Trade logic: Objects are sampleable

All objects are sampleable

I mentioned earlier in passing that in trade logic, all things are sampleable. As I put it, "all variables are ultimately instantiatable".

Things can be finite sets of objects with some probability distribution over them. They can be trivially sampleable, such as single objects, where sampling them always gives the same object. It's even possible that they may measureable collections that have no distinct individuals, from which one selects measured extents.

And the time has come to nail down how Trade Logic is to do sampling (selection).

Population bets

Built-in predicate pick01

For a population to be sampled, we need some sort of random input, and it can't be vague where to get the random or how to use it. The purpose of pick01 is to provide the random parameters that sampling will use.

(pick01 +A) binds A to a real number between 0 and 1, lower-inclusive. Theoretically, A has infinite precision. In practice, precision should be provided lazily. There may need to be some provision against allowing requests for precision to tie up the system.

Settling population bets

I'll call a bet whose formula uses pick01 (explicitly or implicitly) a population bet. Population bets are useful for propositions that can easily be resolved for individuals but less easily for distributions.

Population bets that are trying to be resolved1 can pick particular individuals to resolve. Then they can settle probabilistically on the basis of that. It's basically using statistics.

The procedure for selecting an individual is to:

• independently choose a value for each pick01 directly or indirectly included in the proposition.
• Using those values, assess the issue's truth or falsity. (The Bettable selectors logic below should ensure that this step works)
• Repeat as wanted. We sample with replacement; for simplicity and generality, there is no provision for not looking at the same individual again.
• Using statistical logic (outside the scope here), settle the bet (maybe sometimes just partly settle it)

Selector bets

Of course randoms on the unit interval are not the only kind of random selection one might want. We have to build all sorts of selectors from them. At the same time, we want selection to be uniquely resolved. It won't do for a given selector to select more than one individual for the same randoms, or to select no individual at all.

So I introduce a different sort of bet: selector bets. They are bets that a given selector "works OK".

Any predicate that has only outputs can be the basis of a selector bet. In my current thinking, for each such bet, every output of the predicate would be associated with an equivalence predicate. That's needed so we have a principled way to distinguish individuals.

Unlike issues, the bet is asymmetric and its interpretation is adversarial: One side (challengers) tries to pick values for pick01 that they think give no result or too many results. The other side is betting that no such problems arise. I haven't fleshed out the exact rules for this.

best redux

It seems that I didn't adapt epsilon enough when I borrowed it as best. It doesn't make a sampleable output. Rather, its output is the set of all the most suitable objects in the universe. That's not neccessarily finite, much less measureable. So there's no good general distribution over that. It would be paradoxical if there were.

So best needs another parameter: a sampleable collection of objects. That can be any object in Trade Logic. This parameter will generally be quite boring; often it's simply the whole universe of discourse. Nevertheless, it's needed.

So =(best Pred From To)=² is now true just if:

• Pred is a unary predicate
• To is the part of From that satisfies Pred as well as anything else in From does

NB, I have not called To a "member" of From, as if From were a set. In general, From is a collection. To should be collection in general too. And we don't want to need an identity predicate as another parameter. And finally, we don't try to resolve "sub-part boundaries" here; those are addressed via structurally similar bets that replace calls of best with suitable particularizations. Nevertheless, I am not 100% sure I have supported collections adequately in this mechanism.

Footnotes:

¹ When a bet is "trying to be resolved" is beyond the scope here, but I have some ideas on the topic.

² I took the opportunity to put the arguments into in/out order.

Trade Logic: Missed a type ctor

Trade Logic: Missed a type constructor

I forgot one type constructor before, the one to construct the type of predicates. It was covered by "One of the exposed primitive types", but inadequately. It needs to can express a predicate's type parameters.

Rather than mixing applications and literal lists, or requiring list at the beginning of each list, I will use low-quote and write:

,(pred . Args)

where pred is the symbol pred and Args is a type (named or literal) augmented by mode annotations. This type accepts any predicate whose inputs are all equally or less strict than the respective parts of Args and whose outputs are all equally or more strict than the respective parts of Args. It would also reject predicates that had no equivalent mode.

For example, the type , (pred type +type) would accept/reject various predicates:

Arg1 type	Arg2 type	Disposition
type in	type out	Accept
thing in	type out	Accept
thing in	thing out	Reject
thing in	type out	Accept
thing in	type in	Reject
type out	type out	Reject

I may need to do more for the interaction of the mode system and the type system here.

