Here I explain when and why simplicity is a theoretical virtue.* [*Based on: “When Is Parsimony a Virtue?” Philosophical Quarterly 59 (2009): 216-36.] 1. Two Questions About Simplicity Almost everyone in both science and philosophy agrees that “simplicity is a theoretical virtue”: other things being equal, simpler theories should be preferred to more complex theories. But very few of these people have any idea

I’m way out of my depth here. What would it mean for abstract objects to be real or unreal? Is unreal the same as imaginary?

If something is real, we can make propositions describing it, and be correct or incorrect. We can apply categories and logic to it.

But we can be correct or incorrect about imaginary things, too. “Harry Potter has a scar on his forehead” is true, but it isn’t about a real person, it is about a character from fiction. “Socrates had a big nose” could be cashed out in observations about a historical figure, while the description of Harry Potter gets cashed out by reading Rowling's canonical fiction. Harry Potter the person isn’t real, but Harry Potter the fictional character is real. Santa Claus is not a historical figure, but a cultural ... construction? Product? Entity? A character from a story?

What follows from assuming x is real, or x is unreal? What sort of evidence will give us clues?

Physical objects seem real because we can manipulate them. Johnson refutes Berkeley by kicking a rock.

A few things seem true because their logical negations lead to contradictions. Are they real because we can’t manipulate them?

Is an accusation of unreality just a disguise for questions about the referents of propositions, like “the present king of France is bald?” No such person exists, he isn’t real, so the statement is not a proposition.

Is the English language real? I don’t really know what that means.

Is there a prima facie reason to exclude the possibility that concrete things do not exist, but abstract things do? Every time we look closely at something that appears to be concrete, it always seems to turn out to be an abstraction -- an illusion created by a confluence of events happening at a much smaller scale.

Even when you get down to atoms and quantum fields, all we can really talk about is the statistical patterns we observe when we arrange events in certain ways.

Is it inconceivable that it's abstractions all the way down? Need there be a concrete base layer?

I'm pretty confused by this. Isn't the most obvious understanding of parsimony just the following?

Suppose that theories are sets of propositions and that a theory is true only if all of the propositions within it are true. Then, it just follows that if you add any new proposition to a theory whose truth would not be entailed by the already-included propositions, that additional proposition decreases the probability that the theory is true all-else-being-equal because there is some chance that the additional proposition is false even if all the already-included propositions are true.

If so, then shouldn't we just understand parsimony to be such that a less-parsimonious theory is committed to a set of additional propositions with an all-else-being-equal relatively-higher chance that one of those additional propositions is false even if the already-included (or shared, see below) propositions are all true, with a more-parsimonious theory being committed to a set of additional propositions with an all-else-being-equal relatively-lower chance that one of them is false even if the already-included (or shared) propositions are all true?

The reasoning for such being just that including such propositions decreases the probability that the theory is true all-else-being-equal. I don't get what's supposed to be puzzling about this, even (or perhaps especially) for philosophical theories.

Does this mean that you should always prefer the most parsimonious theory? Well, no. Even if parsimony decreases the probability that a theory is true all-else-being-equal, all else is rarely equal. You could (and usually do) have (other) evidence which increases the probability of the theory with the additional proposition more than the inclusion of the additional proposition would decrease it. In other words, the chances that the additional proposition is true given the evidence could be higher than the chance that the proposition is false even if all the other propositions are true.

If so, then to say that nominalism is more parsimonious than realism is just to say the following: once you factor out the set of shared propositions that both nominalism and realism are committed to, the additional set of propositions that realism is committed to has a higher chance of including at least one false proposition all-else-being-equal even if all the shared propositions are true compared to the additional set of propositions that nominalism is committed to. This could be because realism commits itself to propositions concerning the existence or behavior of entities that nominalism does not commit themselves to, and so either commits itself to more additional propositions or additional propositions that have relatively-higher chance of being false.

