Robert Williams on Decision Making Under Indeterminacy

Summary

Philosophy Bites Podcast Summary

Episode: Robert Williams on Decision Making Under Indeterminacy
Hosts: David Edmonds and Nigel Warburton
Guest: Robert Williams
Date: January 9, 2025

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Episode Overview

This episode explores the philosophical distinction between uncertainty and indeterminacy, focusing on the implications of indeterminacy for rational decision-making. Robert Williams, a philosopher known for work on logic, vagueness, and metaphysics, discusses how indeterminacy challenges our concepts of truth, logic, and ethical decision-making, especially in cases where facts seem to lack determinate answers.

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Key Discussion Points and Insights

1. Uncertainty vs. Indeterminacy

• Uncertainty:
  • Results from ignorance; there is a fact of the matter, but we do not know it.
  • Example: Not knowing whether the bank will invest ethically ([00:52]).
• Indeterminacy:
  • Arises from vagueness or lack of definite facts in the world.
  • Example: The "heap" problem—when does a collection of stones become a heap? Some cases are borderline, and it's objectively undetermined if they qualify ([01:21], [01:54]).
• Quote:
  • Robert Williams: “Those are cases where it may be indeterminate whether what I’ve got is a heap or not... there’s no fact of the matter about whether they’re yellow or not.” ([01:54])

2. Philosophical Positions on Indeterminacy

• Uncertainty Reductionism (Timothy Williamson):
  • All cases are about ignorance, not true indeterminacy; there's always a fact of the matter ([03:09]).
  • Quote:
    • Williams: “He’s saying, well, you thought there was this interesting category...in fact there’s no such phenomenon. All there is is ignorance.” ([03:09])
  • Even with vague concepts, there must be a "magic" cutoff point (e.g., the specific stone that makes a heap) ([03:50]).
• Motivations for Classical Logic:
  • Simplicity and theoretical success of classical logic drive skepticism about indeterminacy ([04:31]).
  • All meaningful statements must be either true or false—no in-betweens ([05:12], [05:45]).
  • Quote:
    • Williams: “[Classical logic]...for any proposition or any meaningful sentence, those things would either be true or false.” ([05:45])

3. Ethical Decision Making under Indeterminacy

• Applying Uncertainty Reductionism:
  • Ethical borderline cases (e.g., the status of a fetus as a person) are treated as uncertain, not indeterminate ([06:30], [06:51]).
  • Quote:
    • Warburton: “You might say that there is a fact of the matter...it’s just you don’t happen to know the fact.” ([07:54])
• Accepting Genuine Indeterminacy:
  • Suggests there are no clear facts of the matter in certain moral contexts.
  • Raises the question: How should we act when it's not simply that we lack knowledge, but the world itself is indeterminate? ([08:14])
  • Williams explores the idea of degrees of truth as a possible response ([08:14]).
    • Example: Something can be “0.75 yellow” in a vague color case.
    • This challenges how we form rational attitudes and decisions ([08:49], [09:35]).

4. Theories of Truth and Alternatives to Classical Logic

• Degrees of Truth:
  • Logic must be revised to account for statements that are true to some degree ([08:14], [09:58]).
  • This introduces complexity and potential challenges to well-established theories ([10:22]).
  • Quote:
    • Williams: “If you’ve got something intermediate between truth and falsity...what should I do in this case? What’s the correct attitude to have when something is kind of halfway between?” ([09:35])
• Alternative Accounts of Indeterminacy:
  • Some try to stay as close as possible to classical logic but admit multiple plausible interpretations due to linguistic openness ([11:32]-[14:30]).
  • Borderline statements occur because our conventions leave gaps in meaning with multiple valid precise interpretations ([12:45]).
  • Even if every interpretation is classical, their collective disagreement creates indeterminacy at the meta-level ([13:31]).
  • Quote:
    • Williams: “[T]here may be more than one [interpretation]…after you’ve...filtered out all the ones that contradict all the paradigm cases that we’ve got, all the settled linguistic conventions.” ([12:56])
    • "It’s a fact that the colour patch is yellow or not yellow, despite being borderline." ([14:20])

5. Philosophical Progress and Open Questions

• Williams suggests we are early in developing adequate rival theories to the classical, uncertainty-based view ([15:32]).
• Quote:
  • Williams: “We’re nearer the beginning than the end…what has to be done is to build up the rivals to the uncertainty reductionist view…so that you can actually measure their virtues and vices…” ([15:32])