Pseudo-quantification in Trade Logic

Pseudo-quantification in Trade Logic via best

Previously

Earlier I introduced Trade Logic. It's a form of logic that I designed to be suitable for connecting prediction markets. It is logic that "lives" within the system, not in individual traders' analyses.

Not quantification

Trade Logic doesn't use quantification as such. Quantification would complicate the mode system, which is already adequate to distinguish free and bound variables. I also have theoretical concerns about vacuous quantification: If there were no objects that the system could refer to, the relative valuation of (forall x (p x)) and (some x (p x)) would be reversed.

The built-in predicate best

Instead of directly using quantification, Trade Logic uses the built-in predicate best, which is adapted from Hilbert's epsilon operator. best(A,B) is true just if:

• B is a unary predicate
• A satisfies B as well as anything else does

I'll expand a little on that last point. That's not the same as "satisfies B". best can be true if no value could satisfy B. In Trade Logic, best can also be true in fuzzy ways:

• If B can only be satisfied to a certain degree, and A satisfies B to that degree, then best(A,B) is true (crisply, 100%)
• if A satisfies B to a certain degree, but a lesser degree than some other value would, then best(A,B) is fuzzily true

Quantifiers can be expressed in terms of best, as they could with epsilon. In standard notation, we would write:

\begin{equation} \forall x p(x) \Leftrightarrow best(x, \neg p(x)) \rightarrow p(x) \end{equation} \begin{equation} \exists x p(x) \Leftrightarrow best(x, p(x)) \rightarrow p(x) \end{equation}

In Trade Logic, the respective formulas are:

(if (best +x (lambda (Y) (not (-p Y)))) (-p -x))

and

(if (best +x -p) (-p -x)) 

Note the addition of modes, and note that "p" is always an in mode. It must be bound outside this (sub)formula.

The behavior of best

A yes of any issue of the form (best +A -B) can be converted to a yes of (& (-X +A) (-B -A)) for any predicate X. Similarly, a no of (& (-X +A) (-B -A)) can be converted to a no of (best +A -B).

X may select A in an arbitrary way, but it will never be better at satisfying B than (best +A -B) is.

This works because no trader would make this conversion unless he got a better price after the conversion. This ensures that the price of best issues is always in fact the highest price. Effectively, existentially quantified issues are always as high or higher in price than each of their particular instances, and universally quantified issues as low or lower than their particular instances.

Best is adapted from epsilon

Best is adapted from Hilbert's epsilon operator. (Also see here) Epsilon (not best) classically has the following properties:

• It is a function
  • Usually it comes with an axiom of extensionality, ie that the function's result is unique.
• It takes one argument, a predicate (as a formula)
• If that predicate can be satisfied, it returns an object that satisfies the predicate
• If that predicate can't be satisfied, it returns any object at all.
• With it, one can build statements equivalent to other statements that contain universal and existential quantifiers.
• The quantifiers all and some can be expressed using it.

\begin{equation} \forall x p(x) \Leftrightarrow p(\varepsilon(x, \neg p(x))) \end{equation} \begin{equation} \exists x p(x) \Leftrightarrow p(\varepsilon(x, p(x))) \end{equation}

But Trade Logic doesn't contain functions. What Trade Logic has are fuzzy predicates¹. So we use best instead.

Footnotes:

¹ When I first saw Epsilon, I got the impression that it wasn't suitable for this reason. But I was wrong, it just needed to be adapted.

Trade Logic: Clarification on guarded conjunction

Clarification on guarded conjunction ("Dynamic")

Previously

Earlier I introduced Trade Logic and I said that the well-formedness criterion for formulas could be dynamic in certain limited circumstances. Essentially, if a subformula is conjoined with an appropriate type-check on an object, the object is statically treated as that.

Clarification

I forgot to distinguish this sort of conjunction from the conjunction that "and" implements. It's really not the same thing.

Simple conjunction can't do this right. Simple conjunction is built from 2 decompositions of $1. But there's no reasonable way to decompose the half-box in which the guard fails. Doing so would mean that the type-incorrect subformula was used despite being type-incorrect.

guard

Instead, these guarded conjunctions are headed by guard. Like:

(guard (accepts-type X Y) (X Y))

It decomposes like this. Note that one cannot further decompose the half-box where the guard fails.

Trade Logic 2

More on Trade Logic

Previously

Earlier I introduced Trade Logic. It's a form of logic that I designed to be suitable for connecting prediction markets. It is logic that "lives" within the system, not in individual traders' analyses.

