be used to generate quite a lot of truths, but these truths rest on human thought, which is to say they are epistemic.

 

Now, it is very important to note that I am not saying that we can't reason formally about ontologically objective objects. We certainly can. Scientists do this all the time. It may even be the case that we can establish a formal truth which gives us knowledge of an ontological truth. But we can't generate ontological truth through formal reasoning. What we generate is epistemic truth. That is the point. We can reason formally about the natural world, and in so doing, build scientific models which establish formal truths. This may lead us to claim knowledge of ontological truths, but we need to keep in mind that our knowledge of these kinds of truths is really just firmly held belief. By contrast, when we establish formal truth, we don't merely establish knowledge of a truth, we actually establish the truth itself. I say that I know the earth is round, but I say it is true that 2+5=7 (on the usual rules, etcetera). This is an important difference.

 

I think that one of the things that science does is build models of the universe. The models have rules and laws. When a particular model becomes well-established and generally accepted, it becomes very tempting to start treating the laws of that model as actual laws of the universe. I think this is a fundamental mistake. What we typically call laws of the universe are actually laws of our models of the universe. Where their truth has been established, it has been established epistemically. It must be this way. This is not to say that we can’t have knowledge about ontological truth, just that we can’t have absolute certainty.

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On 11/6/2019 at 10:34 PM, disillusioned said:

@WalterP you've raised some excellent questions,  which relate directly to the next topic I was hoping to explore. We definitely need to look at how science relates to all of this. Please bear with me. I'll get back to you over the next couple of days.

 

Hello Disillusioned.  :)

 

I intend to do your reply justice over the weekend.

 

Thank you.

 

Walter.

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11 hours ago, disillusioned said:

This is not to say that we can’t have knowledge about ontological truth, just that we can’t have absolute certainty.

 

That seems to be the over arching conclusion.

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1 hour ago, Karna said:

Found a small video on Truth and Belief:

 

https://www.youtube.com/watch?v=wwUd9gHusc0

 

What do you all think of it?

 

 

I want to say that I agree with some of the sentiments expressed, but I'm not sure I can say even that.

 

It isn't at all clear to me what he means by "believe", "know", and "perceive". I think there may be something to what he is trying to say, but I'm afraid I just don't know exactly what it is that he's trying to say.

 

What I've been trying to do in this thread is establish clarity in my use of terms like belief,  knowledge, and truth, so that I can develop some ideas about these things in a coherent fashion. In doing this, I've been taking an axiomatic approach, which is to say that I've been arguing on the basis of assumptions. The gentleman in the video seems to think that assumptions are barriers to knowledge, and that belief is blind necessarily. This clearly conflicts with what I've argued this far, which is fine in itself; I'm happy to look at alternative views. The problem is that I just don't know what exactly he's trying to say. So I can't actually consider his view, because I just don't know what it is.

 

Can you offer any clarity here @Karna?

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On 11/7/2019 at 10:27 AM, disillusioned said:

Walter,

 

Hello Disillusioned.  :)  Its taken me a bit longer to get back to you on this, but here I am.

 

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I think the overarching question of how science fits in with the account that I've given so far is extremely important. I'm going to try to sketch an answer to this question briefly before I address the specific questions you raised in your post.

 

I hope that it is fairly clear that science is a human endeavour. It's a process which aims to generate knowledge about the natural world. That is, it aims to generate knowledge of (primarily) ontological truths. Notice, immediately, that I do not say that science generates ontological truth. What it generates is knowledge. Because of science, we know that the Earth revolves around the sun, that water boils at 100 degrees Celsius at standard atmospheric pressure, and that light bends away from the normal when it passes from a dense medium into one that is less dense. Now, the crucial point is this: it is very tempting to say that science has established the truth of these statements, but I think that this is incorrect. What science has done is establish our knowledge of these things. We know these things, which is to say that we are quite sure that they are true. But we are not certain. We can never be certain.

 

Agreed.  Also, what you say here intersects with almost uncanny accuracy with what I had planned to delve into about David Hume's thoughts on this, in the Failed Cosmology thread.