Then, to say that we should reject realism in favor of nominalism because nominalism is more parsimonious is to say that nominalism has an overall higher probability of being true in part because it commits itself to additional propositions with an all-else-being-equal relatively-lower chance that one of them is false even if all the shared propositions are true. I'm again not sure why this picture of parsimony isn't sufficient to capture what's being talked about in the debate and why it might plausibly be a reason in favor of nominalism over realism.

P.S. The reason why you don't have any reason to believe the nothingism is because if there is nothing then there are no reasons. So, if you had any reason to believe nothingism, that would in fact be a greater reason to reject nothingism, which is just to say that no consideration can ever favor accepting nothingism over rejecting it. Since reasons are just considerations that favor certain actions, beliefs, etc., there can be no reason which favors nothingism.

Nothingism also entails that there are no propositions (or anything like them), so no parsimony, so again parsimony can never favor nothingism.

Doesn't Bayes' Theorem also support the claim that simpler theories are more probable a priori since since the intrinsic probability of any theory plus an additional proposition equals the intrinsic probability of that theory multiplied by the intrinsic probability of that additional proposition? So adding any proposition that has an intrinsic probability lower than 1 to any theory reduces the probability of that theory and as a result, other things being equal, theories containing more propositions - one possible measure of simplicity/complexity of a theory - are less intrinsically probable (and thus less probable overall).

I would add that simplicity not only only matters when the theory can account for the data but it must also cohere best with neighboring fields of inquiry. You should only put a lot of weight on a priori simplicity if the theory is so wide/general that there's no or very few conditions on the theory set by commitments you have to surrounding fields of inquiry.

So if you can account for common sense judgments about abstract objects in a nominalist way and that coheres best with surrounding theories then you should adopt the nominalist view on the basis of simplicity.

This method would have the best outcome in development of a worldview in terms of taking account of the data and having the fewest adjustable parameters.

I think you can get away with merely assuming you have to have *some* prior probability distribution over all possible theories (or at least distinguishable outcomes). The fact your probability sums to one forces you to start assigning lower probabilities to theories at some point. Simplicity is just a bad way to say gets a higher probability in your initial distribution. Sure you might assign high probability to grue based theories rather than green based theories initially but at some point you have to start assigning the theory that has grue_3milAD really low probability.

In other words, there is no evidence that there is some objective notion of simplicity and all we are seeing is the fact that in fact that we judge it unlikely that the universe turns out to be a way we judge unlikely...and that conditionalization works.

I think all of these considerations result in the conclusion that the parsimony of utilitarianism is a virtue. In terms of the first point, I think this is just a meta point--we have some reason to expect reality to be simple. We know from science that most of the ways reality could turn out to be it isn't (most possible laws of physics don't exist). Thus, this should make us somewhat hesitant to accept new entities into our ontology.

I'm a paid subscriber and have been wanting to talk to you about just this issue. So I hope you'll answer/discuss. I begin by discussing a particular scientific domain, which may not interest you. However, I think it may be useful to have a specific example rather than remaining in generalities.

I have conducted research on a phenomenon called Erotic Target Identity Inversion, in which some men are sexually aroused by the idea of being an instance of the kind of person/thing to whom they are attracted, and may subsequently develop the desire to become that kind of person/thing. The best studied example is men sexually aroused by the fantasy of being a woman (this is called autogynephilia), some of whom develop gender dysphoria, or the wish to become a woman. Similar phenomena also seem to occur in men with more unusual sexual interests. Some men attracted to amputees are sexually aroused by the fantasy of being amputees (apotemnophilia), and some of these seek amputations.

Back to parsimony. It feels to me that Erotic Target Identity Inversion Theory likely accounts for both a subset of men seeking sex changes and all men seeking amputations of healthy limbs. But several other hypotheses have been offered to account for either gender dysphoria or limb dysphoria. Importantly, these hypotheses apply only to one or the other of gender dysphoria and limb dysphoria, not to both. Erotic Target Identity Inversion Theory accounts for both and is in this sense more parsimonious.