I planned to define standard as an exercise. But when I started to write it, I realized that there were a number of preliminaries that I needed first.

I also realized I had to change a few things. In the places where this post differs from the previous, it supersedes it.

About definitions

Definitions cannot assert

Definitions in Trade Logic deliberately cannot assert facts. And it would be disastrous if they could. If traders could "prove" things by defining them to be true, the whole system would collapse and be useless.

Instead, definitions simply expand to parameterized formulas. Formulas cannot assert facts.¹

A "classical" definition of standard would have implicitly asserted that there is one unique predicate standard. But that implicit assertion is banned in Trade Logic. We (deliberately) wouldn't be able to construct a formula that asserts that.

Instead, we would define a predicate that is true just if its argument "behaves the same as" the predicate standard. That is, is-standard would be true if its argument is a predicate that satisfies the axioms of Internal Set Theory as standard would.

NB, this won't (and shouldn't) imply that is-standard's argument is defined in the system. It doesn't neccessarily have a global name in the system.

Definitions cannot raise error

Definitions in Trade Logic are not allowed to error. If they could, that would wreak havoc on the system.

They can be undecidable, which causes no great problems for wise bettors. They are also total, meaning that each of their arguments can be of any type. So our definition won't be able to lean on a strong typechecking mechanism.

Definitions are statically simply type-correct

However, there is a weak typechecking mechanism in Trade Logic. It is a well-formedness condition for formulas and predicates and thus for bettable issues. I'm largely borrowing the mechanism from the simply typed lambda calculus. But the simply typed lambda calculus is functional while Trade Logic is relational, and Trade Logic manages modes as well. So I adapt it slightly.

The exposed primitive types are:

• thing
• type
• predicate

The type definitions are:

thing

Everything is a thing. For expressive purposes, either:

• A variable.
• Any object of any of the other types.
• Extensibly, any other literal the system accepts.

type

Either:

• One of the exposed primitive types
• A type literal naming a definition of a type in the system
• A list of types
• A dotted list of types
• Dynamically, anything satisfying is-type

call

Not an exposed type. Of the form (P . Args) where:

• P is a predicate
• Args is a (possibly empty) tree of things, ie a Herbrand term.

acceptable call

Not an exposed type. Either:

• A call where Args is statically accepted by P. Ie, where we can prove that beforehand and using only local information.
• Dynamically, a call satisfying (accepts-argobject P Args)
• Dynamically, a call satisfying both
  • (accepts-type P T)
  • (satisfies-type Args T)

wff

Not an exposed type. Either:

• Any issue (ie, predicate with empty argtree)
• A combination of wffs as defined in the previous post.
• An acceptable call.

predicate

Either:

• A predicate literal naming a built-in predicate in the system
• A predicate literal naming a definition of a predicate in the system
• A lambda term - a call where:
  • P is the built-in literal pred
  • Args is a list of 2 elements
  • The first argument is a wff
  • The second argument is a mode-spec
  • The whole is mode-correct, as defined in the previous post.
• Dynamically, anything satisfying is-predicate

Type acceptance

Type acceptance

A predicate P accepts a type T just if T is the type of P's parameter list or is subsumed by it.

The built-in predicate accepts-type

(accepts-type A B) is a binary predicate. It has two modes:

• (accepts-type - -)
• (accepts-type - +)

It is true just if:

• A is a predicate
• B is a type
• B is a type that A accepts. In the second mode, B is exactly the given type of A's argobject.

The built-in predicate satisfies-type

(satisfies-type A B) is a binary predicate. It has one mode:

• (satisfies-type - -)

It is true just if:

• B is a type
• A is of type B.

The built-in predicate accepts-argobject

(accepts-argobject A B) is effectively the conjunction of (accepts-type A C) and (satisfies-type B C)

Dynamic checking

Sometimes we don't know a thing's type statically, but we still want to use it or reason about how to use it. This often occurs when we use higher-order logic.

The clauses that say "Dynamically" are interpreted as allowing formulas to be conjunctions of type-checking operators and sub-formulas that require a specific type. Such formulas are interpreted as false if the type is incorrect, rather than erroneous. It is as if the type-check was examined first and the erroneous clause was skipped. (But in general, Trade Logic formulas do not have a particular order in which sub-terms are examined except as dictated by the mode system)

Definitions, redone

Types and predicates can be given names, ie defined in the system. Some trivial constructions of predicates deliberately can't be given names because it would be silly:

• The predicate literals - they already have names.
• The dynamic construction. "This predicate is something that satisfies is-predicate" would be pointless.

