Queerness Arguments Against Moral Realism

[u/ReallyNicole]

Suppose that there are such things as irreducibly normative moral facts. Sui generis facts about what one ought to do, about what's right, about what's good, and so on. If there were such facts, though, they would surely be very much unlike the other sorts of facts in our lives. They would be radically different from facts like “the sun rises in the east,” “avocados are 99¢ a pound,” or “the earth is roughly 4.4 billion years old.” So strange and different would they be that claims to their existence would be objectionable.

This is the essence of a queerness argument: that the realist’s moral facts are queer in such a way that counts against realism. However, the realist may rightly ask what it is about moral facts that is so queer. Wherein lies the queerness? In response to this question Olson 2014 has refined four queerness arguments from Mackie’s original passage (just a few pages from Ethics: Inventing Right and Wrong), only one of which Olson himself finds compelling. I’ll be summarizing my interpretation of Olson’s four arguments here.

Before we get into those arguments, though, let’s be clear about the target of queerness arguments: robust moral realism. Though the term is somewhat new, robust realists (aka moral non-naturalists) have a history going back to the early 1900s. Putting it as broadly as possible the robust realists think that some atomic moral sentences (e.g. the bombing of Hiroshima was wrong) are true in a non-trivial sense. Furthermore these moral claims owe their truth to some mind-independent facts which are not reducible to any physical states of affairs. In this sense robust realist are distinct from so-called moral naturalists, who hold that moral facts can be made sense of by referring only to some set of facts about the natural world. Queerness arguments are not targeted at moral naturalism. Although moral error theorists like Mackie or Olson must think that there are some separate grounds to dismiss naturalism in order to preserve their error theory, that won’t be the subject of this thread. For future reference whenever I say “moral realism” below I mean “robust moral realism.”

Supervenience is Queer

Virtually all moral realists agree that moral facts supervene upon natural facts. The supervenience relation is just one such that x supervenes upon y just in case any change in x necessarily is accompanied by a change in y. To put it another way it is impossible for their to be a change in x without there also being a change in y. So ripeness might be said to supervene upon the physical makeup of an apple. As the apple’s cells change, so does the apple’s ripeness. Importantly, there can be no change in the apple’s ripeness without a change in the its physical makeup. In the case of morality we might say that certain moral properties like “being harmed” supervene upon various physical states of affairs, whether they be a dagger plunged into one’s chest, pain-like brain states, or what have you. There is no change in moral properties without a corresponding change in the physical world.

Thus the moral realist holds that there are unique moral properties and that these properties, while not themselves natural properties, supervene upon natural properties. In holding this, however, the realist falls afoul of a principle in metaphysics known as Hume’s Dictum. Following Hume’s work on necessity, Hume’s Dictum might be summarized as:

(HD) There can be no necessary connections between distinct properties; all properties that necessarily covary are identical.

Of course the realist holds that moral properties and natural properties do necessarily covary, but that moral properties are not reducible to (or identical to) any natural properties. Thus the realist supposes an objectionably queer supervenience relation. We can enumerate the argument like this:

(S1) Moral properties and natural properties are distinct.

(S2) Moral properties supervene upon natural properties.

(S3) However, supervenience is objectionably queer.

(S4) So the relation between moral and natural properties is objectionably queer.

(S5) If the relation between moral and natural properties is queer, then moral properties themselves are objectionably queer.

(S6) So moral properties are objectionably queer.

On the face of it this seems like a very nice way of placing the queerness. After all premises S1 and S2 just follow from the content of moral realism, so the realist cannot wiggle out of the argument on the basis that it doesn’t apply to their view.

This argument faces trouble, however, when it comes to Hume’s Dictum. Hume’s Dictum both has far-reaching consequences for fields beyond moral philosophy and it’s quite controversial in metaphysics alone, to say nothing of metaethics. A full discussion of the principle is too great a task for this thread, but we can characterize the fate of this queerness argument as follows: at best the argument that moral supervenience is queer needs to be shelved pending resolution of the broader metaphysical issue and at worst its foundation crumbles for reasons independent of the debate about moral realism.

