Real Presence and primitive locational relations

According to relationalism, space is constituted by the network of spatial relations, such as metric distance relations (e.g., being seven meters apart). If these relations are primitive, then there is a very easy way for God to ensure the Real Presence of Christ: he can simply make there be additional spatial relations between Christ and other material entities, spatial relations that are exactly like the relations that the bread and wine stood in to other material entities.

It might seem contradictory for Christ to stand in two distance relations: for instance, being one mile from me (in one church) and three miles from me (in another). But I doubt this is a contradiction. New York and London are both 5600 km and 34500 km apart, depending on which direction you go.

According to substantivalism, on the other hand, points or regions are real, and objects are in a location by standing in a relation to a point or region. If relations are primitive, again there should be no problem about God instituting additional such relations to make it be that Christ is present where the bread and wine were.

In other words, if location is constituted by a primitive relation—whether to other objects or to space—there is apt to be no difficulty in accounting for the Real Presence. The reason is that we expect, barring strong reason to the contrary, primitive relations to be arbitrarily recombinable.

If location, however, is constituted by a non-primitive relation, there might be more difficulties. For instance, as a toy theory, consider the variant of relationalism on which spatial relations are constituted by gravitational force relations (two objects have distance r if and only if they have masses m₁ and m₂ and there is a gravitational force Gm₁m₂/r² between them). In that case, for God to make Christ present in Waco would require God to make Christ stand in gravitational force relations of the sort that I stand in by virtue of being in Waco. For instance, the earth’s gravitational force on Christ would have to point from Waco to the center of the earth—but since the Eucharist is also in Rome, it would have to point from Rome to the center of the earth as well. And that might be thought impossible. But perhaps there could be two terrestrial gravitational forces on Christ: one along the Waco-geocenter vector and the other along the Rome-geocenter vector. This would require some sort of a realism about component forces, but that’s probably necessary for the gravitational toy theory. And then God would have to miraculously ensure that despite the forces, Christ is not affected in the way he would normally be by these forces. All this may be possible, but it’s less clear than if we have primitive relations.

Python script for Nanson and Black voting

I made a handy little python script for tabulating group votes with more than two candidates using either Black’s Procedure or Nanson’s Method. Both algorithms are Condorcet compliant. The algorithms require as input a text file with the ballots and control information. Once the algorithm finds a winner (or a bunch of tied winners), it deletes them from the ballots and repeats.

For instance suppose sample.txt contains:

method Black's
require 3
ballot Mickey Donald Sonic
ballot Mickey Sonic Donald
ballot Sonic Mickey Donald

Then:

$ python3 vote.py sample.txt
Options: {'method': "Black's", 'require': 3}
Ballots: 3
Valid ballots: 3
Candidates: ['Donald', 'Mickey', 'Sonic']
Method: Black's
position 1 (Condorcet): Mickey
position 2 (Condorcet): Sonic
position 3: Donald

Black’s Procedure works as follows at each stage: see if there is a Condorcet winner; if not, look for a Borda winner (the first person on each ballot gets a (reversed) Borda score of 0 points; the second gets 1 point; and so on; persons not on a ballot get n points where there are n on the ballot; the winner is determined by the lowest sum of points; note that by default the ballots are modified at subsequent stages by deleting candidates who were already selected, which means the Borda scores change from stage to stage). Nanson’s Method deletes everyone with poorer-than-average Borda score, re-ranks, and repeats until there is a winner or a tie. This is also guaranteed to return a Condorcet winner if there is one.

The code marks winners that were Condorcet winners. That may be helpful to group deliberation as it shows that the decision is bit more robust in that case. (Though a Condorcet winner in kth place, with some non-Condorcet winners before, may not mean much if the earlier winners are dubious.)

The require line specifies how many entries a ballot must contain to be valid (by default, all ballots are valid, even ones with varying numbers of votes; any unranked candidates count as tied after the last ranked candidate). The ballot lines contain the candidates that someone voted for, in order from best to least good. Candidate names are case sensitive and cannot contain spaces. To save typing, one can also introduce abbreviations with the key entry. For instance:

method Black's
require 3
key m Mickey
key d Donald
key s Sonic
ballot m d s
ballot m s d
ballot s m d

Previsions for inconsistent credences and arguments for probabilism

Fix a sample space Ω and an algebra F events on Ω. A gamble is an F-measurable real-valued function on Ω. A credence function is a function from a F to the reals. A prevision or price function on a set of set G of gambles is just a function from G to the real numbers. A previsory method E on a set of gambles G and a set of credence functions C assigns to each credence function P ∈ C a prevision E_P on G.