I might require a checkable proof for places in a construction that require static correctness. That would add an extra argument to acceptable-call and the pred call.

A named predicate can be bet on just if it accepts the empty type (null).

Footnotes:

¹ In particular, Trade Logic does not have functions, it has predicates. This rules out Skolemization.

Superpositionality answers Heidegger

Heidegger's famous question

Martin Heidegger famously asked "Why is there something rather than nothing?" There have been many attempts to answer it, but every single attempt I have seen has been wrong in some important respect. I will propose an answer (skip ahead if you can't wait).

But first I will try to convince you that the existing answers don't work, and then lay some groundwork for my answer.

Some sources

How do I know that I've covered the field of attempted answers well? Why should you believe I have? As opposed to me inventing strawmen, or covering some attempts but not "the good ones".

So here are some sources that already surveyed the attempted answers:

• Nothingness (Stanford Encyclopedia of Philosophy) More of a flowing discussion than a list of answer candidates. Section 1 is relevant, the other sections less so.
• The biggest Big Question of all (Shermer)
  1. God
  2. Wrong Question
  3. Grand Unified Theory
  4. Boom-and-Bust Cycles
  5. Darwinian Multiverse
  6. Inflationary Cosmology
  7. Many-Worlds Multiverse
  8. Brane-String Universes
  9. Quantum Foam Multiverse
  10. M-Theory Grand Design
• Why Is There Something Rather Than Nothing? The Only Six Options (Patton)
  1. The universe is eternal and everything has always existed.
  2. Nothing exists and all is an illusion
  3. The universe created itself
  4. Chance created the universe
  5. The universe is created by nothing
  6. An transcendent being (God) created all that there is out of nothing.

Survey of attempted answers

Answers that only push the question back one step farther

"God made it all"

Covering what

Shermer's answer (1), Patton's answer (6)

The failure

The circularity of this has already been hashed to death. 'Nuff said.

Spontaneous generation (Science version)

Covering what

Michael Shermer's answers 3 thru 10 all fall into this category. Patton's (3) and (4) seem to belong in here too.

The problem with it

Usually this is tied to quantum phenomena, often to quantum fluctuations of the (hypothesized) inflation field, as in Shermer's (9).

But look at it thru the lens of the original question. "Why does anything exist?" leads directly to "Why does this something, the inflation field, exist? (if it does)" and "Why do these particular rules for it, that it can fluctuate and inflate, exist?" And the space and time that the quantum fluctuations inflate in are somethings too, so we have to ask why they exist too.

Note that if any of these question have ordinary answers, like "spin foam pre-existed and became the space-time", this merely pushes the question back one step, "Why does the spin foam exist?".

One can ask similar questions of the other science spontaneous generation answers. I won't bore you or myself by ringing changes on this theme across all of the science-y answers.

So this entire pattern of answer is a non-answer that can never truly answer "Why does anything exist?"

Pet peeve

The science answers are an example of a behavior that annoys me. The speaker (not neccessarily Shermer) associates his answer with Science, and even with Deep Important Hard Science. But it doesn't answer the question. Bedazzled with the Deep Science-y Goodness of his answer, he doesn't even really try. He seems to feel that since Science came out of his mouth, he must therefore have spoken wisdom and truth and need trouble himself no further.

Spontaneous generation (Philosophical version)

What it covers

Patton's (5), and Shermer's (2). "Nothingness is unstable".

The problem with it

A "nothingness" that has laws or properties has somethings - the laws or properties. Again, re-ask the original question. "Why does this something, the instability or the rules by which it is unstable, exist?"

Probabilistic generation

What it covers

Discussion in Nothingness

Even if "Nothing exists" [is] the uniquely simplest possibility [], why should we expect that possibility to be actual? In a fair lottery, we assign the same probability of winning to the ticket unmemorably designated 321,169,681 as to the ticket memorably labeled 111,111,111.

The problem with it

Here the "something" assumed in the answer is much more subtle. Why should this cosmic roll of the dice cause a world to exist? I roll dice all the time in tabletop RPGs. This has yet to cause the things I roll up to pop into actual existence. Why is this cosmic roll of the dice different? What "breathes life" into it?

Whatever thing breathes life into it constitutes a subtle something that's assumed by the answer. So again we can ask, "Why does that something exist?"