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Notable Quotes

• “Those are cases where it may be indeterminate whether what I’ve got is a heap or not.” — Robert Williams ([01:54])
• “He’s saying...in fact there’s no such phenomenon. All there is is ignorance.” — Robert Williams on Timothy Williamson ([03:09])
• “If you’ve got something intermediate between truth and falsity...what should I do in this case?” — Robert Williams ([09:35])
• “It’s a fact that the colour patch is yellow or not yellow, despite being borderline.” — Robert Williams ([14:20])
• “We’re nearer the beginning than the end…what has to be done is to build up the rivals to the uncertainty reductionist view…” — Robert Williams ([15:32])

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Key Timestamps

• 00:52 – Distinction between uncertainty and indeterminacy introduced
• 01:54 – Examples of indeterminacy: heap, color spectrum
• 03:09 – Williamson’s view: indeterminacy as ignorance
• 05:45 – Commitment of classical logic: bivalence (true or false)
• 06:51 – Moral indeterminacy: personhood and ethics
• 08:14 – Williams introduces degrees of truth
• 09:35 – Rational attitudes in presence of graded truth
• 12:45 – Multiple classical interpretations and linguistic conventions
• 14:20 – The fact of a disjunction being true even if each component is unclear
• 15:32 – Williams on the need for more development in theories of indeterminacy

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Summary

This episode delves into complex philosophical territory, clearly distinguishing between uncertainty (ignorance about determinate facts) and indeterminacy (the world itself not providing a definite answer). It examines foundational debates between the classical, reductionist theories (as articulated by Timothy Williamson) and emerging alternatives which accept indeterminacy's reality, including approaches based on degrees of truth. The discussion also probes the ethical implications of indeterminacy in real-world decision-making and highlights significant unresolved challenges for philosophers seeking to develop robust theories accommodating vagueness and indeterminacy. Williams concludes that much work remains to be done, situating philosophical inquiry on this topic at its beginning stages.

Transcript

[A]

This is Philosophy Bytes with me, David.

[B]

Edmonds and me, Nigel Warburton.

[A]

Philosophy Bites is available at www.philosophybytes.com. there's a difference between uncertainty and indeterminacy. As Robert Williams explains the latter, indeterminacy poses the deeper problems, for it seems to suggest that there are cases where we can't apply in any conventional sense the concepts of true and false. This episode of Philosophy Bites is made in association with Vagueness and Ethics, a research project funded by the European Commission and based at Uppsala University in Sweden.

[B]

Robert Williams, welcome to Philosophy Bites.

[C]

Very glad to be here, Nigel.

[B]

The topic we're going to focus on today is decision making under indeterminacy. Now, is indeterminacy just when you don't know something?

[C]

I think it's distinct from that. Uncertainty will be the sort of situation, like if we're thinking about a decision situation. You know, I can decide whether to put my money in the bank or not put it in the bank. And if I'm doing that under uncertainty, it might be because, say, I don't know what the bank's going to do with the money, don't know whether they're going to invest it in an ethical way or an unethical way. And that ignorance of what's going to happen combined with a thought that there is a fact of the matter out there about what's going to happen. It's just my shortcoming that's preventing me knowing it. That's the uncertainty place. And there's a question about what are the right rational rules to guide our decision making under uncertainty. But indeterminacy will be a different thing. Let's maybe introduce a few examples of it. So lots of these examples are kind of quite mundane and we'll get to more interesting ones later. But classic example would be indiscemity associated with vagueness. One stone lying on its own doesn't make a heap. You add another one on, you've still not got a heap. If you've piled up a million of them, then you've got a heap. Think about the kind of intermediate cases where you're beyond the case where you've clearly not got a heap, but you're not at the stage where you've clearly got a heap. Those kind of borderline cases in the middle of it. Those are cases where it may be indeterminate whether what I've got is a heap or not. The color case would be another case of this. So, you know, we continuously change the color that appears on our screen from a pure Yellow to a pure red. Some of these changes are indiscriminable. Right. So you can't tell the difference just by looking. But in those kind of cases, it's very hard to think that there's a kind of last case where it's true that it's yellow in the first case where it's true that it's not yellow. You want to think that there's some cases which out there in the world objectively have a question mark over them, that there's no fact of the matter about whether they're yellow or not.

[B]

Well, there is this way of looking at determinacy that some people have taken that basically makes it come out as a kind of uncertainty. It's just there is a right answer about how many stones make a heap or how many hairs you have to have on your head not to be bald. It's just we don't know what the right answer is.

