In one of Ted Sider's recent papers, he's got a nice section trying to explain why philosophers should care about the metaphysical possibility of time travel. Here's a passage.

Before expending too much energy on the topic, it is worth thinking a bit about
its point. Beyond the (perfectly legitimate) desire to set the record straight, is
there any reason to care about time travel?

The most straightforward reason to care is that today’s physics community
cares. Whether the actual laws of nature permit time travel is a live debate
in contemporary physics journals (Earman, 1995). Suppose the arguments
to be discussed in this paper against the possibility of time travel (without
shackles) succeeded. Then, given that many physicists tell us otherwise, that is
a problem! Whatever else metaphysicians must do, they should at least try to
make metaphysical sense out of what physicists take seriously.

I started to wonder exactly how seriously the physics community cares. That led to this post last week.

I found another interesting news story this week. The article is a bit sensationalist, and it's a little older - but it does report on a physicist, Amos Ori, who explains how he thinks we could make time travel happen. I assume this is the Physical Review article the newspaper is referring to. (Note: Amos Ori has an even earlier article here)

Too bad you can only read the abstracts online.

SUNY-Fredonia's own, Neil Feit, has a book coming out this summer.

OUP has a description - plus some nice blurbs from Andy Egan and John Perry on their website. I'm pasting all of that below.

Description

Philosophers typically suppose that the contents of our beliefs and other cognitive attitudes are propositions-things that might be true or false, and their truth values do not vary from time to time, place to place, or person to person. Neil Feit argues that this view breaks down in the face of beliefs about the self. These are beliefs that we express by means of a first-person pronoun. Feit maintains-following David Lewis, Roderick Chisholm, and others-that in general, the contents of our beliefs are properties. Unlike propositions, properties lack absolute truth values that do not vary with time, place, or person.

Belief about the Self offers a sustained defense of the Property Theory of Content, according to which the content of every cognitive attitude is a property rather than a proposition. The theory is supported with an array of new arguments, defended from various objections, and applied to some important problems and puzzles in the philosophy of mind.

Reviews

"Feit's discussion of the arguments for and against the property theory of content is philosophically sophisticated, generous, and fair-minded, and he finds some extremely interesting applications for his version of the property theory."
--Andy Egan, Assistant Professor of Philosophy, University of Michigan

"Belief about the Self is an important contribution to the philosophy of language and philosophy of mind, and useful for the broader field of cognitive science."
--John Perry, Professor of Philosophy, Stanford University

At first I thought, "This can't be real."



But I looked into it more, and found an article that sheds a bit more light on the video. The guy in the video is Ronald Mallett. He's a professor at the University of Connecticut, and yes he intends to build a time machine. Here's a link to an article that discusses it more.

UPDATE: I just found recent RSS feeds for Mind and Australasian. The feeds on Ingenta are never current. Once I plugged those into the mashups, the returns for metaphysics papers went through the roof!

For some reason, it takes a while for the tweaks to take effect in the widget. Stay tuned and you should see more returns in the widgets.

I've added a metaphysics mashup. The mashup didn't yield nearly the number of results that the epistemology mashup yielded. That kind of surprised me.

I'll post the keywords that I used later under the main journal mashup post.

Alexander Pruss just posted an interesting argument against Presentism. Here is the thought experiment that gets the ball rolling.

You and I are watching an exciting game of tennis. Our particular interest is drawn by Federer's next serve which is at a match point. With eager anticipation I speculate about how the serve will go. Federer is serving. You briefly respond to my remark during the serve itself, saying that my speculation doesn't look right. Federer has served and wins the match. We continue disagreeing about the serve for the next fifteen minutes. Such a conversation is perfectly natural.

As Pruss notes, this conversation is perfectly natural. Furthermore, you and I seem to be talking about the same event. Presentism seems committed to saying that we're not. That's a problem for presentism.

Here's a link to the whole discussion.

Attention all philosophers - be careful when you teach your students about freewill. You may end up with a classroom full of cheaters.

A recent article in Psychological Science argues that when students believe that they do not have freewill, they are more likely to cheat.

In one of the studies students were given literature on freewill and determinism. They were then asked to rate their confidence that they had freewill. Once they determined which students believed in determinism, they conducted a series of tests where an obvious cheating option was made available.