 

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Recall that on my account, knowledge reduces to firmly held belief. I have no qualms about saying that I know that the Earth revolves around the sun. There's all kinds of good, scientific evidence to support this belief. So it is very well justified. But it's still just a firmly held belief. I think it has to be this way. Suppose for the moment that it actually is ontologically true that the Earth revolves around the sun. What this means is that it needs to be true regardless of our knowledge of it's truth. Moreover, it would also need to have been true in previous eras, when basically everyone who knew anything knew that the sun revolved around the Earth. Tycho Brahe was a pretty serious scientist, but he managed to produce what we now know to be a more or less entirely incorrect model of the solar system. This seems to entail exactly what I've been arguing so far: that science produces knowledge, but not necessarily truth, and also, that today's knowledge is quite often tomorrow's misapprehension.

 

And this agrees with the uncertainty of knowledge, your very point above.

 

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So where does this leave us? Well, we've seen that science generates knowledge of ontological truth, but we haven't looked in detail at how it does this. And this is where I think things get really interesting. Previously on these boards I've written that I think science offers epistemically objective descriptions of an ontologically objective reality. What I mean by this is that science builds models of the universe. The models make all kinds of ontological truth claims, because they are attempts to describe the natural world. But the models themselves are constructed by humans. They operate according to assumptions we make, and lead to conclusions which are based on both observation and inference. I think it is correct to say that the models can establish formal truth, which I view as a kind of epistemic truth (there's quite a bit more that I want to say about formal truth as a type of epistemic truth, but I think it's tangential for now, so I'll come back to it later if it is of interest), but they do not establish ontological truth.

 

Agreed.  If ontological truths are absolute, then the inherent uncertainty of epistemic truths would seem to indicate that things epistemic cannot establish things ontological.  The ephemeral cannot generate the permanent.

 

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Take, for example, the Hawking-Penrose Theorems. On their assumptions, it follows logically that the universe began in a singularity. So on their model, it is formally true that the universe began in a singularity. It's mathematically provable. The problem is, their model doesn't fit the observational data, so something is wrong with their assumptions. It doesn't seem to be ontologically true that the universe began in a singularity. Nevertheless, whether it did or not is a matter of ontological truth. Hawking and Penrose offered a particular model, and on that model it was true. And for a while, everyone knew that the universe began to exist. Nowadays, we can't really claim to know this anymore, because the model that Hawking and Penrose offered is outdated. This is what science does all the time. It builds models of the universe which establish formal (read: epistemic) truths. It's very easy to confuse these with ontological truths, but that is a disastrous mistake, on my view.

 

Yes, yes and yes again.  

 

Now for a confession, Disillusioned.  I much prefer the neatness and cleanness of hard science data to the slipperiness of these philosophical concepts.  But, I know that these concepts are of great importance.  So, like a teenager who tries to get out of doing the chores, I've found myself putting off dealing with them.  You can even see evidence of my reluctance in the way I've suggested that you and Josh and I put off dealing with the philosophical aspects of WLC's apologetics until after we've tackled the hard science. 

 

Mea culpa!  

 

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Neils Bohr said that "It is wrong to think that the task of physics is to find out how Nature is. Physics concerns what we say about Nature." I think this is basically the same thing that I'm trying to say: physics, and science in general, concerns our knowledge, not truth per se. Where science does concern truth directly, the truth in question is formal, or epistemic, rather than ontological in nature.

 

There's a lot more that can be said about this, but for now I want to move to the questions you actually asked.

 

Agreed.  Bohr can be a bitter pill for some to digest because there's still a widely prevailing, but incorrect, view that science tells us exactly how nature is.  No.  Science provides a tentative, incomplete and provisional working description of how we think nature is.

 

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I hope that what I wrote above clarifies this somewhat. I think that science in general can generate ontological knowledge, but it's important to note that knowledge is not certain. For fields of science like astronomy and cosmology which rely more heavily on assumption and inference than do some other fields, our level of certainty in the ontological knowledge we obtain must be lessened. This is why I tend to take novel cosmological theories with rather large grains of salt.