A previsory method on G and C has the weak domination property provided that if f and g are two gambles such as that f ≤ g everywhere on Ω, then E_P(f)≤E_P(g) for every f and g in G and P in C. It has the strong domination property provided that it has the weak domination property and if f < g everywhere on Ω, then E_P(f)<E_P(g). It has the zero property provided that E_P(0)=0.

Mathematical expectation is a previsory method on the set of all bounded gambles and all probability functions. It has the zero and strong domination properties.

The level set integral is a previsory method on the set of all bounded gambles and all monotonic credence functions (P is monotonic iff P(⌀)=0, P(Ω)=1 and P(A)≤P(B) whenever A ⊆ B). It has the zero and weak domination properties.

The level set integral has the strong domination property on the set of weakly countably additive monotonic credence functions, where P is weakly countably additive provided that Ω cannot be written as a countable union of sets each of credence 0. If F (or Ω) is finite, we get weak countable additivity for free from monotonicity.

A previsory method E requires (permits) a gamble f given a credence P provided that E_P(f)>0 (E_P(f)≥0); it requires (permits) it over some set S of gambles provided that E_P(f)>E_P(g) (E_P(f)≥E_p(g)) for every g in S.

A previsory method with the zero and weak domination properties cannot be strongly Dutch-Booked in a single wager: i.e., there is no gamble U such that U < 0 everywhere that the method requires. If it also has the strong domination property, it cannot be weakly Dutch-Booked in a single wager: there is no U such that U < 0 everywhere that the method permits.

Suppose we combine a previsory method with the following method of choosing which gambles to adopt in a sequence of offered gambles: you are required (permitted) to accept gamble g provided that E_P(g₁ + ... + g_n + g)>E_P(g₁ + ... + g_n) (≥, respectively) where g₁ + ... + g_n are the gambles already accepted. Then given the zero and weak domination properties, we cannot be strongly Dutch-Booked by a sequence of wagers, and given additionally the strong domination property, we cannot be weakly Dutch-Booked, either.

Given that level set integrals provide a non-trivial and mathematically natural previsory method with the zero and strong domination properties on a set of credence functions strictly larger than the consistent ones, Dutch-Book arguments for consistency fail.

What about epistemic utility, i.e., scoring-rule, arguments? I think these also fail. A scoring-rule assigns a number s(p, q) to a credence function p and a truth function q (i.e., a probability function whose values are always 0 or 1). Let T be truth, i.e., a function from Ω to truth functions such that T(ω)(A) if and only if ω ∈ A. Thus, T(ω) is the truth function that says “we are at ω” and we can think of s(p, T) as a gamble that measures how far p is from truth.

If E is previsory method on a set of gambles G and a set of credence functions C, then we say that s is an E-proper scoring rule provided that s(p, T) is in G for every p in C and E_ps(p, T)≤E_ps(q, T) for every p and q in C. We say that it is strictly proper if additionally we have strict inequality whenever p and q are different.

If E is mathematical expectation, then E-propriety and strict E-propriety are just propriety and strict propriety.

It is thought (Joyce and others) that one can make use of the concept of strictly propriety to argue for that credence functions should be consistent. This uses a domination theorem that says that if s is a strictly proper additive scoring rule, then for any inconsistent credence function p there is a consistent function q such that s(p, T(ω)) < s(q, T(ω)) for all ω. (Roughly, an additive scoring rule adds up scores point-by-point over Ω.)

However, I think the requirement of additivity is one that someone sceptical of the consistency requirement can reasonably reject. There are mathematical natural previsory methods E that apply to some inconsistent credences, such as the monotonic ones, and these can be used to define (at least under some conditions) strictly E-proper scoring rules. And the domination theory won’t apply to these rules because they won’t be additive. Indeed, that is one of the things the domination theorem shows: if C includes an inconsistent credence function and E has the strong domination property, then no strictly E-proper scoring rule is additive.

So, really, how helpful the domination theorem is for arguing for consistency depends on whether additivity is a reasonable condition to require of a scoring rule. It seems that someone who thinks that it is OK to reason with a broader set of credences than the consistent ones, and who has a natural previsory method E with the strong domination property for these credences, will just say: I think the relevant notion isn’t propriety but E-propriety, and there are no strongly E-proper scoring rules that are additive. So, additiveness is not a reasonable condition.

