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How to Deduce that a Decision is Justifiable Chris Lang, UW-Madison, clang@students.wisc.edu

ABSTRACT: This paper represents one project in the modern endeavor to bring formal logic to practical use. Recognizing that many practical situations arise in which one would like know whether they should act as though a given statement is true, the logic presented here is restricted specifically to answering such questions. Without eliminating the practical usefulness of our logic, this restriction buys us some important advantages: it allows us to derive our rules and semantics purely from aspects of definitions (as one can in intuitionistic logic), and the rules include analogs of the law of excluded middle, the law of mass/energy conservation, Heisenberg’s uncertainty principle, and a generalized version of evolution by natural selection. It does NOT allow us to deduce that scientific laws as they have traditionally been defined are “really” true, but it DOES allow us to deduce that we should act as though they (or analogs of them) are true. The similarity of scientific laws to the theorems of this logic is not coincidental—we will argue that any successful project to justify decisions, whether scientific, theological or otherwise, must be isomorphic to the purely deductive, yet empirical, method demonstrated here (criticism of specific inductive alternatives will appear elsewhere).

Introduction

One important advantage of intuitionistic logic is that its rules can be justified purely on

the basis of definitions.i Decision-justification using other kinds of logic, ones for which one can

only justify the rules through proofs of soundness with respect to an assumed semantics and

definition of “well-formed formula”, must be premised on the assumption that the semantics

relate to reality in the right way. Thus, people who try to use such logics to resolve a

disagreement may find that it stems from a disagreement about what should be taken to follow

from what, and that this boils down to a disagreement about which semantics should be assumed.

Then, as in the dreaded “religious-style” debate, the only amiable recourse is to agree to

disagree. With intuitionistic logic, however, disputes about whether one claim follows from

another are purely verbal ones that can usually be remedied. For example, to dispute the

intuitionistic rule of “and introduction” is merely to dispute the meaning of “and”.

The remedy to verbal disputes is clear: Whenever one believes that a term is used

improperly in a proof, one is obliged to treat it as a homonym having a (perhaps never-before-

seen) meaning different from what we deem “proper”. To be formal, we might substitute a

subscripted version of the disputed term throughout the proof and the lemmas and definitions it

employs. So long as this subscripted version is used consistently, the dispute is resolved, since

the subscripted version is not bound by the same rules of “proper” usage as the unsubscripted

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one. The obligation to perform such a substitution comes from the fact that the validity and

soundness of an argument must be independent of how it is expressed (e.g. if we substituted the

word “and” for that of “if” and vice -versa throughout an otherwise brilliant proof and all the

definitions and lemmas it employs, the proof would remain as brilliant, only in an altered

language).

The danger in such substitution is that a proof will be useless to its reader if the terms of

its conclusion are (subscripted) ones they can’t use. This creates a potential disadvantage for

intuitionistic logic—if its definitions (and thus its rules) are taken to be complete, then most

people are liable to suspect that the term “not (intuitionistic)” means something quite different from

any normal usage of the term “not”, so any conclusion containing the term “not (intuitionistic)” is

useless to them. Since people generally tend to give incomplete definitions (and further explicate

them only when the need arises) anyway, one very natural way to reduce the impracticality of

subscripting is to consider one’s definitions as potentially incomplete, as ones that name

conditions that are either necessary or sufficient but not both. Any logic built like this on mere

aspects of definitions would also have potentially incomplete rules—not everything true would

have to be provable by them.

To give up on the quest for complete logics would rob intuitionistic logic of what makes

it interesting, since intuitionistic logic is differentiated from classical logic only in what it cannot

prove. However, where one claims to have justified a decision, it is only the soundness of the

logic employed the matters in evaluating this claim—its completeness is irrelevant—and the

attempt to make a complete logic for decision-justification would probably be impractically

ambitious anyway. Therefore, I will follow the recommendations described above, justifying

each rule purely on the basis of aspects of definitions, not even trying to construct complete

definitions or a complete logic. Incompleteness will not prevent us from constructing purely

deductive sound arguments that a given decision is justified.