One of the experiments involved two groups that took a test with a monetary incentive for correct answers. The first group was scored by the experimenter. The second group was left to score themselves. Look at how the believers in determinism in the self-scoring group differ on the chart with respect to everyone else across both test groups.

Here's the link to the full article over at Cognitive Daily.

If you're like me and interested in philosophy of time, you may have thought this article which is titled "You Can't Travel Back in Time, Scientists Say" might involve some recent research that shows that time travel (contrary to what we think now) is incompatible with the current laws of physics.

It doesn't.

It basically says that the laws of physics do not rule out time travel, and that even if it is theoretically possible people shouldn't expect that we are going to have the technical ability anytime soon. But this is simply something that a lot of people already acknowledge. Talk about a misleading title.

It's a good lesson in modal ambiguity.

In a previous post I presented an argument from Jubien aimed at direct reference theory that relied on mereological essentialism. Here is the post. Below is the argument again so you don't have to click away.



Michael Jubien's Argument Against Direct Reference

1. If Direct Reference theory is true, then 'Venus' in 'Venus could have had different parts' contributes a physical object to the proposition expressed and nothing more.
   
   
2. If 'Venus' in 'Venus could have had different parts' contributes a physical object to the proposition expressed and nothing more, then the sentence 'Venus could have had different parts' expresses a falsehood.
   
   
3. The sentence 'Venus could have had different parts' does not express a falsehood.
   
   
4. Therefore, it's not true that 'Venus' in 'Venus could have had different parts' contributes a physical object to the proposition expressed and nothing more.
   
   
5. Therefore, Direct Reference theory is not true.

I've been thinking about this all week. The comments from the previous post noted two very plausible ways to go. Give up on mereological essentialism, and reject (2). I'm inclined to give up on mereological essentialism too, but I must confess I have my moments where I wake up groggy and ask myself - why should I reject that view again?

The other option suggested was to give up on (3). If you're a mereological essentialist, why not stick to those guns and say that Venus couldn't have had different parts?

Let's pursue this option of rejecting (3) a little further. I think if you're a mereological essentialist, you're going to have a tough time finding a plausible semantic theory that allows you to keep (3).

Jubien takes it for granted that his descriptivism would allow us to keep (3). But consider the sentence.

(V) Venus could have had different parts.

It seems that Jubien's version of descriptivism entails that (V) is synonymous with (V*)

(V*) There is an X such that X has the property being-Venus and X could have had different parts.

(V*) is false if you're a mereological essentialist. If you're a mereological essentialist and a standard descriptivist then you'd have to say that (V) doesn't express a truth. It seems like Jubien would have to reject (3) in his own argument. Or make it more clear how his version of descriptivism when combined with mereological essentialism doesn't entail that (V) is false.

Neil Levy (over at Garden of the Forking Paths) just pointed out a pretty interesting study that may be of interest to philosophers interested in freewill.

The short version: A group of scientists have some confirmation of the hypothesis that the neural activity correlated with conscious decisions happens a full 7 seconds before the conscious decision is registered by the person making the decision.

In the comments from this post - Joshua writes:

Google images has taught me that I have several false views. Here are some questions that I asked and my interpretation of the answers:

Q: Is endurantism or perdurantism true?
A: Perdurantism

Q: Is the pointy view of simples true?
A: Yes

Q: Is there a God?
A: Yes and he is Muslim.

You can verify that these are the correct interpretations of the answers yourself.

I decided to go and ask Google Images Joshua's questions. Google images has spoken to me, and I concur with Joshua's interpretation of the Google Image answers. You can verify these. Here they are.

Q: Is endurantism or perdurantism true?















Q: Is the pointy view of simples true?














Q: Is there a God?

This might be a stronger way to frame the argument for freewill and eternalism incompatibilism. It's more difficult to dismantle than the argument I presented here.

First let's do a warm-up exercise. Here's an argument for Incompatibilism.

An Argument For Incompatibilism

1. If determinism is true, then facts outside of your control entail your actions.
2. If facts outside of your control entail your actions, then you do not have freewill.
3. Therefore, if determinism is true, then you do not have freewill.
   