Are there any strongly E-proper scoring rules in such cases?

[The rest of the post is based on the mistake that E-propriety is additive and should be dismissed. See my discussion with Ian in the comments.]

Sometimes, yes.

Suppose E is previsory method with the weak domination condition on the set of all bounded gambles on Ω. Suppose that E has the scaling property that E_p(cf)=cE_p(f) for any real constant c. (Level Set Integrals have scaling.) Further, assume the separability property that there is a countable set of B of bounded gambles such that for any two distinct credences p and q, there is a bounded gamble f in B such that E_pf ≠ E_qf. (Level Set Integrals on a finite Ω—or on a finite field of events—have separability: just let B be all functions whose values are either 0 or 1, and note that E_p1_A = p(A) where 1_A is the function that is 1 on A and 0 outside it.) Finally, suppose normalization, namely that E_p1_Ω = 1. (Level Set Integrals clearly have that.)

Note that given separability, scaling and normalization, there is a countable set H of bounded gambles such that if p and q are distinct, there exist f and g in H such that E_p requires f over g (i.e., E_pf > E_pg) and E_q does not or vice versa. To see this, let H consist of B together with all constant rational-valued functions, and note that if E_pf < E_qf, then we can choose a rational number r such that r lies between E_pf and E_qf, and then E_p and E_q will disagree on whether f is required over r ⋅ 1_Ω.

Let H be the countable set in the above remark. By scaling, we may assume that all the gambles in H are bounded by 1. Let (f₁, g₁),(f₂, g₂),... be an enumeration of all pairs of members of H. Define s_n(p, T(ω)) for a credence function p in C as follows: if E_p requires f_n over g_n then s_n(p, T(ω)) = −f_n(ω), and otherwise s_n(p, T(ω)) = −g_n(ω).

Note that s_n is an E-proper scoring rule. For suppose that q is a different credence function from p and E_ps_n(p, T)>E_ps_n(q, T). Now there are four possibilities depending on whether E_p and E_q require f_n over g_n and it is easy to see that each possibility leads to a contradiction. So, we have E-propriety.

Now, let s(p, T) be Σ_n = 1^∞ 2⁻ⁿs_n(p, T). The sum of E-proper scoring rules is E-proper, so this is an E-proper scoring rule.

What about strict propriety? Suppose that p and q are credence functions in C and E_ps(p, T)≤E_ps(q, T). By the E-propriety of each of the s_n, we must have E_ps_n(p, T)=E_ps_n(q, T) for all n. Thus, for all pairs of members of H, the requirements of E_p and E_q must agree, and by choice of H, p and q cannot be different.

Forgiveness of sins

It is very plausible that God can forgive wrongs we do to him. But a very difficult question which is rarely discussed by philosophers of religion is how God can forgive wrongs done to beings other than God.

This puzle seems to me to be related to the mystery of the line: “Against you [God], you alone, have I sinned” in Psalm 51:4, a line that seems on its face to contradict the obvious fact that the sins in question (David’s adultery with Bathsheba and murder of Uriah) seem to be primarily against human beings. Perhaps also related is Jesus’s puzzling statement: “No one is good but God alone” (Mark 10:18).

I think the answer to all of these questions may lie in a metaphysics and axiology of participation on which all the value of creatures is value had by participation in God, so that only God is good in the primary sense and only God is sinned against in the primary sense, which in turn gives God the normative power to forgive all wrongs, including wrongs directly against God as such as well as wrongs against God’s goodness as participated in by creatures.

Joint powers

Suppose neither Alice nor Bob has the power to budge the sofa, but together they can lift it. Causal powers belong to substances, and Alice and Bob do not compose a substance, so it seems the causal power to lift the sofa does not belong to the pair as a pair. Rather, the power must belong to the pair in virtue of the substances composing it. But how can that work?

Here is what I used to think. Causal powers come with actuation conditions. So we can say:

1. Alice has the power to lift the sofa when Bob is helping.

2. Bob has the power to lift the sofa when Alice is helping.

But now suppose both are working together. Then both causal powers’ actuation conditions are met. But when each of two causal powers for an effect E is actuated, then E is overdetermined. Thus, the sofa’s upward movement is overdetermined. But that is clearly false. So something is wrong.