For ease of reading, I will express the logic as a system of natural deduction rather than

as a set of axioms (although this is, of course, equivalent to a set of axioms). Taking a cue from

Hartry Field’s evaluativist epistemology,ii we will consider only statements of the form “To

<goal> we should act as though <decision-statement A> is true”, where the punctuation ‘<>’

signifies metavariables. More formal explication of aspects of definitions of the terms in this

form will be given shortly, but it may be helpful to offer some informal explication upfront: The

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“<goal>” may be a personal goal, an institutional one, a mandate of moral obligation, or

whatever standard there may be against which the quality of a decision is to be judged. To “act

as though a statement is true” means to do whatever the truth of that statement would entail one

should do (perhaps in addition to doing other things). If the truth or falsity of a statement would

have no impact on what one should do (i.e. if to act as though it were true would be the same as

acting as though it were false) then we will call that statement “irrelevant”. We will call all other

statements “decision -statements”. Thus, much as classical logic is inapplicable to ill -formed-

formulas like “Anger banana through”, so will logics of decision -justification be inapplicable to

irrelevant statements (including ill-formed-formulas).

At the start, we will entertain the possibility that, since different decision-makers may

pursue different goals, questions of relevance and justification may be relative to the goals of the

decision-maker. We shall eventually discover, however, that the consequences that follow from

the intersection of all goals entail that all goals have the same consequences. That is, much as

some statements are irrelevant, some goals (such as the goal “to fail”) are not pursuable, so many

that evaluativism turns out not to be relativistic.

The Justificatory Power of the Law of Excluded Middle

Let’s start with partial definitions of some common logical terms. Recall that partial

definitions merely pick out conditions that are necessary or sufficient (not both), thus the same

term may have multiple partial definitions, each of which further fixes the meaning of the term.

Here’s how these partial definitions can justify rules of logic:

SPECIAL FORM: The definition of “if…then” justifies lines of the form: “To <goal>, we should act as though if <decision-statement A>, then <decision-statement A>.” GENERAL FORM: The definition of “if…then” justifies lines of the form: “To <goal>, we should act as though if <decision-statement C> and <decision-statement A>, then <decision-statement A>.”

Commonly know as the rule of “assumption”.

The definition of “if…then” justifies following lines of the form: “To <goal>, we should act as though if <decision-statement C>, then <decision-statement B>.” with the line “To <goal>, we should act as though if <decision-statement C> and <decision-statement A>, then <decision-statement B>.”

Commonly known as the rule of “reiteration”

The definition of “if…then” justifies following lines of the form: “To <goal>, we should act as though if <decision-statement C> and <decision-statement A>, then <decision-statement B>.” with the line “To <goal>, we should act as though if <decision-statement C>, then if <decision-statement A>

Commonly know as the rule of “material implication introduction”.

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then <decision-statement B>.” The definition of “if…then ” justifies following any two lines of the form: “To <goal>, we should act as though if <decision-statement C>, then <decision-statement A>.” “To <goal>, we should act as though if <decision-statement C> and <decision-statement A>, then <decision-statement B>.” with the line: “To <goal>, we should act as though if <decision-statement C>, then <decision-statement B>.”

Commonly known as the rule of “material implication elimination” or modus ponens.

The definition of “and” justifies following any two lines of the form: “To <goal>, we should act as though if <decision-statement C>, then <decision-statement A>.” “To <goal>, we should act as though if <decision-statement C>, then <decision-statement B>.” with the line “To <goal>, we should act as though if <decision-statement C>, then <decision-statement A> and <decision-statement B>.”

Commonly known as the rule of “and-introduction”

The definition of “and” justifies following lines of the form: “To <goal>, we should act as though if <decision-statement C>, then <decision-statement A> and <decision-statement B>.” with the line: “To <goal>, we should act as though if <decision-statement C>, then <decision-statement A>.” and/or the line: “To <goal>, we should act as though if <decision-statement C>, then <decision-statement B>.”