This one is just a warm-up exercise. I'm sure we've all encountered something like this argument. Now something similar to this argument can be run for eternalism and freewill incompatibilism.

An Argument that Freewill and Eternalism are Incompatible

1. If eternalism is true, then facts outside of your control entail your actions.
2. If facts outside your control entail your actions, then you do not have freewill.
3. Therefore, if eternalism is true, then you do not have freewill.

Motivation for (1)
If eternalism is true, then the universe is supposed to be like a big frozen block that (in some sense) always has and always will exist. One might think that the existence of this big frozen block is something that I could have absolutely no control over. Since my actions are a part of that big frozen block, one might think that the existence of the block entails my actions. So if eternalism is true, then there is something I have no control over (the existence of this block) and it entails my actions.

Motivation for (2)
Whatever motivates this premise in the first argument should motivate it here.

This argument seems a bit better to me than the previous argument. I'll say something more about it after I've thought more. (I haven't forgotten that I want to say something about the argument against Direct Reference Theory that I posted this morning.)

This seems like a very quick and hasty objection to direct reference theory from Michael Jubien, but it's interesting. Direct Reference Theory recall is the thesis that the meaning of a name is the thing to which it refers (and nothing more).

From the present perspective [direct reference] cannot be right. It is an indisputable modal fact that (the planet) Venus could have had some different parts. If the name 'Venus' simply contributed a physical object to the claims expressed with the help of that name, it would follow that some physical object could have had different parts. But we have apparently just seen that no physical object could have different parts. And all we needed to see it was a seemingly innocent and naturalistic conception of physical stuff. The falsity of direct reference theory is a very important consequence of these seemingly innocent and straightforward metaphysical considerations. (Michael Jubien. 2007. "Analyzing Modality" in Oxford Studies in Metaphysics: Volume 3: pp. 116-117)

Wow. So some kind of mereological essentialism leads to the denial of Millianism? Let's grant Jubien the consequences of his thought experiment and assume that no physical object could have different parts. I may lay that out in a future post soon, but for now I'll leave it as homework.

Michael Jubien's Argument Against Direct Reference

1. If Direct Reference theory is true, then 'Venus' in 'Venus could have had different parts' contributes a physical object to the proposition expressed and nothing more.
   
   
2. If 'Venus' in 'Venus could have had different parts' contributes a physical object to the proposition expressed and nothing more, then the sentence 'Venus could have had different parts' expresses a falsehood.
   
   
3. The sentence 'Venus could have had different parts' does not express a falsehood.
   
   
4. Therefore, it's not true that 'Venus' in 'Venus could have had different parts' contributes a physical object to the proposition expressed and nothing more.
   
   
5. Therefore, Direct Reference theory is not true.
   

That's my summary of the argument. Let me know if you think I'm being uncharitable. I've got a lot to say about this argument. This may involve laying out Jubien's thought experiment that alleges to show that physical objects could not have had different parts. This will all have to wait. I have to get to school.

Calling all metaphysicians! Would you like a simplified explanation of the multiverse interpretation of quantum mechanics? Would you like it to be presented to you using Super Mario World? Well, look no further.

Interesting Philosophical Applications
Metaphysical Modality
Some people think that the parallel universes in the multiverse hypothesis could play the role of Lewisian Possible Worlds. I have serious doubts about this. The main issue is that the multiverse that some physicists take seriously probably won't have enough universes to represent all metaphysical possibility.

The Fine-Tuning Argument for the Existence of God.
One possible response to The Fine-Tuning Argument for the Existence of God involves appealing to some kind of Multiverse Hypothesis. (Shameless plug - Check out Beebe's presentation of the Fine-Tuning Argument over at Young Philosophers)

Anyway, whatever your thoughts about the potential philosophical applications of the multiverse hypothesis - the video is pretty excellent. Enjoy.

[HT: Popsci.com - Checkout the full article here]

Thanks for the prodding in the previous post. Also, thanks to the anonymous comment with that list of readings. I knew there had to be literature on this.

Here is a quick and dirty formulation of the argument that eternalism is incompatible with some robust conception of freewill. Three different people have given me something like this argument. Ultimately, I think it's unsound.