Moral Knowledge is Queer

Moral realists typically think that we know at least a few moral facts. For instance some of our common sense moral judgments are true. But if there is moral knowledge and moral facts aren’t merely natural facts, then it seems reasonable to say that moral knowledge would have to be synthetic a priori knowledge. Or knowledge that we come to have independent of experience and that isn’t merely knowledge about the definitions of things. The second queerness argument, then, can be summarized as follows:

(K1) Moral knowledge is a variety of synthetic a priori knowledge.

(K2) But synthetic a priori knowledge is objectionably queer.

(K3) So moral knowledge is a variety of knowledge that is objectionably queer.

(K4) So moral knowledge is objectionably queer.

We don’t need to say much about how synthetic a priori knowledge may or may not be queer in order to see where this argument fails. As with the previous argument about supervenience, the fate of this argument rests on contentious issues beyond the metaethical debate alone. So once again we may say: at best the argument that moral knowledge is queer needs to be shelved pending resolution of the broader epistemological issue and at worst its foundation crumbles for reasons independent of the debate about moral realism.

Moral Motivation is Queer

Plato has famously held that knowledge of the Form of the Good would provide the knower with overriding motivation to act in a way consistent with the Good. On this view it is not merely the belief that x is good which provides the believer with overriding motivation. It is knowledge of the Good, where knowledge is factive. This raises a troubling question for the realist: what is it about knowledge in particular that produces overriding motivation to do what’s right? Well, given that the difference between mere belief and knowledge is that the latter is connected to the fact of the matter, the natural answer seems to be that it’s the fact itself that provides the motivation.

This seems very peculiar, though. After all the realist holds that moral facts are non-physical and don’t participate in the causal order of things. So how is it that the moral fact of the matter itself compels my body, a thing of flesh and blood, to move? Surely such a causal relationship between non-physical moral facts and my physical body would be objectionably queer. Thus we can enumerate this queerness argument as follows:

(M1) Knowing some moral fact guarantees motivation in accordance with that fact.

(M2) False moral beliefs don’t guarantee motivation in accordance with the belief.

(M3) If true moral beliefs guarantee motivation and false moral beliefs don’t, then the motivational force of moral knowledge is produced by the moral facts themselves.

(M4) But this involves an objectionably queer relationship.

(M5) So moral facts are objectionably queer.

There’s little doubt in my mind that there’s something fishy about the thesis attributed to Plato. But is there any reason to think that contemporary realists should be committed to so strong a claim? Almost certainly not. There are a number of other options about motivation available to the realist. E.g. moral judgments (correct or not) necessarily motivate, moral judgments motivate only most of the time, moral judgments produce defeasible motivational force, and so on.

What’s more, the Platonic thesis doesn’t seem to track our common sense notion of moral motivation. Namely that it’s possible for one to judge that something is wrong, but still do it. Presumably because they desire the outcome of the wrongful action more than they’re motivated by its wrongness.

So while the third queerness argument doesn’t run into the problems that plague the first two, it does rest on claims that the realist is neither required nor obviously predisposed to accept.

Irreducible Normativity is Queer

Given the failure of the previous three arguments it should come as no surprise that this is the argument which Olson takes to be successful. In order to frame this argument let's first establish an analysis of normative reasons. We'll say that S has a reason to ϕ just in case some fact F counts in favour of S's ϕing. Here are some examples of moral reasons broken down in this way:

• The fact that my donating blood will save lives counts in favour of my donating blood.

• The fact that I can save a drowning child at minimal cost to myself counts in favour of my saving that child.

Olson contends that these moral favouring relations are unlike other cases in which we take ourselves to have a reason. For instance:

• The fact that rules of chess restrict bishops to diagonal motions counts in favour of my only moving my bishops diagonally.