 

Agreed.  I might add that particle physics relies just as heavily upon assumption and inference, if not more so.  The Higgs boson was not actually detected, per se.  Instead, a number of events and interactions were detected by the LHC and when these were matched against simulations of how the Higgs was expected to behave, there was a high degree of correspondence.  When the scientists were satisfied that the level of confidence was at 5 sigma, they announced the detection.

 

It's also sobering to note that the complete range of decay products from the interactions couldn't be fully detected.  This was known before the machine was even built.  The ingenious solution to that problem was to precisely calculate the amount of energy going in to a collision and then subtract the amount being detected leaving the event.  The energies of the detected muons, photons, W and Z particles, etc. was known and when all of these had been accounted for, the shortfall equaled the predicted energy of the undetectable decay products.  Perform that procedure often enough, eliminate as many variables as possible, account for human error and if what you have left matches what you were looking for, then (even though you couldn't detect 100% of the resulting particles) you can say that you've detected the Higgs.

 

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What I would say is that there is clearly a realm which is directly accessible to our senses, and this allows us to claim ontological knowledge about this realm with much more surety than we can claim such knowledge about cosmology, for example. I can claim with quite a lot of certainty that granite is hard. For all intents and purposes, I know this for sure. I can directly verify it. The only thing keeping me from claiming direct access to ontological truth in this case is the possibility that I might not be able to trust my senses. But on the assumption that I can (which seems reasonable), it follows that granite is hard. So I know this with much more certainty than I know even that the Earth revolves around the sun, which I'm pretty damn sure about.

 

The above agrees with what Hume's had to say about the difference between Relations of Ideas and Matters of Fact. (More about this to follow, I think.  The time seems right.)

 

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With respect to the piano and the black hole, I want to say that the existence of these things and the ontological truths associated with them are entirely independent of our sense experiences. This is the mark of ontological truth, after all: it's true irrespective of what we think about it, or even whether we think about it, or whether we can think about it. So yes, ontological truths cannot be directly linked to our senses. Using our senses to gain knowledge is a primitive way of doing science. And science, as we've seen, doesn't establish ontological truth, just knowledge.

 

 

I can't fault your logic here, Disillusioned.  I find myself agreeing with you all the way.  Mostly because I've had to cover similar ground in the five years I spent researching, checking and testing WLC's claims about singularity theory.  All I would say about that period is that I felt much more certain about the science aspects I covered than the epistemic/philosophical aspects.  But now might be the very time for me to engage more fully with the latter.

 

That being so, I'll follow this post with another that contains some material that i believe is very relevant.

 

Thank you.

 

Walter.

 

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Disillusioned,

 

Here are two excerpts from Julian Baggini's book, A Short History of Truth: Consolations for the Post-Truth World.

 

Chapter 5, Empirical Truths.

 

Pages 54 / 56.

 

Etymologically, empirical means ‘from experience’, and experience seems to be telling us that an empirical approach leaves us with uncertainty, rather than knowledge.  Far from being a weakness, however, the open-endedness of empirical inquiry is actually its strength.  David Hume made this point wonderfully when he observed that ‘all the objects of human reason or enquiry may naturally be divided into two kinds, to wit, Relations of Ideas, and Matters of Fact.’

 

Relations of ideas concern truths of maths, geometry and pure logic.  As we have seen, such truths are, in effect, true by definition, but they tell us nothing about the real world.  Matters of fact, in contrast, cannot be established by pure logic.  That also means they cannot be established with 100 per cent certainty.  ‘The contrary of every matter of fact is still possible,’ warned Hume.  ‘That the sun will not rise tomorrow is no less intelligible a proposition, and implies no more contradiction than the affirmation, that it will rise.’

 

Indeed, we can easily imagine circumstances in which we would have to accept that the sun is unlikely to rise tomorrow, such as if a massive asteroid were about to hit the Earth.

A lack of certainty is therefore part of the deal with empirical truth.  We need to give up on it in order to take up the possibility of knowledge of the world.  Absolute certainties can only be obtained about purely conceptual matters, such as axioms of mathematics and laws of logic.