Past Entails Future Argument

1. If eternalism is true, then there is some past fact that entails all of my future actions.
2. If there is some past fact that entails all of my future actions, then I do not have freewill.
3. Therefore, If eternalism is true, then I do not have freewill.
   

Motivation for One:
If eternalism is true, then for any of my future actions A, there will be some past fact at any past time of the form Andy will A. But if that's true, then there will be an entailment relation between that past fact and my future actions.

Motivation for Two:
The freewill literature is loaded with premises that fit this form. The idea is that if past facts entail what you do in the future, then what you do in the future is somehow not under your control. So, learning that the past facts entail what you do in the future should be sufficient to think that you're not free in the future.

My Main Problem:
Premise 2 - is only plausible if you're thinking like a presentist. If eternalism is true, it may be true that there is an entailment relation between some past fact and what you do in the future, but that past fact is made true by what you do in the future.

It's only true in the past that you will do some future action (according to the eternalist) because you're future self is there freely doing it in the future doing it.

If we learn that past facts entail our future actions, we're inclined to think that this entails we don't have freedom because we're inclined to think that we simply cannot have any control whatsoever over the past facts - but we can have control over the past facts if eternalism is true. It's our engrained presentist way of thinking that (I submit) inclines people to accept (2).

I've had some other versions of the argument presented to me, but I'm going to hold off for now.

In other news:
I've been reading Paul Boghossian's Fear of Knowledge and Timothy Williamson's The Philosophy of Philosophy. Interesting stuff in both. I may be posting something about this soon.

I thought it was obvious that libertarian freedom was compatible with eternalism, but I'm starting to realize that this isn't true across the board. Some colleagues here think that the two are likely incompatible. After talking with some folks at the Pacific APA, I discovered others who thought that the two are obviously incompatible.

I was also told that there isn't much in the literature on this - so I think I'm going to start posting some more thoughts on this.

First, let's get some terms out of the way.

Eternalism - The past, present, and future all exist and are equally real.

Libertarian Freewill - While there is little agreement about how to define freedom, the Libertarian Conception of freedom is supposed to be the robust notion of freedom that we're after. A cluster of concepts get thrown around as part of this robust notion including - could-have-done-otherwise, and not-caused-by-events-that-are-not-under-your-control.


(...more on this soon...)

I'm off to the Pacific APA in a couple of days. The following week is our spring break. I assume that I'll have decent internet access while in California, so posting should continue.

I'm commenting on a good paper on causation by Jonathan Matheson. Here's the abstract (pulled from the Pacific APA website).

Fragile Events and the Causal Relation by Jonathan Matheson In this paper I defend the claim that maximally-fragile-events are the proper relata of the causal relation. In other words, the things that are causes and effects are maximally-fragile-events alone. Call this thesis the Fragility Thesis. It is standard, though not uncontroversial, to take events as the relata of the causal relation; but it is highly contested that maximally-fragile-events alone play this role. In this paper I show how a counterfactual account of causation coupled with FT can provide a simple conceptual account that avoids the problems that have faced other counterfactual accounts of causation, as well as suggest that the consequences of adopting such an account are not as outrageous as they may seem.

This is a very interesting article in Seed Magazine that should definitely be of interest to LEMMings and anyone interested in metaphysics and philosophy of mind.

They're trying to build a model of the brain from the bottom up. Each neuron in the model is an IBM microchip. It's pretty fascinating stuff, and it may help shed some light on issues concerning the possibility of thinking machines and the possibility of reducing mental events to brain events.

I've been writing about Weak Substantivalism. Here are the two previous posts.

1. Two Kinds of Substantivalism
2. They Are There: Some Consequences for Weak Substantivalism

In the second post, I promised to post about some more counter-intuitive consequences of weak substantivalism. Here they are.

More Counter-Intuitive Consequences for Weak Substantivalism
Suppose we have an Andy-shaped bag of turnips. Suppose I pick out the region of space that it occupies with the word 'there' - Now consider proposition (C).

(C) I could have been there.

(C) seems true. If Weak Substantivalism is true, then (C) is committed to the claim that I could have been a bag of turnips - which is false.