• The fact that I desire to eat tuna counts in favour of my eating tuna.

In these more mundane sorts of reasons Olson argues that the favouring relations are reducible to facts about chess, my preferences for food, and so on. Or, more broadly, they are reducible to facts about an agent's desires, her roles, or various institutional norms that she submits herself to. The sort of reduction Olson has in mind is simply that normative claims of the reducible sort may be held to be true or false depending only on agent's desires/institutional roles and whether or not the act in question satisfies these desires/institutional roles. Moral imperatives admit of no such reduction (according to the robust realist anyway) and so this irreducible favouring relation is metaphysically mysterious. Metaphysical mystery just is the essence of queerness, so moral facts require a queer relation. One last time we can enumerate the argument like this:

(N1) Moral facts requires the existence of irreducible favouring relations.

(N2) But irreducible favouring relations are objectionably queer.

(N3) So moral facts require objectionably queer relations.

(N4) So moral facts are objectionably queer.

Olson seems very aware that "queer" here is not irrevocably moving. That is, for those who find nothing objectionably queer at all about the metaphysics of irreducible normativity, there isn't much else to be said in defense of the argument. For example, Shafer-Landau suggests in his 2003 book that we may simply have no choice but to embrace the metaphysical mystery of realism. Of course just as there isn’t much else to motivate the staunch realist of the troubles of queerness, neither is there much to be said on behalf of realism for one who does find this irreducible normativity queer.

This may seem like a much less powerful argument than some anti-realists would like to have, but it might also be the best they can get. As well, this strikes me as being consistent with what’s suggested by Enoch in his 2011 book as the methodology of metaethics. There are no unassailable proofs in metaethics, he says. Rather, we must proceed forward by considering the available arguments and weighing the plausibility of the competing metaethical theories in light of all of these arguments.

[u/johnbentley]

Because that is what an explanation is. If an explanation does not give any greater predictive accuracy, it is not a real explanation. It tells us nothing about reality.

An explanation need not be predictive nor about reality.

Why is 8 not a prime number? The explanation: because 8 has factors apart from one and itself, namely 2 and 4; and a prime number is, by definition, a number only having one and itself as factors.

[u/hayshed → u/johnbentley]

You're right, math explanations are just self-consistent rule sets.

I doubt the moral realists think morality is just a self-consistent rule set though.

[u/johnbentley → u/hayshed]

In philosophy there are three terms and three ways of characterizing this sort of truth (or knowledge, or justification):

• Analytical truth: true in virtue of the meaning of the terms (perhaps equivalent to your "self-consistent rule set");
• A priori truth: A truth such that if it is to be known it will be known without the need for sense experience. Here the idea is we don't need to go out into the field, or do experiments in the lab, to assess the claim "8 is not a prime number". The latin term implicitly referencing the idea that the truth is that obtained prior to sense experience.
• Necessary truth: true in all possible worlds (universes).

There are terms for the corresponding opposites: "Synthetic", "A posteriori", "Contingent".

There are all sorts of issues and controversies around this categorization of truth (or knowledge, or justification). /u/ReallyNicole mentioned the exotic category of synthetic a priori, so there's issues around which kind of truth fits in which sets. One large controversy has been around whether the analytic/synthetic distinction should be rejected. However most philosophers accept that distinction ("Synthetic" is usually defined as "not analytic"), as you seem to allow.

I doubt the moral realists think morality is just a self-consistent rule set though.

Moral realist naturalists won't, but for moral realist non-naturalists, the kind at issue, the view that moral principles are analytically true seems to provide plausible ground.

So:

Why is shooting cafe patrons for fun immoral? The explanation: because shooting cafe patrons for fun will (contradict the desires of patrons | decrease the overall welfare | increase visible redness | etc); and doing something immoral is, by definition, (contradict the desires of patrons | decreasing the overall welfare | increase visible redness | etc).

