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 don't know if these words have particular meanings in the philosophical literature that deviates from their informal meanings (because I haven't read the relevant literature). If you have a better idea of that distinction than me, I'd be happy to hear it.
But given their informal meanings my assumption is that composites are just one sub-category of abstraction -- but are still clearly abstractions.
I thought they were distinct, even informally. Maybe I am being more formal than I thought.
My body is composed of organs, my organs composed of cells, my cells composed of molecules, those molecules composed of atoms, and the atoms of subatomic particles or something that the physicists are still investigating. None of these are abstractions, they are concrete composites. You can kick them.
An abstraction is an idea, a generalization, a description that applies to a class of objects but leaves out some particular details. You can’t kick them. Newtons's laws are abstractions that apply to masses without reference to other details about the mass. Numbers are abstractions of things you can count or compare their magnitudes, leaving out all the details that have nothing to do with counting or comparing lengths. Abstractions are idea you can think, which apply to some concrete objects and not to others.
It's a good amount of pedantic. Sorry for the length of this reply, I really tried to be concise!
The distinction as you draw it seems to be awfully close to "physical" vs "non-physical", which to me doesn't intuitively seem right. After all, in the article Huemer suggests even numbers might be concrete things (although I disagree with that).
> An abstraction is an idea, a generalization, a description that applies to a class of objects but leaves out some particular details.
Do we agree that the concepts, "body", "organs", and "left kidney", *as categories* are necessarily abstractions? After all, any given left kidney will be different than any other. Some are bigger, some smaller, some have tumors, etc.
Assuming we agree on that, that leaves open the question of whether a *particular* left kidney is an abstraction or a concrete thing. Or a particular chair, or a particular star.
To me, intuitively, concrete things should have identifiable, concrete properties -- how can a thing be concrete if you can't say anything definite about it?
Consider temperature. Is temperature concrete or an abstraction? I'd say it's clearly an abstraction, as temperature is *defined* as an average of discrete events (of a totally different sort!) happening at a much smaller scale.
But actually, the closer you look, the more it becomes apparent that many or most physical properties turn out to be macroscopic descriptions of microscopic "sums". "Smoothness" is a macroscopic description of a kind of average geometry at a small scale. "Hardness" (and solidity itself!) is a macroscopic description of the behavior of interacting electric fields at a molecular scale. Temperature, smoothness and hardness are all emergent properties of collections of objects to which those properties do not apply. Spatial extent itself may even be this sort of property if you look at a small enough scale.
These are all simplifying abstractions (in my opinion) which are possible only as a result of the central limit theorem -- that many independent (effectively) random events will, when added together, tend towards a unimodel normal distribution. This is also why a property like general intelligence (another abstraction) follows a normal distribution -- it is the sum of the effects of millions of genes and millions of experiences, each of which has a tiny effect.
And then there are all sorts of questions and paradoxes about the existence of composite objects. Think "the left kidney of Theseus". Questions about whether and when they can be said to have definite, finite boundaries. It seems implausible to me to say an object with infinite extent is concrete, so where exactly is the boundary of a star? Questions about whether concrete things can suddenly pop into or out of existence, or be in some sort of fuzzy (opposite of concrete!) quasi-existing state -- did that chair from Ikea exist before you assembled it? When it got old and you tossed it into a bonfire, did it continue to exist, or did it cease at some point?
I guess when it all boils down, my thesis is that *all macroscopic/composite objects* are abstract manifestations of the central limit theorem in various forms. In other words, I think each *particular* kidney, chair or star is just (which isn't necesarily to say "merely") the central (probablistic) mass of a multivariate normal distribution of microscopic things.
I should add that I don't think concrete things can be built from abstract things, and so the question left to me is: Does there need to be something concrete at the bottom?
(I'm kind of just riffing here, so I could conceivably be argued out of much of this.)
“ Huemer suggests even numbers might be concrete things.”
If so, wouldn’t they be abstract and concrete at the same time? 2 can’t be concrete if we don’t know 2 whats. Two horses are concrete. How is 2 concrete without … something for there to be two of? 2 is an abstraction of counting when there are two countable things.
“Do we agree that the concepts, "body", "organs", and "left kidney", *as categories* are necessarily abstractions?”
Yes, “body” is abstract until a specific body is referred to. But “my body” is never abstract. It has all the details filled in, though we may not be aware of them.
“Assuming we agree on that, that leaves open the question of whether a *particular* left kidney is an abstraction or a concrete thing. “
No, I don’t think so. .What would it mean for it to be an abstraction? An abstraction of what? An abstraction is a simplification, it leaves out the details and so can apply to a class of objects, rather than a specific object.
“To me, intuitively, concrete things should have identifiable, concrete properties -- how can a thing be concrete if you can't say anything definite about it?”