If you think it is metaphysically possible for me to have been a bag of turnips (which it's not), we can press this point a bit more. Suppose I'm trying to make a point to the class about Weak Substantivalism, and I bring an Andy-Shaped Bag of Turnips to class to talk about the view. I can't decide where to stand. I'm about to stand to the left, but at the last minute decide to stand more toward the right. I place Andy-shaped bag of turnips in the spot where I was going to stand. Then an anvil drops from the ceiling and crushes the turnips. I say, "Whew, I'm glad I wasn't there. I almost was there." Consider (D)

(D) I was almost there

If Weak Substantivalism is true, then (D) says that I was almost a bag of turnips. That's definitely false. However, (D) is definitely true.

Note: All of this is on the assumption that weak substantivalists will collapse the location relation to the identity relation - In the comments to my previous post, I noted that weak substantivalists could collapse the location relation to the part-whole relation. However, I think many of the counter-intuitive consequences will remain.

A few days ago I laid out three views about the nature of space-time. Here's a quick summary of those views. For those of you who read the last post, you can probably skip down to the section titled "They are There"

Relationalism - Space is not real. Talk about space is reducible to talk about objects.

Strong Substantivalism
Space is a real, genuine entity. Objects that occupy space are real. Regions of space are distinct from the objects that occupy them.

Weak Substantivalism
Space is a real, genuine entity. And material objects JUST ARE regions of space.

In my last post, I briefly mentioned some counter-intuitive consequences for Weak Substantivalism, and I promised to offer more. Here are some more.

They are There
The pronoun ‘they’ is an indexical that when used in a particular context can pick out a group of objects. The pronoun ‘there’ is an indexical that when used in a particular context can pick out a region of space (and I assume a scattered region).

Suppose I use ‘they’ in a particular context to pick out Alex, Bobbi, Sam, and Jackson. Suppose I then use ‘there’ to pick out the region of space that I think they occupy. Here are some odd consequences of Weak Substantivalism.

First: My use of ‘they’ and ‘there’ are synonymous. That alone is a little odd.

Second: 'They are watching' is synonymous with 'There are watching'

Now of course this assumes some kind of direct reference theory meaning and compositionality of meaning. Those seem like OK assumptions to me, but suppose you're not convinced that these consequences are problematic. You might reject my linguistic assumptions, or (if you accept the assumptions) employ a Ways-Millian strategy.

If you are not worried about the above consequences, we can generate some consequences that may still seem problematic to you. I assume that, according to Weak Substantivalism, location relations would collapse into identity relations. Assuming that's true, consider the following proposition.

(B) They are there

It seems that if Weak Substantivalism is true, then (B) is an identity claim. It sure doesn't seem like an identity claim. Furthermore, assuming identity is necessary - (B) would be necessary. It certainly doesn't seem like a necessary truth. I've got some more counter-intuitive consequences for Weak Substantivalism. Stay tuned.

[Update: Here are some more counter-intuitive consequences for Weak Substantivalism]

Substantivalism is the view that space is a real entity. A lot of substantivalists believe that there are (at least) two fundamental kinds - there is space and there are the material objects that occupy space. These kinds of objects are distinct from each other and equally real

It’s easier to understand what Substantivalism is by contrasting it with the main rival, relationalism. Relationalism is the view that all talk about space can be reduced to talk about the material objects that many substantivalists think occupy space. We don’t need space, says the relationalist. Space is not a real entity. Anything you say that you think commits you to the reality of space can be translated into talk about relations between objects.

The relationalist looks at the substantivalist and says, “You’ve got too many kinds of things in your ontology! You’ve got this stuff called space (whatever that is), and you’ve got these material objects. I can get by with just material objects. So I will.”

There is a third way to go. I was a little misleading above. I suggested that Substantivalism is the view that there are two kinds of substances – space and material objects. It is probably best to call that view Strong Substantivalism. Strong Substantivalists keep space and objects. Relationalists think this is unnecessary, and they get rid of space. You could agree with the relationalist that both kinds of substances are unnecessary, but instead of getting rid of space, you could get rid of material objects and reduce them to talk about space. This view maintains that space is a real genuine entity. Let’s call this view Weak Substantivalism. According to Weak Substantivalism, what we call material objects just are regions of space, and space is the real thing.