 

If we want to know about the world then there is potentially no end of discoveries – for ourselves or the entire human race – that might force us to alter our opinions.  (That’s why despite my best efforts, it is almost inevitable that I have unintentionally stated at least one falsehood in this book.)  What we hold to be true is constantly open to being tested, which makes the truths that pass the test more reliable.  The strength of empirical truth resides in the fact that it is always open to scrutiny, revision and rejection.

 

Chapter 4, Reasoned Truths.

 

P 44.

 

In modern philosophy, the two great representatives of this optimistic ‘rationalist’ tradition were Rene Descartes and Baruch Spinoza.  Both were impressed by the ways in which proofs were generated in mathematics and geometry.  They thought that with due care and diligence, it would be possible to replicate this precision in all areas of human knowledge.

 

‘Those long chains composed of very simple and easy reasonings, which geometers customarily use to arrive at their most difficult demonstrations,’ wrote Descartes, ‘had given me occasion to suppose that all the things which come within the scope of human knowledge are interconnected in the same way.’

 

David Hume worked out the basic flaw in rationalism back in the eighteenth century.  All pure reason could analyse was the relationship between concepts.  But this tells us nothing about the relationship between the things in the world those concepts relate to.

 

‘1 + 1 = 2’ is a truth about numbers, but says nothing about what happens when you put two physical things together, where they might annihilate each other, merge into one, or multiply.

 

 

I lighted upon these Disillusioned because they seemed to be telling me something important about the way WLC was presenting H & P's entirely mathematical 'proof' of singularity theory as a Matter of Fact.  As a brute fact of reality.  As an ontological truth. 

 

This cannot be so!   Singularity theory is a construct of human endeavour and so MUST BE an epistemic truth. 

 

Thank you.

 

Walter.

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For good measure Disillusioned, here are links to sites and articles I thought would be relevant to our examination of WLC's claims about H & P's 'proof'.  Given what's gone between us here in this thread, I think it's now right for me to share this info with you, for your consideration.

 

https://www.physicsforums.com/insights/proofs-in-mathematics/

https://www.nsta.org/publications/news/story.aspx?id=52402

https://oregonstate.edu/instruction/bb317/scientifictheories.html

 

https://en.wikipedia.org/wiki/Mathematical_proof

https://undsci.berkeley.edu/teaching/misconceptions.php

https://www.birmingham.ac.uk/Documents/college-eps/college/stem/Student-Summer-Education-Internships/Proof-and-Reasoning.pdf

 

Thank you.

 

Walter.

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Walter,

 

Thanks for a very thorough and interesting couple of posts. I just have a few brief remarks for now, but I will have more to say over the next few days. 

 

On 11/12/2019 at 10:14 AM, WalterP said:

 

Etymologically, empirical means ‘from experience’, and experience seems to be telling us that an empirical approach leaves us with uncertainty, rather than knowledge.  Far from being a weakness, however, the open-endedness of empirical inquiry is actually its strength.  David Hume made this point wonderfully when he observed that ‘all the objects of human reason or enquiry may naturally be divided into two kinds, to wit, Relations of Ideas, and Matters of Fact.’

 

Relations of ideas concern truths of maths, geometry and pure logic.  As we have seen, such truths are, in effect, true by definition, but they tell us nothing about the real world.  Matters of fact, in contrast, cannot be established by pure logic.  That also means they cannot be established with 100 per cent certainty.  ‘The contrary of every matter of fact is still possible,’ warned Hume.  ‘That the sun will not rise tomorrow is no less intelligible a proposition, and implies no more contradiction than the affirmation, that it will rise.’

 

Indeed, we can easily imagine circumstances in which we would have to accept that the sun is unlikely to rise tomorrow, such as if a massive asteroid were about to hit the Earth.

A lack of certainty is therefore part of the deal with empirical truth.  We need to give up on it in order to take up the possibility of knowledge of the world.  Absolute certainties can only be obtained about purely conceptual matters, such as axioms of mathematics and laws of logic.