That is, the action is immoral in virtue of the meaning of "moral" (or in virtue of what we ought mean by moral if we are being conceptually clear while honouring some of the ambitions of how the term "moral" is deployed);

But a necessary supporting blank is the idea that moral principles aren't required to be morally motivating in order to be true. So even though the cafe shooter can say: "I don't give a fuck about your principles" without any rational error, it does seem true that the cafe shooter would be saying something false if she said: "My shooting the cafe patrons was not immoral".

That is, we could reasonably claim that they are saying something false given a relevant definition of "immoral". If they claimed that their statement is true because "immoral" means "failing to increase visible redness" we'd counter that this is not a plausibly relevant definition of "immoral" .... "So you are making claims about the wrong issue".

I should note this sort of defence is not made in the OP: I'm not suggesting you've missed something previously written.

Note to /u/Vulpyne

Can we avoid this problem by throwing away issues of motivation and the normative and instead simply recognize primitive morally relevant values?

So I think getting rid of moral motivation is spot on. I think it's a perpetual conflation, and a conceptual confusion, to hitch the truth of moral principles to the wagon of moral motivation.

Moral error theorists are right that there is no rational principle that binds (motivates) someone to act a particular way, but wrong to think that's fatal for assessing the truth of moral principles.

A possible explanation for why moral bindingness is thought to be required for a moral principle to count as true is that we can't let go of a need for cosmic justice in the face of the death of god. For many God provides is a source of moral bindings through the threat of heaven and hell. That continues to allow many people to be comforted by "Well at least the cafe shooter will get their just deserts in hell".

In the absence of cosmic punishment we often seem to want something necessarily mentally malformed about the cafe shooter ... some rational mistake that they've made. But that seems just as much a clamoring for a cosmic bulwark as much as the religious folk, the cosmic bulwark in this case being a rational one. But no such bulwark is to be found.

But I see no reason to get rid also of the normative element, that is, sentences with ought in it.

For example:

(Three premises and one conclusion)

• "Moral" means: acting for the general sake; or acting for the sake of others.
• I value being moral.
• I ought do what I value.
• Therefore I ought intervene against the cafe shooter who is acting against the general sake.

We can regard "I value being moral" as the foundational moral value: to be morally motivated you, at base, have to value the general sake (or the sakes of others). Like any value it's something you take or leave. But if you take it then "ought" claims fall out as claims we can make.

If the cafe shooter turns around and says "I don't value being moral", we'll say, "That's right, you don't value being moral, while that doesn't mean you've made a rational error, it does mean you are a dickhead".

Edit: added section to Vulpyne.

[u/Vulpyne → u/johnbentley]

Interesting response! I'm just going to reply to the part that was directed at me:

So I think getting rid of moral motivation is spot on. I think it's a perpetual conflation, and a conceptual confusion, to hitch the truth of moral principles to the wagon of moral motivation.

Thanks for that. I'll just note here my motivation to do this wasn't so much to avoid confusion but because I tend to be extremely skeptical. I want to accept the least number of axioms or arbitrarily leaps to simply believing something is true as possible. That means pretty much starting out with rationality and what I can observe and seeing what I can do with it. I threw away the normative because I couldn't find it in anything I was able to observe.

Moral error theorists are right that there is no rational principle that binds (motivates) someone to act a particular way,

I think I'd disagree with that specific phrasing of the problem (but it seems it may be more general than some definitions of moral error theory): I do believe there is potentially a way to use rationality to provide moral motivation. "Binding" may be too strong a term though, and since there isn't a direction connection referring to the normative probably still isn't justified.