Ted Sider briefly mentions these two substantivalist views in Four-Dimensionalism (page 110). The main pro for Weak Substantivalism over Strong Substantivalism is that it posits the existence of fewer kinds of things. Of course there are some cons. Some odd sentences of English end up being true – e.g. A region of space-time bounded out the door and barked at the mailman. I bet you can think of many more.

Sider doesn’t think these cons are enough to give up on the view. I want to add some more things to the con list. I doubt the cons that I want to add to this list would persuade Sider, but they strike me as even more odd than the con listed above. I’ll post those cons soon.

This is a pretty interesting article that was just posted on Slashdot. It summarizes some pretty cool findings that should be of interest to philosophers interested in issues related to epistemology and perception.

It turns out that there are many cases in which what people expect to see tricks them into thinking they saw it. For example, they had people watch someone throw two balls. The thrower then pretended to throw a third ball. Most people think they see a third ball that suddenly disappears in mid-air. They don't even realize that a third ball wasn't thrown. Their first thought is usually that the person somehow made the third ball disappear.

The research article that Slashdot summarizes is available here.

A couple of months ago Adam Arico over at Aspring Lemming noted that the TV Show Numb3rs gave a quick and dirty presentation of Searle's Chinese Room argument.

I decided to see if I could find the clip on YouTube - Here it is...



The clip cuts off short...but Adam says that the presentation fails to note that Searle's Thought Experiment is supposed to show that machines can't think.

I really want to find time to read Trenton Merrick's new book Truth and Ontology. It looks really interesting.

There are a wide range of metaphysical theses that are rejected because they are alleged to be incompatible with any kind of truth maker principle (or Truth Supervenes on Being Principle). Presentism is example of one of these views.

Defenders of these views usually try to find a way to explain how there views are compatible with some plausible truth maker principle.

Merricks takes a different tack. He denies the main candidate truth maker principles (including the Truth Supervenes on Being Principle).

Ben Caplan's review of the book just came out here.

In a recent post, I led up to the problem sentence for Nominalism.

(3) Red resembles Orange more than Square-ness.

The task for nominalism is to find an acceptable paraphrase for (3). (3) seems true, so whatever the paraphrase we come up with - it better be true too. We left off with (3**) as our candidate paraphrase.

(3**) The red-set resembles the orange-set more than the square-set

(Note: Red-set = set of all red things. Orange-set = set of all orange things. square-set = set of all square things.)

(3**) seems true. Imagine if you could have a God's eye view of all the red objects out there, and you could compare them side by side with the set of all the orange objects and the set of all the square objects. I bet you'd be inclined to say that this set (or grouping, or fusion, or whatever) of red things does resemble the set of orange things more than the set of square things.

My New Concern
I think my knowledge that (3) is true substantially different from my knowledge that (3**). First, I know (3) immediately and directly on the basis of perception. I can know that the property red that I am looking at right now is more similar to the property orange than it is the property square, merely by looking at any collection of a red, an orange, and a square object. It doesn't seem like my knowledge that (3**) works like that.

Now on the face of it, this looks like another one of those arguments where someone argues that one thing is not identical to another thing, because of the different ways in which the two things are knowable - (Think: Arguments from Introspection for Dualism - check out the bottom of page 14).

However, now I think the problem might run a little deeper and that there is another way to cast the argument. I think my knowledge that (3**) is true evidentially depends on my knowledge that (3) is true. How do I know that from a God's eye view the set of red things would resemble the set of orange things more than the set of square things? It's because I know that red resembles orange more than square.

Now, does that lend more support to the claim that (3**) cannot be an adequate paraphrase of (3)?

One version of nominalism holds that properties just are sets of things. There is no abstract universal red-ness. There just is a set of red things. The problem is that ordinary sentences of English look like they are talking about something that could only be something like a universal. There is no talk of sets.

Consider the following three sentences.

(1) The ball is red
(2) Red is a color
(3) Red resembles orange more than square-ness

Each of these appears to be talking about a property, and proponents of abstract universals maintain that their view makes more sense of the truth of (1)-(3) than nominalism.
Nominalism can handle (1) pretty easily, by offering an acceptable paraphrase.

(1*) The ball is a member of the red-set.