 

If we want to know about the world then there is potentially no end of discoveries – for ourselves or the entire human race – that might force us to alter our opinions.  (That’s why despite my best efforts, it is almost inevitable that I have unintentionally stated at least one falsehood in this book.)  What we hold to be true is constantly open to being tested, which makes the truths that pass the test more reliable.  The strength of empirical truth resides in the fact that it is always open to scrutiny, revision and rejection.

 

This seems like an interesting book. I might need to give it a read. 

 

This particular passage makes mention, among othe things, of Hume's distinction between matters of fact and relations of ideas. If I recall correctly, it was Hume's writings on these (and other) topics that played a key role in inspiring Kant to formulate some of his most crucial ideas. In particular, it seems to me that there are stong parallels between Hume's "relations of ideas" and Kant's "analytic judgements" as well as between Hume's "matters of fact" and Kant's "synthetic judgements". Kant and Hume are both philosophers for whom I have a great deal of respect, even if I am still only barely beginning to scratch at the surface of their ideas.

 

One thing that is interesting to me at the moment is that it seems that both Kant and Hume, as I currently understand them, tried to ground philosophy in epistemology rather than ontology. I think these things go hand in hand,  but ontology comes first. This is why I start with basic assumptions about nature, use these to formulate an idea of truth, and try to build a concept of knowledge from there.

 

I have more to say about this, but I'm pressed for time at the moment, so I'll have to come back to it. 

 

On 11/12/2019 at 10:14 AM, WalterP said:

 

In modern philosophy, the two great representatives of this optimistic ‘rationalist’ tradition were Rene Descartes and Baruch Spinoza.  Both were impressed by the ways in which proofs were generated in mathematics and geometry.  They thought that with due care and diligence, it would be possible to replicate this precision in all areas of human knowledge.

 

‘Those long chains composed of very simple and easy reasonings, which geometers customarily use to arrive at their most difficult demonstrations,’ wrote Descartes, ‘had given me occasion to suppose that all the things which come within the scope of human knowledge are interconnected in the same way.’

 

David Hume worked out the basic flaw in rationalism back in the eighteenth century.  All pure reason could analyse was the relationship between concepts.  But this tells us nothing about the relationship between the things in the world those concepts relate to.

 

‘1 + 1 = 2’ is a truth about numbers, but says nothing about what happens when you put two physical things together, where they might annihilate each other, merge into one, or multiply.

 

This is an excellent quotation, and it clearly illustrates one of the reasons why I'm a great admirer of Hume. Descartes, I think, for all his brilliance, made a number of critical errors, and Hume went a long way towards correcting some of those errors.

 

On 11/12/2019 at 10:14 AM, WalterP said:

 

I lighted upon these Disillusioned because they seemed to be telling me something important about the way WLC was presenting H & P's entirely mathematical 'proof' of singularity theory as a Matter of Fact.  As a brute fact of reality.  As an ontological truth. 

 

This cannot be so!   Singularity theory is a construct of human endeavour and so MUST BE an epistemic truth. 

 

Agreed.

 

I want to look more at the relationship between Hume's 'matters of fact' and my 'ontological truths' , as well as what you've pointed out here about the H-P theorems, and the larger issue of formal truths in general, and their relation to science. I'm hoping I'll be able to get around to writing a more rigorous response in the next few days.

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Since @WalterP brought it up, and since it has direct bearing on the main topics of this thread, I want to spend a bit more time exploring the connections between Hume’s matters of fact and relations of ideas, and my ontological and epistemic truths, and the connections that all of these ideas have to science.

 

Hume’s notion of “relations of ideas” corresponds roughly to our knowledge of statements which are logically necessary. Mathematical truths, such as “3+2=5”, and tautological sentences such as “all bachelors are unmarried” are typical examples of relations of ideas. Such things cannot be asserted to be false without giving rise to contradictions. As such, we may claim a priori knowledge of these types of claims.

 

By contrast, matters of fact concern knowledge that we gain from experience. That the sun rose this morning is a matter of fact, as is the fact that it set last night. Matters of fact cannot be shown to be true or false using pure reason; experience is necessary. Moreover, denial of a matter of fact need not lead to a logical contradiction. If you say it is day, I can say it is night. One of us is wrong, but either way, there is no huge logical crisis. We can only know who is right through experience. Thus, we may only claim a posteriori knowledge of these types of claims.