A concrete object has all the details; whether or not we can name them doesn’t matter. They are identifiable in principle, but not necessarily identified. An abstraction will be missing details. For example , abstractions usually lack a location. Where is “tree”, unless we mean a specific tree?
“Consider temperature. Is temperature concrete or an abstraction? “
It is an abstraction of whatever it is the temperature of. My temperature is an abstraction of me?
“Questions about whether and when they can be said to have definite, finite boundaries” does not seem to affect their abstractness or concreteness. How would it? The Pacific Ocean has indefinite boundaries. It is no less concrete. Boundaries are a concept we impose on it. Concreteness is itself. It is probably comfortable having depths, wavy surfaces, and edges that move around and are hard to define. That is allowed. My idea of the Pacific Ocean can be abstract. The Pacific Ocean is not.
“ Questions about whether concrete things can suddenly pop into or out of existence, “ seem separate from their status as abstract or concrete.
“ -- did that chair from Ikea exist before you assembled it?” Existence is an odd predicate, and a separate topic. I am not making claims about existence. But the parts of the chair are concrete, and the chair, when it exists, is concrete. The idea of the chair is abstract, and doesn’t require that any parts exist.
“ each *particular* kidney, chair or star is just (which isn't necesarily to say "merely") the central (probablistic) mass of a multivariate normal distribution of microscopic things.”
This seems like poetry to me, not something that could be interpreted literally. But perhaps I don’t understand. Are the microscopic things concrete or abstract, or shall we dispense with the distinction?
“I don't think concrete things can be built from abstract things”
Here we agree, with the exception perhaps that maybe thoughts are concrete, and in a way thinking of an abstraction would create something concrete, the thought.
“Does there need to be something concrete at the bottom?”
I think so.
Abstractions are incomplete descriptions or perspectives, concretes are the things described or observed. Abstractions are classes, concretes are members of classes. It’s like the difference between a photograph and the subject of the photograph, or a sentence and the topic of a sentence.
We have some trouble observing things at the smallest scale we know about. All the concretes we can deal with easily are composites. Does logic prevent it from being composites all the way down? There's no way to be certain, is there? Some things are beyond our current abilities of observation, and if we improve those, that just means there will be more things to observe suggesting more things we can’t yet observe.
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?
Isn’t there an important distinction between abstractions and composites?
I don't know if these words have particular meanings in the philosophical literature that deviates from their informal meanings (because I haven't read the relevant literature). If you have a better idea of that distinction than me, I'd be happy to hear it.
But given their informal meanings my assumption is that composites are just one sub-category of abstraction -- but are still clearly abstractions.
I thought they were distinct, even informally. Maybe I am being more formal than I thought.
My body is composed of organs, my organs composed of cells, my cells composed of molecules, those molecules composed of atoms, and the atoms of subatomic particles or something that the physicists are still investigating. None of these are abstractions, they are concrete composites. You can kick them.
An abstraction is an idea, a generalization, a description that applies to a class of objects but leaves out some particular details. You can’t kick them. Newtons's laws are abstractions that apply to masses without reference to other details about the mass. Numbers are abstractions of things you can count or compare their magnitudes, leaving out all the details that have nothing to do with counting or comparing lengths. Abstractions are idea you can think, which apply to some concrete objects and not to others.
I apologize if this seems pedantic.
It's a good amount of pedantic. Sorry for the length of this reply, I really tried to be concise!
The distinction as you draw it seems to be awfully close to "physical" vs "non-physical", which to me doesn't intuitively seem right. After all, in the article Huemer suggests even numbers might be concrete things (although I disagree with that).
> An abstraction is an idea, a generalization, a description that applies to a class of objects but leaves out some particular details.
Do we agree that the concepts, "body", "organs", and "left kidney", *as categories* are necessarily abstractions? After all, any given left kidney will be different than any other. Some are bigger, some smaller, some have tumors, etc.
Assuming we agree on that, that leaves open the question of whether a *particular* left kidney is an abstraction or a concrete thing. Or a particular chair, or a particular star.
To me, intuitively, concrete things should have identifiable, concrete properties -- how can a thing be concrete if you can't say anything definite about it?
Consider temperature. Is temperature concrete or an abstraction? I'd say it's clearly an abstraction, as temperature is *defined* as an average of discrete events (of a totally different sort!) happening at a much smaller scale.
But actually, the closer you look, the more it becomes apparent that many or most physical properties turn out to be macroscopic descriptions of microscopic "sums". "Smoothness" is a macroscopic description of a kind of average geometry at a small scale. "Hardness" (and solidity itself!) is a macroscopic description of the behavior of interacting electric fields at a molecular scale. Temperature, smoothness and hardness are all emergent properties of collections of objects to which those properties do not apply. Spatial extent itself may even be this sort of property if you look at a small enough scale.