Is the claim that Erotic Target Identity Inversion Theory is more parsimonious and in that sense better than competing theories justified?

I’m way out of my depth here. What would it mean for abstract objects to be real or unreal? Is unreal the same as imaginary?

If something is real, we can make propositions describing it, and be correct or incorrect. We can apply categories and logic to it.

But we can be correct or incorrect about imaginary things, too. “Harry Potter has a scar on his forehead” is true, but it isn’t about a real person, it is about a character from fiction. “Socrates had a big nose” could be cashed out in observations about a historical figure, while the description of Harry Potter gets cashed out by reading Rowling's canonical fiction. Harry Potter the person isn’t real, but Harry Potter the fictional character is real. Santa Claus is not a historical figure, but a cultural ... construction? Product? Entity? A character from a story?

What follows from assuming x is real, or x is unreal? What sort of evidence will give us clues?

Physical objects seem real because we can manipulate them. Johnson refutes Berkeley by kicking a rock.

A few things seem true because their logical negations lead to contradictions. Are they real because we can’t manipulate them?

Is an accusation of unreality just a disguise for questions about the referents of propositions, like “the present king of France is bald?” No such person exists, he isn’t real, so the statement is not a proposition.

Is the English language real? I don’t really know what that means.

Re: Nominalism vs Realism

Is there a prima facie reason to exclude the possibility that concrete things do not exist, but abstract things do? Every time we look closely at something that appears to be concrete, it always seems to turn out to be an abstraction -- an illusion created by a confluence of events happening at a much smaller scale.

Even when you get down to atoms and quantum fields, all we can really talk about is the statistical patterns we observe when we arrange events in certain ways.

Is it inconceivable that it's abstractions all the way down? Need there be a concrete base layer?

edited Mar 12I'm pretty confused by this. Isn't the most obvious understanding of parsimony just the following?

Suppose that theories are sets of propositions and that a theory is true only if all of the propositions within it are true. Then, it just follows that if you add any new proposition to a theory whose truth would not be entailed by the already-included propositions, that additional proposition decreases the probability that the theory is true all-else-being-equal because there is some chance that the additional proposition is false even if all the already-included propositions are true.

If so, then shouldn't we just understand parsimony to be such that a less-parsimonious theory is committed to a set of additional propositions with an all-else-being-equal relatively-higher chance that one of those additional propositions is false even if the already-included (or shared, see below) propositions are all true, with a more-parsimonious theory being committed to a set of additional propositions with an all-else-being-equal relatively-lower chance that one of them is false even if the already-included (or shared) propositions are all true?

The reasoning for such being just that including such propositions decreases the probability that the theory is true all-else-being-equal. I don't get what's supposed to be puzzling about this, even (or perhaps especially) for philosophical theories.

Does this mean that you should always prefer the most parsimonious theory? Well, no. Even if parsimony decreases the probability that a theory is true all-else-being-equal, all else is rarely equal. You could (and usually do) have (other) evidence which increases the probability of the theory with the additional proposition more than the inclusion of the additional proposition would decrease it. In other words, the chances that the additional proposition is true given the evidence could be higher than the chance that the proposition is false even if all the other propositions are true.

If so, then to say that nominalism is more parsimonious than realism is just to say the following: once you factor out the set of shared propositions that both nominalism and realism are committed to, the additional set of propositions that realism is committed to has a higher chance of including at least one false proposition all-else-being-equal even if all the shared propositions are true compared to the additional set of propositions that nominalism is committed to. This could be because realism commits itself to propositions concerning the existence or behavior of entities that nominalism does not commit themselves to, and so either commits itself to more additional propositions or additional propositions that have relatively-higher chance of being false.

Then, to say that we should reject realism in favor of nominalism because nominalism is more parsimonious is to say that nominalism has an overall higher probability of being true in part because it commits itself to additional propositions with an all-else-being-equal relatively-lower chance that one of them is false even if all the shared propositions are true. I'm again not sure why this picture of parsimony isn't sufficient to capture what's being talked about in the debate and why it might plausibly be a reason in favor of nominalism over realism.