Maybe we just need a better account of overdetermination? Or maybe there need to be irreducibly joint powers?

More on fake assertions

In my previous post I argued that if Bob writes and posts a letter of recommendation for himself purporting to be from Alice, and saying all sorts of false stuff like that Bob is very honest, then the contents of the letter are not asserted by Bob, and hence while they are deceptions—and, obviously, immoral—they are not lies.

Here are some more cases that I think support this. In all of the stories, I assume Alice is honest and well-informed.

1. Bob has deceived Alice into thinking that he is actually very honest. She writes him a letter of recommendation asserting this, and Bob reads the letter (e.g., by steaming open the envelope) and mails it to the potential employer.

2. Bob breaks into Alice’s office and finds a letter of recommendation for another guy—a really honest guy—with the same name as Bob. He sends the letter in support of his job application.

3. After an accident, Alice has been engaging in handwriting exercises by writing joke letters of recommendation. One of these joke letters is a letter of recommendation for Stalin as a kindergarten teacher, praising his compassion, and another is a letter for Bob as a bank teller, praising his honesty. Bob breaks into Alice’s office, finds the letter for him. He knows full well it is a joke, since he knows what Alice actually thinks of him, but he posts the letter in support of his job application.

4. Bob has a bunch of monkeys employed randomly typing on typewriters. One day, a monkey produces a letter praising Bob’s honesty and purporting be from Alice. He sends the letter as part of his job application.

5. Bob obtains a letter of recommendation from Alice where one line ends with “Bob is utterly dis-” and the next line begins with “honest.” He carefully erases the “dis-” and posts the letter in support of his job application.

6. The original case where Bob fakes the entire letter.

Case 1: There is no lie in the letter, and nothing in the letter is asserted by Bob. Bob is still being deceitful by knowingly mailing a letter containing false information about him, which false information comes from his deceit of Alice. But there is no lie in the letter.

Case 2: Alice asserts truths in the letter. Bob manipulates the reader into thinking that the letter is about him, which it is not. The reader misunderstands the letter as about Bob. But the one person doing any asserting in the letter is Alice, who cannot be said to be asserting falsehoods.

Case 3: Alice neither asserts that Stalin is compassionate nor that Bob is honest. She is just joking and jokes aren’t assertions. Bob manipulates the reader into misunderstanding the jokes as assertions. No one does any asserting in the letter, certainly not Alice, but also not Bob.

Case 4: This one is a little bit trickier, but in the end it’s hard to see a difference between case 3 and case 4. In both cases, the writer of the letter made no assertions. And Bob just posted it.

Case 5: Here things are, I think, even a little bit murkier. But imagine a version of case 5 where Bob sees his pet monkey playing with an eraser and erasing the “dis-”, and then he posts the letter. In that case, this is just like case 4 with respect to Bob’s authorship, and hence Bob is not lying in the letter. But I also don’t think it matters whether Bob physically does the erasing himself or the monkey does it with Bob’s knowledge. Bob isn’t lying in the letter.

I could imagine someone caviling at my judgment in case 5, so let’s go back to case 4 some more.

Imagine that Bob has all the time in the world on his hands, and he has hired a bunch of monkeys as secretarial staff. Whenever he wants to write a letter, he composes it is in his mind, and then waits for the monkeys to type exactly it at random. When they do so, he posts the letter. This is just an inefficient way of writing letters: the letter is just as fully from Bob as it would be if he typed it himself. If the letter is signed “Bob” and contains claims that Bob knows to be false, Bob is lying in the letter. But note that if the letter is signed “Alice”, this is just case 4, and in case 4, Bob isn’t lying in the letter. So, it looks like whether Bob is or is not lying in the letter depends on whether it purports to be from him, and hence in cases 5 and 6, Bob isn’t lying in the letter either.