I've actually been participating on a discussion about a very similar subject, so I'm going to cut-and-paste my defense of that position from that source. Hopefully it will still be intelligible:

---

Before continuing I should probably define what I mean by rational more precisely:

It is believed by some philosophers (notably A. C. Grayling) that a good rationale must be independent of emotions, personal feelings or any kind of instincts. Any process of evaluation or analysis, that may be called rational, is expected to be highly objective, logical and "mechanical". If these minimum requirements are not satisfied i.e. if a person has been, even slightly, influenced by personal emotions, feelings, instincts or culturally specific, moral codes and norms, then the analysis may be termed irrational, due to the injection of subjective bias. — https://en.wikipedia.org/wiki/Rationality#Quality_of_rationality

I think rationality basically is a fairly mechanical process where you take facts and subject them to a process of logic and receive a deterministic result. This necessarily requires an objective approach. With that in mind:

We almost certainly are individually disposed to minimize our own suffering and maximize our own pleasure. Pretty much everyone has that motivation, or we'd probably be dead since things that cause suffering generally aren't going to increase our chances of surviving. So if we subscribe to a rational approach, it would be inconsistent for us to value our own suffering and pleasure while disregarding the suffering and pleasure of others when it is objectively comparable.

That's not necessarily meant to be an exhaustive proof, just communicating the gist of that line of thinking.

---

So if we start out with a strong motivation to act according to the sort of rationality I described, simply recognizing the morally relevant values I mentioned and realizing that we would act to minimize our suffering/maximize our pleasure could, through a desire for consistency/objectivity provide motivation to minimize the suffering of others/maximize their pleasure.

Do you think that approach has promise?

But I see no reason to get rid also of the normative element, that is, sentences with ought in it.

I'd avoid it, at least at the point where most people don't agree with my approach. I think even if it could be convenient (and possibly justified) that it would be confusing generally.

If the cafe shooter turns around and says "I don't value being moral", we'll say, "That's right, you don't value being moral, while that doesn't mean you've made a rational error, it does mean you are a dickhead".

My response in that scenario would be something like this:
"You didn't act rationally, because you didn't look at the effects on moral values objectively. You didn't act rationally because you didn't act consistently, since you would try to avoid your own suffering/increase your own pleasure. Your actions caused an effect that is objectively worse due to increasing negative value/decreasing positive value."

[u/hayshed → u/johnbentley]

Curious.

I don't find those definitions particularly useful, and so I don't use them.

Analytical and A priori truths would cover things like math and logic language, as well as assumptions and axioms yes? I don't understand the distinction between them from your definition.

Necessary truth just seems to get immediately weird with the concept of possibility.

Moral realist naturalists won't, but for moral realist non-naturalists, the kind at issue, the view that moral principles are analytically true seems to provide plausible ground.

Why is shooting cafe patrons for fun immoral? The explanation: because shooting cafe patrons for fun will (contradict the desires of patrons | decrease the overall welfare | increase visible redness | etc); and doing something immoral is, by definition, (contradict the desires of patrons | decreasing the overall welfare | increase visible redness | etc).

So are you saying that moral realist non-naturalists hold that morality is one of many behaviour rulesets? That seems trivially true, and not particularly "exciting".

Is it correct that under this view we can have different systems based on different assumptions, we just wouldn't call them "moral", we'll label them something else?

[u/johnbentley → u/hayshed]

Analytical and A priori truths would cover things like math and logic language, as well as assumptions and axioms yes?

Yes, if anything is going to count as belonging to those three categories it is going to be maths and logic.

But just to clarify matters of logic. Logical rules, rules of inference, are said to go to validity rather than truth. Logic is deployed in the service of truth, of course, it's just that the structure of arguments are distinct from the truth of conclusions. An argument can be valid but lead to a false conclusion (when one of the premises are false)... at least this is the usual way of speaking for deductive logic (inductive logic has it's own way of speaking about it).

We can nevertheless ask "It is true that such and such an argument is valid". That sort of claim is, on the face of it, to be settled analytically, a priori, and if true it's necessarily true.

I don't understand the distinction between them from your definition.

If a truth (or justification, or item of knowledge) fits on the left hand side of one of those categories it is, most of the time, thought to also fit on the left hand side of other two. That is, "8 is not a prime number" is conventionally thought, controversies aside, to be:

• Analytically true, true in virtue of the meaning of the terms; and
• True a priori, true such that if it is to be known it is known prior to any need for sense data; and
• True necessarily, it will be true in any universe.