P.S. The reason why you don't have any reason to believe the nothingism is because if there is nothing then there are no reasons. So, if you had any reason to believe nothingism, that would in fact be a greater reason to reject nothingism, which is just to say that no consideration can ever favor accepting nothingism over rejecting it. Since reasons are just considerations that favor certain actions, beliefs, etc., there can be no reason which favors nothingism.

Nothingism also entails that there are no propositions (or anything like them), so no parsimony, so again parsimony can never favor nothingism.

Doesn't Bayes' Theorem also support the claim that simpler theories are more probable a priori since since the intrinsic probability of any theory plus an additional proposition equals the intrinsic probability of that theory multiplied by the intrinsic probability of that additional proposition? So adding any proposition that has an intrinsic probability lower than 1 to any theory reduces the probability of that theory and as a result, other things being equal, theories containing more propositions - one possible measure of simplicity/complexity of a theory - are less intrinsically probable (and thus less probable overall).

Or am I mistaken?

I would add that simplicity not only only matters when the theory can account for the data but it must also cohere best with neighboring fields of inquiry. You should only put a lot of weight on a priori simplicity if the theory is so wide/general that there's no or very few conditions on the theory set by commitments you have to surrounding fields of inquiry.

So if you can account for common sense judgments about abstract objects in a nominalist way and that coheres best with surrounding theories then you should adopt the nominalist view on the basis of simplicity.

This method would have the best outcome in development of a worldview in terms of taking account of the data and having the fewest adjustable parameters.

edited Mar 12I think you can get away with merely assuming you have to have *some* prior probability distribution over all possible theories (or at least distinguishable outcomes). The fact your probability sums to one forces you to start assigning lower probabilities to theories at some point. Simplicity is just a bad way to say gets a higher probability in your initial distribution. Sure you might assign high probability to grue based theories rather than green based theories initially but at some point you have to start assigning the theory that has grue_3milAD really low probability.

In other words, there is no evidence that there is some objective notion of simplicity and all we are seeing is the fact that in fact that we judge it unlikely that the universe turns out to be a way we judge unlikely...and that conditionalization works.

I think all of these considerations result in the conclusion that the parsimony of utilitarianism is a virtue. In terms of the first point, I think this is just a meta point--we have some reason to expect reality to be simple. We know from science that most of the ways reality could turn out to be it isn't (most possible laws of physics don't exist). Thus, this should make us somewhat hesitant to accept new entities into our ontology.

I'm a paid subscriber and have been wanting to talk to you about just this issue. So I hope you'll answer/discuss. I begin by discussing a particular scientific domain, which may not interest you. However, I think it may be useful to have a specific example rather than remaining in generalities.

I have conducted research on a phenomenon called Erotic Target Identity Inversion, in which some men are sexually aroused by the idea of being an instance of the kind of person/thing to whom they are attracted, and may subsequently develop the desire to become that kind of person/thing. The best studied example is men sexually aroused by the fantasy of being a woman (this is called autogynephilia), some of whom develop gender dysphoria, or the wish to become a woman. Similar phenomena also seem to occur in men with more unusual sexual interests. Some men attracted to amputees are sexually aroused by the fantasy of being amputees (apotemnophilia), and some of these seek amputations.

Back to parsimony. It feels to me that Erotic Target Identity Inversion Theory likely accounts for both a subset of men seeking sex changes and all men seeking amputations of healthy limbs. But several other hypotheses have been offered to account for either gender dysphoria or limb dysphoria. Importantly, these hypotheses apply only to one or the other of gender dysphoria and limb dysphoria, not to both. Erotic Target Identity Inversion Theory accounts for both and is in this sense more parsimonious.

Is the claim that Erotic Target Identity Inversion Theory is more parsimonious and in that sense better than competing theories justified?