Let me push a bit further. Go back to case 1, which was perhaps the clearest case of Bob’s not lying in the letter. Imagine that Bob has the following inefficient technique for avoiding doing any typing himself. When he wants to write a particular letter purporting to be from himself, he finds another person with the same name as his own, and he manipulates them into believing the content of the letter, and then puts them in circumstances where the other person has a reason to honestly write such a letter. He then steals the letter and posts it as if it were his own. This seems, once again, to be a case of an inefficient letter composition procedure, and Bob is the author of the letter, just as much as he would be if he waited for a monkey to type it at random or if he trained a monkey to write it. Yet the main difference between this and case 1 is that in case 1, Bob isn’t purporting the letter to be from himself, but from Alice, which it in fact is. So, if we grant, as I think we have to, that Bob isn’t lying in the letter in case 1, but that he would be if he used the inefficient secretarial technique of manipulating namesakes into writing letters just like the ones he wants, then we have to say that what makes the difference as to whether Bob is lying in a letter that he fully approves of despite knowing it contains falsehoods is whether the letter purports to be from Bob.

We can make similar points about some of the other cases. For instance, suppose we agree that there is no lie in the joke letter in case 3. But we can imagine Bob having an inefficient secretarial technique where letters from him are written by getting lots of people to do handwriting exercises until one of them writes something signed “Bob” that has the exact content he wants it to have. In that case, Bob is lying in the letter, if the letter has falsehoods.

If this is right, then lies are tightly connected to a personal endorsement of a claim. If instead of personally endorsing a claim one fakes an endorsement by someone else, one is engaging in deceit but one isn’t lying.

Fake assertions

Suppose Bob faked a letter of recommendation from his dissertation director Alice, in which letter lots of stuff was said which Bob knew to be false, and then posted the letter to Carl.

Bob clearly deceived Carl, or tried to. But did he lie to Carl? Let’s consider three representative example sentences from the letter:

1. I am Bob’s dissertation director.

2. I think the world of Bob.

3. Bob is impeccably honest.

I will also take that Bob knows that Alice is his dissertation director, that Alice thinks poorly of him (which is why he faked the letter) and that he’s dishonest, and I will also assume that Bob thinks the world of himself.

If Bob lied, which of these sentences did he lie in?

One important question is who “I” refers to in the letter. If it refers to Bob, then (1) and (3) are false and (2) is true. If it refers to Alice, then (2) and (3) are false and (1) is true. Basically, we need to decide which of (1) and (2) is true.

It seems clear that by (2), Bob intended to communicate that Alice thinks the world of him, and he had no intention at all to communicate that Bob thinks the world of himself (indeed, perhaps another sentence in the letter is “I have never met a humbler person”). So it seems that “I” refers to Alice, and hence (2) and (3) are false, but (1) is true.

On this reading, Bob has knowingly written two false things: (2) and (3), and one truth: (1). Has Bob lied in the false things he wrote? I have some doubts. The reason is this. What makes lying be lying is that one is betraying a trust that one has solicited in speaking. But Bob has not solicited Carl’s trust in Bob: rather, he is relying on Carl’s trust in Alice. But one can only betray trust in oneself. So Bob cannot betray Carl’s trust in Alice, and hence Bob is not lying when Alice is the object of Carl’s trust. Here’s another way to think about this: To lie is to stand behind a falsehood. But Bob isn’t standing behind the falsehood—he is, instead, putting Alice in front of it, as is clear from the fact that “I” refers to Alice.

In asserting something one implicates that one believes it. But Bob isn’t implicating that he believes it, only that Alice does. And it’s not, it seems, that Bob has canceled the implicature of belief (as one sometimes can, pace Moore). I think Bob not only isn’t lying, but he isn’t asserting anything.

This seems paradoxical. But consider this. Suppose Drew, who is dishonest but not a racist, fakes an open letter from Adolf Hitler, hoping to sell it off to the Holocaust Museum.. The letter contains all sorts of false statements, such as that various minority groups are subhuman. Drew is clearly committing fraud. But is he making racist statements? I don’t think so. Rather, he is faking racist statements by Hitler. Similarly, the falsehoods in the letter are not lies by Drew, for if Drew were lying in the letter, he would be making racist statements. But he is faking, not making, racist statements.

I think the same may be true of Bob: he is faking, not making, various assertions in the letter. There is a difference between Bob and Drew, of course. Drew is not trying to get the audience to believe the fake assertions, but only to believe that they were made. Bob is trying to get the audience to believe the fake assertions. But this difference aside, I still suspect that Bob is deceiving, not lying.

Of course, this difference doesn’t let Bob or Drew off the hook. They have engaged in a massive failure of integrity, indeed in fraud.