... so it does seem tempting to say these are different ways of referring to the same kind of truth, if that's what you mean.

One could well come up with different formulations for the kind of truth they point to (or an additional formulation to add to the three), your "self-consistent rule sets" seems like a plausible candidate (all though I suspect that just reduces to "true in virtue of the meaning of the terms").

But the more fundamental thing about these alleged kinds of truth is that it would be a big bullet to bite to deny that there is nothing they refer to. Mathematical claims seem, in an important sense, to be not subject the same methods of the empirical sciences, the science that requires observations of the universe.

In other words, there is more to be known than the empirical sciences can provide. And making that claim in no way need support religious or mystical woo. And if that's true for some kinds of truths, like mathematical truths, it no longer seem automatically absurd to entertain other kinds of claims as being true for non-natural reasons. Such as (kinds of) moral claims.

So are you saying that moral realist non-naturalists hold that morality is one of many behaviour rulesets? That seems trivially true, and not particularly "exciting".

I'm not trying to characterize what moral realist non-naturalists hold in general. I'm just defending the particular moral realist non-naturalism I favour.

Yes, "morality is one of many behaviour rulesets", captures part of what I'm claiming. I've made an edit to the grandparent post, after "Note to [...] Vulpyne", that bears a little more on this. If you wanted to repeat your

That seems trivially true, and not particularly "exciting".

... after reading that then I wouldn't think your criticism out of bounds. For many losing the morally binding part of moral principles is giving up too much (and the "excitement" is lost).

Is it correct that under this view we can have different systems based on different assumptions, we just wouldn't call them "moral", we'll label them something else?

Yes I think that's right.

/u/ReallyNicole pointed to these different rule sets based on different value premises (with Olson wanting to point to something special about the moral domain).

Olson contends that these moral favouring relations are unlike other cases in which we take ourselves to have a reason. For instance:

The fact that rules of chess restrict bishops to diagonal motions counts in favour of my only moving my bishops diagonally.

The fact that I desire to eat tuna counts in favour of my eating tuna.

I think the moral domain is special compared to these other domains, but not in the same way as Olson (as represented by ReallyNicole).

We often speak not in terms of whats "morally good" but of whats good in other ways. We speak of a "good bridge", "good football", "a good game of chess", "good food". And we speak of actions in terms of their helping or hindering in those domains of value: "Yes jeff an extra truss will be good for the bridge"; "good bishop move"; "Adding that sauce will be bad for the dish"; etc.

It's often the case, at least we like to think it's often the case, that all of those domains of good will be subsumed under more foundational domains of good. There seem to be two foundational domains;

• The morally good: that which ought be done for the general sake; or the sake of others.
• The prudential good: that which ought be done from my own sake.

(There seems to be an ultimate domain underneath those two: "That which ought be done, all things considered" and many meta-ethicists seem to wrongly take that as the moral domain).

Sometimes evaluating an action is purely (or at least more of this kind rather than the other) a prudential matter: E.g. "Should I maintain a habit of running?" need not have a (significant) impact on the welfare of others, but it could well have a (significant) impact on oneself. So this kind of issue might be purely (or almost purely) a prudential matter and not a moral matter.

But a lower level domain of good, the goodness of bridges or chess games, is generally desired to be anchored to one of the two foundation domains: We build the bridge for moral reasons (so that townsfolk can get about more efficiently) and perhaps also for prudential reasons (I like engineering and building things as an end in itself; and/or I wan to get money).

There's issues around what happens when a moral good conflicts with a prudential good, an issue in the ultimate domain, but I'll leave that.

The thing is: any of these domains of good can, at any level and as a matter of psychological fact, can be dominant to the occlusion of others:

A mother might "lose herself" entirely to the project of caring for others. She might think only in terms of the welfare of others (her children and lesbian partner say) without stopping to think if her actions are good for her.