Another issue

The Stanford Nothingness notes that the assumption that there's one empty world (nothingness) can be questioned. Is there at most one empty world?

Not too far off though

Nevertheless, this approach does hint at the answer that I give.

Answers that try to change the question

"Why not?"

What it covers

Discussion in Nothingness

The problem with it

When it's put as simply as this, it's obvious that it's just dodging the question. Next I'll look at some more sophisticated attempts to undercut the coherence of the question.

The universe has always existed

What it covers

Patton's (1)

The problem with it

It's a sleight of hand. It focusses on a tangential element of the question and then removes that element. The essential question goes unanswered.

Ordinarily when we speak of something existing, there was a moment at which it came into existence, or at least a time-frame in which it did. But that's a misleading intuition pump; easy to imagine, because it's commonplace, but really doesn't fit the question. The question wasn't "When did stuff come into existence?" or even "Why, when it came into existence, did it do so?"

If the universe has always existed and stretches backwards in time forever, well then, the question becomes why that backwards stretch:

• contains something rather than nothing.
• itself exists

"Wrong Question"

What it covers

Shermer's answer (2) at first glance appears to fall here (but it mostly won't)

"Somethingness" is the natural state of things.

The problem with it

Saying that somethingness more natural than nothingness is saying that there is some meta-rule that favors somethingness over nothingness. Well, that meta-rule is a something. So ask again, why doe that something it exist? So on closer inspection, this answer is mostly a species of Spontaneous generation (Philosophical version).

But one part of the issue that belongs under this subheading, not there. Having asked "Why does the meta-rule exist", one might answer the same way again: "Its existence - its somethingness - is more natural than its non-existence". Ie, appeal again to the meta-rule itself. So re-raising the original question does not immediately defeat this answer. The fixpoint here is in positive territory, as it were, not in negative territory. Before, in the answers that only push the question back one step farther, the fixpoint was in negative territory.

This answer still has serious problems.

• It's entirely circular; not neccessarily false but it doesn't resolve anything.
• One needs to ask why this fixpoint of meta-rules is selected as "real" and capable of self-support, when other fixpoints are not. What breathes life into somethingness-is-natural and not into others? NB, this question is "why choose this?", not "why does anything exist?"
• And not least, Occam's Razor. I've ignored it thru this whole discussion so far, but it's important. Occam's Razor is completely contrary to somethingness-is-natural and has enormous empirical and intuitive support.

"Everything exists" is as simple as "Nothing exists"

What it covers

Discussion in Nothingness.

As far as simplicity is concerned, there is a tie between the nihilistic rule "Always answer no!" and the inflationary rule "Always answer yes!". Neither rule makes for serious metaphysics.

The problem with it

"Everything exists" not the same as "Something exists". So this argument fails to put "Something exists" on an equal footing with "Nothing exists".

Answers that deny experience

Nothing exists

What it covers

Patton's (2).

The problem with it

C'mon, you've noticed things existing. Of course you have.

Even if everything you've ever seen is an illusion, you still have two somethings to ask about: the illusion and yourself.

Experiencing nothingness

Experiencing nothingness itself

If nothing existed, what exactly would you notice?

Of course you wouldn't see big dark shadows and hear the hollow echoes of sounds you make. You wouldn't have eyes to see them, or ears, or a brain to appreciate the experience. You would notice exactly nothing.

Experiencing both

So if you experienced normal existence and nothing at the same time, what would you see? Normal existence. Add the experience of existence and the experience of nothingness (none) together and what do you get? The contribution from the nothingness is always zero, so you get exactly the experience of existence.

This gives a broad hint of my answer, but it will wait until I tie a few loose ends up.

Experiencing everythingness

Earlier, we saw that "Everything exists" is as simple as "Nothing exists". So Occam's Razor is as favorable to everythingness as it is to nothingness. If my answer is to be reasonable, it can't ignore everythingness just because Heidegger didn't mention it.

So let's ask, in exact parallel: If everything existed, what exactly would you notice?

Of course you wouldn't see a big pink elephant and then a leprechaun dancing with a poodle in a kaleidoscope. That's a chaotic parade of some the individual things you could possibly see, but it's not experiencing everything at once. Not by a long shot.

What would you experience, if you experienced everything at once, with nothing at all left out?

Well, you couldn't localize it. You couldn't understand it, or pin it down as being some particular thing. You couldn't even pin it down as some particular thing that it wasn't.