But the difference between deceiving and lying could still be relevant. I think a challenge for those of us who think lying is always wrong is to articulate some sort of a theory of clandestine military and police operations that allows for non-lying deceit. If lies require that the liar be taken to be the author, then this opens up the way for various things like Operation Mincemeat being deceit but not lies.

I fear, however, that at this point I am engaging in the kind of casuistry that gives casuistry a bad name. Here is one way of highlighting this. Surely one can’t just write a letter with falsehoods putatively from oneself and claim that one faked one’s own letter, and hence one didn’t lie in it. But now imagine that Alice and Bob conspire to each write a fake letter purporting to be from the other. Surely that shouldn’t escape the moral prohibitions against lying. Maybe, though, it depends on the details of the conspiracy. If Bob is just writing in the letter putatively from Alice things that Alice asked him to write, then the letter is no fake, and Bob is just Alice’s secretary.

Fake counting

When someone’s walking speed is two miles per hour, there are not two things, “one mile per hour walkings”, that are present.

When we say that a sculpture has three dimensions, we are not saying there are exactly three things—dimensions?—that are present in it. But are there not width, height and depth? In a way. But rotate the sculpture by 45 degrees, and “width”, “height” and “depth” refer to measurement along three other axes. There are, it seems, infinitely many axes along which the sculpture can be non-trivially measured.

These are examples of what one might call “fake counting”. We speak as if there were n of something, but the following argument is invalid:

1. There are n Fs.

2. n ≥ 1.

3. So, there are some Fs.

And, similarly, this is invalid:

4. There are exactly two Fs.

5. So, ∃x∃y(F(x)&F(y)&∀z(F(z)→(z = x ∨ z = y))).

In fake counting of Fs, there is counting involved, but it is not counting of Fs. For instance, when we say that the sculpture has three dimensions, we mean something like this:

• there are three mutually perpendicular axes such that the sculpture has non-zero extent along each of them, but there are no four such axes.

So, there is a counting of axes, but it is not a counting of dimensions. If we were counting dimensions, we would have to have say what the first one is, what the second one is and what the third one is, and as the rotation thought experiment shows, that doesn’t work. And the counting of axes doesn’t involve counting axes overall, but rather axes in a particular set of them.

We need to beware of fake counting when making metaphysical arguments for the existence of entities of some sort. For instance, topologists have ways of “counting holes”. But topological properties are invariant under deformations. Now, imagine a pancake with, as we would say, “one hole in the middle”. Well, however we distort the pancake, it has one topological hole. But if we ask where that hole is, there is no topological answer to it (in the animation below, is the hole outlined in red or in blue?). So, topological hole counting is fake counting.

Silencing and epistemic harm

Suppose that Arthur is about to give a lecture on trope theory but the lecture is canceled due to Platonist protests.

It is intuitive to say that unjust epistemic harms have been perpetrated. But on whom?

The primary epistemic harms from Arthur’s silencing are to the audience who is prevented from hearing his arguments, and hence is in a poorer epistemic state to adjudicate the truth of the matter about tropes. Arthur potentially receives some secondary epistemic harms, in that he is deprived of the benefits of challenging questions or of the potential growth of understanding of a subject that a speaker gains by speaking. But notice that these are accidental to his silencing. The loss of the benefit of challenging questions is due to the silencing of the audience, not due to Arthur’s silencing, and the benefit of thinking through one’s position in presenting it could be had by presenting the position to an empty room. However, the audience’s epistemic loss is primary.

Now, Arthur receives all sorts of potentially serious non-epistemic harms. He has been insulted. A promise to him has been reneged on. He has lost the value of being the intentional cause of the audience’s epistemic benefits. His CV is shorter by one item. Perhaps he has lost an honorarium, or at least he has lost the opportunity to have pre-scheduled something else for that day. He may come to be in fear for his personal safety. Some of these harms may result in epistemic harms down the road: for instance, he may abandon a promising line of research as a result of these insults or get a job at a department with poorer research opportunities. But these epistemic harms are secondary to the non-epistemic harms.

I suppose there could be the following epistemic harm to Arthur: if public proclamation of p carries negative consequences for one, then one will be tempted to cease to believe p. If Arthur was in fact right in his views, and he abandons those views due to the opposition, then he will suffer epistemic harm. But while people do change their views because of social consequences, I suspect this is much more common when the social consequences are subtle than when they are highly overt. I suspect that highly overt cases, such as lecture cancelation, are more likely to entrench one in one’s beliefs. Of course, such entrenchment could itself be an epistemic harm, especiallyif if the beliefs are false.