These are all simplifying abstractions (in my opinion) which are possible only as a result of the central limit theorem -- that many independent (effectively) random events will, when added together, tend towards a unimodel normal distribution. This is also why a property like general intelligence (another abstraction) follows a normal distribution -- it is the sum of the effects of millions of genes and millions of experiences, each of which has a tiny effect.
And then there are all sorts of questions and paradoxes about the existence of composite objects. Think "the left kidney of Theseus". Questions about whether and when they can be said to have definite, finite boundaries. It seems implausible to me to say an object with infinite extent is concrete, so where exactly is the boundary of a star? Questions about whether concrete things can suddenly pop into or out of existence, or be in some sort of fuzzy (opposite of concrete!) quasi-existing state -- did that chair from Ikea exist before you assembled it? When it got old and you tossed it into a bonfire, did it continue to exist, or did it cease at some point?
I guess when it all boils down, my thesis is that *all macroscopic/composite objects* are abstract manifestations of the central limit theorem in various forms. In other words, I think each *particular* kidney, chair or star is just (which isn't necesarily to say "merely") the central (probablistic) mass of a multivariate normal distribution of microscopic things.
I should add that I don't think concrete things can be built from abstract things, and so the question left to me is: Does there need to be something concrete at the bottom?
(I'm kind of just riffing here, so I could conceivably be argued out of much of this.)
“ Huemer suggests even numbers might be concrete things.”
If so, wouldn’t they be abstract and concrete at the same time? 2 can’t be concrete if we don’t know 2 whats. Two horses are concrete. How is 2 concrete without … something for there to be two of? 2 is an abstraction of counting when there are two countable things.
“Do we agree that the concepts, "body", "organs", and "left kidney", *as categories* are necessarily abstractions?”
Yes, “body” is abstract until a specific body is referred to. But “my body” is never abstract. It has all the details filled in, though we may not be aware of them.
“Assuming we agree on that, that leaves open the question of whether a *particular* left kidney is an abstraction or a concrete thing. “
No, I don’t think so. .What would it mean for it to be an abstraction? An abstraction of what? An abstraction is a simplification, it leaves out the details and so can apply to a class of objects, rather than a specific object.
“To me, intuitively, concrete things should have identifiable, concrete properties -- how can a thing be concrete if you can't say anything definite about it?”
A concrete object has all the details; whether or not we can name them doesn’t matter. They are identifiable in principle, but not necessarily identified. An abstraction will be missing details. For example , abstractions usually lack a location. Where is “tree”, unless we mean a specific tree?
“Consider temperature. Is temperature concrete or an abstraction? “
It is an abstraction of whatever it is the temperature of. My temperature is an abstraction of me?
“Questions about whether and when they can be said to have definite, finite boundaries” does not seem to affect their abstractness or concreteness. How would it? The Pacific Ocean has indefinite boundaries. It is no less concrete. Boundaries are a concept we impose on it. Concreteness is itself. It is probably comfortable having depths, wavy surfaces, and edges that move around and are hard to define. That is allowed. My idea of the Pacific Ocean can be abstract. The Pacific Ocean is not.
“ Questions about whether concrete things can suddenly pop into or out of existence, “ seem separate from their status as abstract or concrete.
“ -- did that chair from Ikea exist before you assembled it?” Existence is an odd predicate, and a separate topic. I am not making claims about existence. But the parts of the chair are concrete, and the chair, when it exists, is concrete. The idea of the chair is abstract, and doesn’t require that any parts exist.
“ each *particular* kidney, chair or star is just (which isn't necesarily to say "merely") the central (probablistic) mass of a multivariate normal distribution of microscopic things.”
This seems like poetry to me, not something that could be interpreted literally. But perhaps I don’t understand. Are the microscopic things concrete or abstract, or shall we dispense with the distinction?
“I don't think concrete things can be built from abstract things”
Here we agree, with the exception perhaps that maybe thoughts are concrete, and in a way thinking of an abstraction would create something concrete, the thought.
“Does there need to be something concrete at the bottom?”
I think so.
Abstractions are incomplete descriptions or perspectives, concretes are the things described or observed. Abstractions are classes, concretes are members of classes. It’s like the difference between a photograph and the subject of the photograph, or a sentence and the topic of a sentence.
We have some trouble observing things at the smallest scale we know about. All the concretes we can deal with easily are composites. Does logic prevent it from being composites all the way down? There's no way to be certain, is there? Some things are beyond our current abilities of observation, and if we improve those, that just means there will be more things to observe suggesting more things we can’t yet observe.
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).
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.
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?