[C]

Yeah, that's right. So maybe most famously put forward by Timothy Williamson in recent years, and the way I think about this, Timothy Williamson wouldn't be happy about me characterizing this way, but I think of that as a kind of eliminativism about the phenomenon. The way that I think about this, he's saying, well, you thought there was this interesting category, these cases where there's no fact of the matter, these cases where it's indeterminate whether or not something's yellow, that in fact there's no such phenomenon. All there is is ignorance.

[B]

Would you say the same about a pile of stones? That there's this. There's one stone that you put on that changes it from something that wasn't a heap into it being a heap.

[C]

Yeah, exactly. He's going to say that there's a particular, if you like, magic stone, that when you add it to the heap, turned it from it, a non heap into a heap. And it's very hard to imagine yourself identifying which that stone was. But that's grist to his mill in the sense that he'd say, yeah, I can explain to you in independent terms why you'd be unutterably, irredeemably ignorant of that fact. For him, it's all about ignorance and nothing about whether the categories in the world are themselves objectively fuzzy.

[B]

And what's his motivation for taking that counterintuitive position?

[C]

So, as in a lot of his work, he's very interested in having an overall theory that has worked in the past and that we understand really well and that has many theoretical virtues like simplicity and power and the rest of it. And he thinks that when it comes to matters of logic and theory of truth, then this classical package that we've inherited over the decades, a lot of it in the 20th century, that a classical package is just kind of the best candidate out there. That classical package says, among other things, that if you take any meaningful predicate like red or heap, that for everything, it'll either be a heap or not a heap for everything. It's either red or not. Read. It says when it comes to truth, that for any proposition or anything meaningful sentence, those things would either be true or false. And if we think that indeterminacy and the idea of indeterminacy in the world conflicts with either of those two theoretical claims, what we'd have to go is go back, ditch our successful theory, and construct, as it were, from the ground up, a rival. And then we'd have loads of work to do, because all the good things that were done by the classical theory over the last decades would have to be rebuilt and done again with this new hypothetical rival theory.

[B]

So it's logic, classical logic, driving it to some extent. If you were to apply that style of thinking to moral thinking about indeterminacy, am I right in saying it would turn what looks to be indeterminacy into just further cases of uncertainty? So there may be an indeterminate point at which a fetus becomes a person. Let's say we know that there is a stage where it's not a person, and then we know a stage that we consider it as a person, even if that stage is after it's been born. Let's say there's this continuum and we have to make a decision about where the cutoff point is. On his view, we make a decision, but we're just ignorant of where it really is. Whereas if you think that indeterminacy actually does occur, there may not be a straightforward right answer about where the cutoff point is.

[C]

Yeah, I think that's right. So let's take a case which matters of life and death turn. There's a house. In order to stop fire spreading down a street, we have to blow up this house. We might be uncertain whether there's somebody still left inside it. And that's a matter of ordinary uncertainty. Right? It's. There's a fact of the matter about whether somebody's inside it. But, you know, maybe to save other lives, the best thing to do would be to blow up the house, or maybe it wouldn't be, but it's not worth that risk. So that's the kind of life or death decision making under uncertainty. And then you think about cases like the case you brought up. You know, if you thought, well, is this just a cluster of cells or is this a person with kind of moral rights and on the view where indeterminacy in whether that cluster of cells counts as a person is just a matter of uncertainty, then the decision about whether it's permissible to destroy that cluster of cells would be analogous to knocking down this house, being uncertain about whether there's somebody inside it.

[B]

So if you take the kind of line that Timothy Williamson has done and apply it in a moral case, you might say that there is a fact of the matter, if you believe in moral facts about whether someone's a person or not, it's just you don't happen to know the fact. What would you say from the point of view of somebody who believes that there is genuine indeterminacy in the world?

[C]

Yeah. So one approach to these questions of no fact of the matter that some people have explored and that I've explored myself in some of my work, are thinking that rather than there being a kind of binary of truth and falsity, you've got degrees of truth. So for any kind of intermediate degree between 1 and 0, like 0.75, there's a property of being true to degree 0.75. When you've got a case of one of these intermediate color patches, for example, something intermediate between red and yellow, then you might say, well, this kind of yellowish patch is only 0.75 yellow, for example. If you've got that conception of what's truth going there, number one, you're going to have to do something different at the level of the logic to fit with that truth. So you might have a different system of reasoning that comes out, and that's part of the package deal that you'll have to build up. But another thing you have to do is say something different about how those properties, these truth properties, fit with our rational attitudes and our rational decision making. If you've got truth and falsity and you're thinking about what the correct attitudes are to have them, ideally you want to believe the true things and disbelieve the false things. Now, if you've got something intermediate between truth and falsity, the question is like, okay, what should I do in this case? What's the correct attitude to have when something is kind of halfway between? So one thing you need to start doing is revising your account of what correct attitudes are and how they fit with these properties. And that's going to have knock on consequences then for what happens when you combine beliefs, desires and what decisions they recommend.