So, Arthur’s being silenced results in:

• primary epistemic harms to the audience

• primary non-epistemic harms to Arthur

• secondary epistemic harms to Arthur.

So, it is correct to say that unjust harm has been done to Arthur, but that harm is not primarily epistemic. The people to whom unjust epistemic harm has been done are the people who would have been in Arthur’s audience.

The same is true if the form the injustice takes is one’s prejudiced refusal to take seriously another’s testimony or arguments. In this case, one is doing injustice to the speaker, but the speaker does not suffer epistemic harms by one’s refusal to take their testimony or arguments seriously. The speaker is insulted—whether they know it or not (the speaker may not know that one is refusing to take them seriously)—but the epistemic harm is to oneself.

In my initial example, Arthur’s lecture was on trope theory, a highly theoretical topic. But nothing changes when the topic becomes more personal. Suppose Arthur is silenced and kept from speaking out about the injustices that he has received over his lifetime because of his disability. The primary epistemic harms are, again, to the audience. But Arthur is harmed by being insulted, and prevented from convincing people to stop perpetrating injustice on him. These, however, are not, primarily, epistemic harms.

When I was initially writing this post, I was thinking this was going to be an argument that we shouldn’t think of epistemic violence or epistemic injustice as something that is done to a person who is silenced, but as something that is done to the audience.

But I then realized that “epistemic” in “epistemic violence” and “epistemic injustice” can be understood as qualifying either the types of harm imposed or the means by which the harms are imposed. If we understand it as qualifying the types of harm imposed, then I think my original thesis is quite correct: epistemic violence and injustice are done not to those who are silenced but to those who are prevented from hearing them (and that could, I think, be the silencers themselves). But it seems more faithful to the intent of those who have been writing on these topics to take “epistemic” to qualify the means. And this fits with our usage in some other cases: Bob perpetrates “gun violence” just in case he perpetrates violence with a gun, rather than when he harms someone’s gun collection. When Arthur is silenced, epistemic violence/injustice is done to him because he is unjustly harmed by epistemic means, namely he is harmed by others’ epistemic malpractice (whether in the narrow sense, as when a prejudiced audience refuses to listen, or in a broad sense, when protesters make it impossible for others to listen). But he is not epistemically harmed.

Shapes of holes

The ordinary notion of a hole is kind of dubious. Consider the hole in the thin wavy sheet of rubber on the right. What is the shape of that hole? How thick is it? Is it exactly as thick as the rubber sheet? But the rubber sheet varies in thickness, actually. How does it stretch from its wavy edges to the middle? Does it have a sinewave bump in the middle, to correspond to where there are sinewave bumps in the sheet elsewhere? Or does that depend on the history of its formation (e.g., maybe if the sheet used to have a bump there but then a hole was made--that's how my code generating this picture works--then the hole has a bump, but if the sheet was pre-made with a hole, then the hole is flatter)? I think there really are no good answers to these questions, and hence holes don't exist.

Holes and substantivalism

Suppose substantivalism about space is correct. Imagine now that the following happens to a slice of swiss cheese: the space where the holes were suddenly disappears. I don’t mean that the holes close up. I mean that the space disappears: all the points and regions that used to be in the hole are no longer there (and any air that used to be there is annihilated). The surfaces of the cheese that faced the hole now are at an edge of space itself.

The puzzle now is that in this story we have an inconsistent triad:

1. There is no intrinsic change in the cheese.
2. The slice of cheese no longer has holes.
3. Changing with respect to whether you have holes is intrinsic.

Here are my arguments for the three claims. There is no intrinsic change in the slice of cheese as something outside the cheese has changed—space has been annihilated. The slice of cheese no longer has holes, as it makes sense to talk of the size or shape or volume of a hole, but there is no size or shape or volume where there is no space. And changing with respect to whether you have holes is change of shape, and changes of shape are intrinsic.
It seems that the above story forces you to reject one of the following:

4. Substantivalism about space
5. Intrinsicness of shape.

But there is another way out. Deny (3). Whether you have holes is not intrinsic. What is intrinsic is your topological genus with respect to your internal space and similar topological properties.

Note, also, a lesson relevant to the famous Lewis and Lewis paper on holes: the counting of holes should not involve the counting of regions, but the computation of a numerical invariant, namely the genus.