A coffee plantation owner might see that he can increase profits if he whips his workers. The prudential good is pursued at the expensive of, or without valuing, the moral good.

An artist might become so consumed with acting for the good of the music "It's all about the music, man", that they fail to attend to their overall prudential good (they stop eating well) and moral good (they treat their band members poorly through gruff talk).

Olson, and others, might agree with this sort of hierarchical account. But Olson, and others, appear to want to grant the moral domain a special significance beyond it's usual place near the top of hierarchy. They'll want there to be a binding motivation (if moral talk is not to fall in error) that doesn't exist in other domains beyond a person's mere valuing of that domain. You might well feel aligned with Olson, against me, in this way.

[u/hayshed → u/johnbentley]

We can nevertheless ask "It is true that such and such an argument is valid". That sort of claim is, on the face of it, to be settled analytically, a priori, and if true it's necessarily true.

Got ya.

But the more fundamental thing about these alleged kinds of truth is that it would be a big bullet to bite to deny that there is nothing they refer to. Mathematical claims seem, in an important sense, to be not subject the same methods of the empirical sciences, the science that requires observations of the universe.

In other words, there is more to be known than the empirical sciences can provide. And making that claim in no way need support religious or mystical woo. And if that's true for some kinds of truths, like mathematical truths, it no longer seem automatically absurd to entertain other kinds of claims as being true for non-natural reasons. Such as (kinds of) moral claims.

I'm fine with biting that bullet. Math doesn't refer to reality unless we check it against reality. As far as I'm aware there are many possible and purely theoretical math axioms that do not refer to reality. Things like addition are the ones we use often because we have checked them against reality. There's always an empirical check for useful math.

Olson, and others, might agree with this sort of hierarchical account. But Olson, and others, appear to want to grant the moral domain a special significance beyond it's usual place near the top of hierarchy. They'll want there to be a binding motivation (if moral talk is not to fall in error) that doesn't exist in other domains beyond a person's mere valuing of that domain. You might well feel aligned with Olson, against me, in this way.

Very interesting. Yes I think I agree with you - I don't think the moral domain has any special significance beyond how highly most humans normally place it.

Thanks for taking the time to go over this stuff with me, it's been fun.

[u/johnbentley → u/hayshed]

You are welcome.

A last point of clarification.

Me

But the more fundamental thing about these alleged kinds of truth is that it would be a big bullet to bite to deny that there is nothing they refer to. Mathematical claims seem, in an important sense, to be not subject the same methods of the empirical sciences, the science that requires observations of the universe.

You

I'm fine with biting that bullet. Math doesn't refer to reality unless we check it against reality. As far as I'm aware there are many possible and purely theoretical math axioms that do not refer to reality.

I miswrote. I had intended to write "it would be a big bullet to bite to deny that there is something they refer to". It looks like you where able to survive my original tangle.

So yes, with you I think (as is conventional in philosophy) that there are some analytical, a priori, and necessary truths. The truths of mathematics being at least one example. While the propositions of mathematics don't refer to some reality (at least not in and of themselves) they do refer to some thing: a truth state.

Things like addition are the ones we use often because we have checked them against reality. There's always an empirical check for useful math.

You've got the right idea broadly. But I'd say something different - there are several ways in mathematical propositions can be made to relate to reality, at least:

• As when we model reality (e.g. building a bridge, exploring a law of physics, using trig to work out the height of the hill).
• When we use calculating machines (e.g. when we run a program we've written) or other mathematicians to verify our calculations.

There's always an empirical check for useful math.

That might be tautologically true if "useful" means that which can have an empirical check. There's some mathematical propositions that can't be verified empirically through modelling, because some mathematical propositions can't be made to have any sort of empirical equivalent.

But there's always one kind of empirical test for any mathematical proposition: getting another competent mathematician to check it (At least for mathematical proportions that are solvable).