[B]

If I've understood you correctly, you're saying that you've explored the idea that things can be true to a greater or lesser extent. It's like more true, but they're not necessarily true. True, 100% true. Whereas the classical logic theory says that every meaningful proposition is either true or false. That seems intuitively appealing to somebody not immersed in the world of logic. But why would logicians be worried about that?

[C]

I mean, one thing is it just doesn't feature in their best theories. So if you remember what we said about Williamson earlier, he was saying, look, we've got a standing theory that's been presupposed by all these guys and that's been really successful. And now what you're doing is knocking out a bit of it, the bit that is the theory of truth that says everything is either true and false. And you're replacing it by saying, well, we'll have rather than those two truth values, we might have infinitely many. It's the thought that for this local problem you might think about vagueness. We're going and just kind of knocking out one piece kind of at the foundations of successful theory. And that looks like something that you don't want to do without checking that it doesn't make broader structural difficulties for the whole edifice.

[B]

Okay, that's one way out. You can have degrees of truth and that's going to have its own complications about how you play that out and discover those degrees of truth and how you assign particular values to various statements about the world. Are there other ways of explaining indeterminacy which don't go down the line of saying it's really just another kind of uncertainty.

[C]

So the other thing that you might do, which is try to preserve that classical structure as much as possible and really bring a lot of scrutiny to the question about whether you're committed to thinking there's facts of the matter about whether something's read or not read, whether something's a person or not a person, just by saying that statements about that are either true or false and there's no intermediate status. Think about it this way. There's a lot of people who think that it's compatible with thinking there's no fact of the matter about whether this bundle of cells is a person or not, with saying, well, it either is a person or isn't a person. They say, well, it's either a person or Not a person, but it's indeterminate, which they've got themselves comfortable with saying that, and then they might give a revisionary theory of truth on top of that. But if you've gone that far, if you think that we can be realist about there being no fact of the matter about whether the bundle of servants is a person, while still admitting it's either person or not a person, doesn't seem all that much of a stretch to say, well, it can still be indeterminate. There's no fact of the matter about whether it's a person, even though it's either true or false, that it's a person. That is, the properties of truth and falsity themselves might be indeterminate. There may be no facts of the matter whether this thing is true or false. So the thought that people are having is that you can say this disjunction, this complex statement, this bundle of selves, it either is a person or isn't a person, without admitting there's a fact of the matter whether it's a person. So the one way that some people think about the colour case is the following. We've already, as a matter of linguistic conventions, settled the clear cases of yellow and the clear cases of not yellow in the middle, where the borderline cases are going to live. That's an area where our linguistic conventions have left things pretty open. Now imagine that what we've got to play with in terms of the interpretations of our language are all classical interpretations, the sort of thing that Williamson gives the thumbs up to. But because of this sort of openness in our conventions, there may be more than one of those that are still in the running after you've kind of filtered out all the ones that contradict all the paradigm cases that we've got, all the settled linguistic conventions. So maybe among the things that are still in the running, the interpretations of our language still in the running, is one that puts the boundary between yellow and non yellow early in the series, and one that puts the boundary between yellow and non level late in the series. So that's the view of kind of borderline ness, that it would be a matter of these interpretations that are still in the running disagreeing between themselves over the classification of one of these middle cases. And that's one view that's out there about what it takes for there to be no fact of the matter about whether this patch is yellow, that these kind of interpretations still in the running disagree among themselves over its classification. But notice, each of these classifications was a classical interpretation and so it said the same thing about all the things that classical interpretations agree on. One thing that all classical interpretations agree on is that it's yellow or not yellow. That gets to be true for different reasons on the two cases. On one, because the patch in question counted as not yellow. For the other one it counted as yellow, but. But both of them at the level of it's yellow or not yellow. Agreed. And so this overall theory says, look, it's a fact that the colour patch is yellow or not yellow, despite being borderline.

[B]

Do you feel that, having investigated this quite deeply, that you're anywhere nearer to resolving the issue, or are we just at the beginning?

[C]

So I guess my view will be that we're nearer the beginning than the end of that kind of project, and that what has to be done is to build up the rivals to the uncertainty reductionist view that we've been exploring, so that they're kind of complete enough theories that you can actually measure their virtues and vices against the virtues and vices of the kind of eliminating no fact of the matter and doing everything with ordinary uncertainty.

[B]

Robert Williams, thank you very much.

[C]

Thank you very much.

[A]

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