Apparent talk about universals turns into talk about the the ball, and how that ball is a member of some particular set. No universal talk is required.
Paraphrasing (2) is a bit trickier since it seems that red-ness is referred to in the subject slot, but nominalists have offered (2*)

(2*) All things that are members of the red-set are members of the colored-set.

Again, (2*) gets rid of talk about universals. All we have in (2*) is talk about particular objects and sets.
It's when we get to (3) that Nominalists have difficulties. (3*) is clearly unacceptable.

(3*) All things that are members of the red-set resemble all things that are members of the orange-set more than things that are members of the square set

Why is (3*) unacceptable? Because (3) is true, but (3*) is false. A red square does not resemble an orange goldfish more than a yellow square. That's enough to falsify (3*), and since you can't translate a true sentence to a false sentence and have succeeded in preserving the meaning - we have an unacceptable paraphrase.
For a while, I thought that nominalists actually might have a good translation of (3). I thought that the nominalist could translate (3) as...

(3**) The red-set resembles the orange-set more than the square-set.

I thought that you might be able to talk about resemblance relations between properties as resemblance relations between the actual sets.

I'm now worried about this...More on that in a moment...

When I teach personal identity in Intro and Metaphysics, I often have a student suggest that what it takes to have the same person across time is for the persons to have the same DNA structure.

A good response to this has always been to point out that identical twins have the same DNA structure, but are not the same persons. That won't work anymore. According to this article, we've discovered that we were wrong in thinking that identical twins have identical DNA structures.

Of course, I think there is still a pretty decent counterexample that would involved identical twins in the neighborhood. It turns out that identical twins differ only slightly in their DNA structure. So, imagine we discovered that there were twins who lacked those slight differences. I take it they wouldn't be the same person. So the counterexample, isn't completely undermined - but we do need to run it using nearby possible worlds. We can't rely on something that's actually true.

That seems interesting and worthy of note.

A common view in philosophy is that counterfactual conditionals with impossible antecedents are all vacuously true. But I'm very worried about that view. There are several counterfactuals with impossible antecedents that seem false. Here are some examples.

Counterfactuals involving Metaphyical Claims
Consider Metaphysical Nihilism, the thesis that there are no composite objects (just simples). According to Nihilism, composition doesn't occur. Suppose you think that metaphysical facts about composition are necessarily true. Under that assumption if Nihilism is false, then (1) is a false counterfactual with an impossible antecedent. If Nihilism is true, then (2) is a false counterfactual with an impossible antecedent.

(1) If Nihilism were true, then composition would occur. (seems false)

(2) If Unrestricted Composition were true, then there would be no composition.

If you think that Metaphysical Facts about composition are not necessarily true, then you should think that (3) is a false counterfactual with an impossible antecedent.

(3) If Nihilism were necessarily true, then composition would occur. (seems false)

Any way you go on the answer to the Special Composition Question, and any way you go concerning the modal status of composition facts - we can generate a false counterfactual with an impossible antecedent.

Counterfactuals Involving Math and Geometry
Here's another fun one...

(4) If triangles had exactly four sides, then the sum of the angles of a triangle would equal 30 degrees.

(False, right?)

However...
I also have some sympathy toward the view that counterfactuals with impossible antecedents are vacuosly true. I can post about that later. I can also post about why I think this matters.

A lot of materialists will admit that there are some kinds of entities that are a little more difficult to make sense of within a materialist ontology. For example - propositions. Here's an argument for immaterialism that I encountered that seems to be aimed at materialists who would accept the existence of propositions.

I've encountered this argument before, but I recently came across it in a dialogue written by Keith Yandel. I think it's an interesting argument, so I decided to try and reconstruct it as carefully as I could. Here it is.

An Argument Against Materialism

1. Some propositions are necessarily true.
2. It is possible for there to be a world with no material entities.
3. If (1) and (2), then it is possible for a proposition to be true in a world without material entities.
4. Therefore, it is possible for a proposition to be true in a world without material entities.
5. If it is possible for a proposition to be true in a world without material entities, then propositions are not material entities.
6. Therefore, propositions are not material entities.
7. If propositions are not material entities, then materialism is false.
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8. Therefore, materialism is false.
   

I've got some thoughts on this argument, but I'm going to mull it over for a bit. If anyone cares to comment - the thread is open.