What about your eyes and your brain? That's the most bizarre part. You'd have every possible eyes and every possible brain. In everythingness, every question of the form "Does X exist?" gets the answer "yes". "Does brain X exist?" (yes) "Does brain X, additionally having the property of being your very own thinking organ, exist?" (yes)

So I think that what you'd experience in everythingness would be completely formless and indistinct. Essentially the same as the experience of nothingness. And I think that if you experienced normal existence and nothing and everything at the same time, it would again add up to just normal experience.

Superpositionality

Briefly

Superpositionality or "quantum superposition" considers that a system is "really" in a state that is an overlapping of all of the possible configurations. By "really", we mean in the view of someone outside the system - in the birds-eye view, as it were.

Co-incidentally, Shermer's answer (7) is about Many-Worlds (M-W), which implies superpositionality. He didn't seem to notice the connection to his question.

M-W also implies something else that I will use in my argument: superpositions are parsimonious. M-W is extremely Occam-friendly. This seems to surprise people who don't understand M-W.

The question assumes too much

Earlier, I chided answers that try to change the question. So I have to be careful not to commit the same sin myself. Nevertheless, if a question assumes too much, it's OK to challenge those assumptions. Just play fair.

There is one very subtle assumption in the question. "Why is there something instead of nothing?" ¹.

The question assumes that one or the other is the case. It's an obvious and mundane assumption, but one that doesn't work in such a basic philosophical question. I propose that it's one assumption too many. I'm going to remove that one assumption and then answer the question.

The answer

So I remove the assumption of "something instead of nothing". Now the question is harder to put into words, but it's something like "Why is the state (or superposition of states) of anything existing what it is?" With that removed, I can answer:

Because there is no possible more parsimonious model than this: A superposition of all the existential states.

So the model is a superposition of all the somethingness state(s), the nothingness state, and the everythingness state. By the principle of parsimony, this is preferable to any model that could answer the original question.

And what would/do we experience when we are in that superposition? Normal existence. Even if we include an everythingness state. So it reproduces normal experience.

Why it is a satisfactory answer

• It is well motivated by the principle of parsimony
• It adds up to normality, a property that good theories have.
  • It doesn't deny the fact of existence.
• It doesn't just push the question back one step. There are no stray rules or entities whose existence we now ought to ask about.
• It does change the question, but only in a scrupulously fair way.

Misunderstanding averted

I'm not saying that superpositionality gives rise to physical existence. That would be wrong in several ways.

• It's not that superpositional principles "act on" the nothingness and generate things out of it. The nothingness remains completely intact, as it were.
• Superpositionality just doesn't do that. It does not create things.
• And if I said that, I'd be sinning again one of my own pet peeves. By no means am I trying to dazzle anyone with Deep Science. Quite the contrary, I'm building my explanation from reasoning that I hope will already be familiar to my readers.

Footnotes:

¹ The same assumption may occur in a more subtle form in "Why does anything exist?" - which can be taken as constrasting to the possibility of that thing not existing, ignoring the possibility of both being the case.

Prosperity defined?

Prosperity defined? (Maybe)

I recently read a paper called Information, Utility & Bounded Rationality, by Pedro A. Ortega and Daniel A. Braun.

They define what they call "free utility", akin to free energy in thermodynamics. They propose that free utility can be used as a variational principle as in control theory, leading to bounded optimal control solutions and recovering some well-known decision theory results.

So they found a connection between decision theory and thermodynamics. And it looks to be a deep one.

Another thing I liked

Decision theory tends to start by neglecting the cost of making decisions. It adds it on later, as Value Of Perfect Information (VOPI) and bounded rationality. It tends to feel bolted on, heterogeneous.

Free utility OTOH feels like a homogeneous concept. If I had to give that concept a familiar name, it would be "prosperity".

Abstract of the paper

Perfectly rational decision-makers maximize expected utility, but crucially ignore the resource costs incurred when determining optimal actions. Here we employ an axiomatic framework for bounded rational decision-making based on a thermodynamic interpretation of resource costs as information costs. This leads to a variational "free utility" principle akin to thermodynamical free energy that trades off utility and information costs. We show that bounded optimal control solutions can be derived from this variational principle, which leads in general to stochastic policies. Furthermore, we show that risk-sensitive and robust (minimax) control schemes fall out naturally from this framework if the environment is considered as a bounded rational and perfectly rational opponent, respectively. When resource costs are ignored, the maximum expected utility principle is recovered.