 

There is a clear similarity, I think, between my notion of ontological truth and Hume’s notion of matters of fact. Both are clearly referring to the natural world, in general. There is an important difference though: matters of fact are what I would refer to as knowledge claims which are often about ontological truths. They are not ontological truths themselves.

On my view, there are some things which are actually ontologically true. Real brute facts about the world. The problem is, whenever we try to give examples of such things, we can only speak from our experiences. So when I say “the earth is round”, or even “granite is hard”, I am making an ontological truth claim, and my contention is that I know that each of these statements is actually ontologically true. This is roughly equivalent to saying that I claim each thing to be a “matter of fact”. Notice, however, that my claim to know that each statement is true does not in any way necessitate that it actually is. The history of science is littered with things that people used to know, which we know to be incorrect. This does not necessarily mean that any ontological truths have changed. Knowledge claims, on my account, concern what we believe about ontological truths. So it isn’t quite correct to draw a direct equivalence between matters of fact and ontological truths. Rather, matters of fact are knowledge claims. They are often about ontological truths, but they don’t always have to be, as I’ll explain in a moment, and they are not ontological truths themselves.

 

Relations of ideas, on the other hand, are most similar to what I have called formal truths. Recall that I am treating formal truths as a subset of epistemic truths. Formal truths can actually be shown to be true logically and necessarily (using a formal language if required). Relations of ideas seem to me to be basically the same as this. These are things which are either true by definition (for example, “all bachelors are unmarried”) or which follow directly deductively from axioms (for example, “3+2=5”). Thus, relations of ideas concern a type of epistemic truth, namely, formal truth, but I do not think that they account for all epistemic truths. Take the case of the statement “money is valuable”. This is an epistemically true statement. However, our knowledge that it is true comes from experience. Thus, when we claim to know that money is valuable, we are claiming this to be a matter of fact. What I think is really interesting here is that the truth of the statement “money is valuable” derives from our knowledge that money is valuable (this is what it means for it to be epistemically true), but our knowledge of the truth of the statement “money is valuable” derives from experience (when we try to use money, we find that it has value). Each experience of money’s value reinforces our belief that money is valuable, and we end up in a self-reinforcing cycle. This is not a problem logically, because no one is claiming that it is necessarily true that money is valuable. It just happens to be the case. It’s a matter of fact, but it’s a matter of fact which corresponds to an epistemic truth. This is another reason why I think we can’t draw a direct line between Hume’s matters of fact and my ontological truths. Some matters of fact refer to epistemic truths.

 

Alright, now back to science for a moment. When we do science, it seems to me to be fairly clear that we are reasoning on the basis of observation and experience. Thus, scientific knowledge is a posteriori in nature. Science aims at matters of fact. Where things get murky is that when we move into more sophisticated science, we end up building (sometimes formal) models which we then use to make predictions about what we should see. We begin to reason inductively. On the basis of what we have observed, together with some assumptions, we make predictions about we expect to observe. This is the essence of inductive reasoning. Hume is famous for pointing out that there is a problem with induction: we have no logical reason for thinking that our experiences of the past should be representative of the future. It simply doesn’t follow that because the sun has risen every morning of my life, it will therefore rise tomorrow. Nevertheless, we all feel fairly confident in claiming to know that it will. This is a very famous philosophical problem which we can spend some more time looking at if it is of interest, but for now I just want to say that I think this is basically correct, but it isn’t really a problem. We can’t help but reason inductively. It’s the only card we’ve got to play. And it seems to work pretty damn well, so we carry on.

 

Where scientists sometimes run into trouble is when they lose track of the fact that things which have been shown to be true on a particular model are not necessarily actually ontologically true. The Hawking-Penrose theorems are good examples here. These are formal truths (ie, relations of ideas), but the model under which they are provable is out-dated. So they can’t be said to be matters of fact, let alone to actually be ontologically true. This is where WLC makes one of his many fatal errors.

 

There is a lot more that can be said about this, but that’s probably enough for one post.

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