Commonly known as the rule of “and-elimination”

To this we add partial definitions of “should” and “act for a go al”:

The definition of “acting for a goal” justifies following any lines of the form: “To <goal>, we should act as though if <decision-statement C> and <decision-statement A>, then <decision-statement B>.” “To <goal>, we should act as though if <decision-statement C> and <decision-statement A>, then not <decision-statement B>.” with the line “To <goal>, we should act as though if <decision-statement C>, then not <decision- statement A>.”

Commonly known as the rule of “not-introduction” or non-contradiction. Action cannot be premised on contradictory premises.

The definition of “should” justifies following any line of the form: “To <goal>, we should act as though if <decision-statement C>, then [not <statement A>] is not (fore)seeable.” with the line “To <goal>, we should act as though if <decision-statement C>, then <statement A>.”

One cannot be obliged to account for the unforeseeable.

The definition of “(fore)seeable” justifies following any line of the form: “To <goal>, we should act as though if <decision-statement C>, then <decision-statement A> is (fore)seeable.” with the lines “To <goal>, we should act as though if <decision-statement C>, then <decision-statement A> is predictatype and <decision-statement A>.”

An event is (fore)seeable if and only if destined and of the sort that could be (fore)seen if destined.

The definition of “predictatype” justifies following any line of the form: “To <goal>, we should act as though if <decision-statement C>, then (not <decision-statement A>) is predictatype.” with the line “To <goal>, we should act as though if <decision-statement C>, then <decision-statement A> is predictatype.”

An event and its negation must be equally predictatype, for to predict one is to predict the negation of the other.

As Aristotle pointed out thousands of years ago, one cannot “act as though” a decision -

statement is both true and false.iii Quantum physicists may ponder the claim that Schrodinger’s

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cat is (simultaneously) both dead and alive, but we must either choose to feed it or not— there is

no in between— so each of our actions must align with one possibility or the other (assuming the

possibilities are not irrelevant). Aristotle cited the philosophy of Heraclitus as an example of one

which rejects the law of non-contradiction. Heraclitean philosophy may seem self-consistent, but

Aristotle argued that, since it debilitates decision-making, use of the law of non-contradiction is

therefore justified. Allowing for the possibility of logics other than ones of decision-justification,

we merely come to the weaker conclusion that it is justified for logics of decision-justification.

The definition of “should” is even more powerful, although we employ here only that

aspect of it which entails that we cannot be obliged to do the impossible. Since we cannot be

obliged to act on knowledge we cannot have, if we cannot (fore)see the negation of a statement,

then we cannot be obliged to act as though that statement is false. Thus, to act as though it were

true cannot be a failure to act as we should. Therefore, if there is a way we should act, it cannot

be different from the way we should act if it were true, so the way we should act must be as

though the statement were true.

To understand this result, it may be helpful to anticipate the proof we will give later that

all decision-statements must be predictatype. If the negation of a statement is not (fore)seeable it

must be either because that statement is not predictatype or because its unnegation is

(fore)seeable. Generally, people have no difficulty accepting that we should act as though the

unnegation is true in the latter case— it is the other one that creates confusion. But in that other

case, since the unnegation would not be predictatype, it must be irrelevant. The accuracy of

predictions about non-predictatype events may be relevant to our success, but they cannot be

relevant to how we should act, since we cannot be obliged to incorporate unattainable knowledge

into our decision-making. As a concrete example, suppose the interference of omnipotent

malicious demons were not predictatype. Then, even though such interference might impact our

success, it must be irrelevant to how we should act, since one cannot act as though an omnipotent

malicious demon will unpredictably interfere— to do so would be to ignore the demon (since the

average anticipation of the unpredictable cannot be productive), which is no action at all. The

potential interference of such malicious demons is irrelevant, so we are justified both in acting as

though they will interfere and in acting as though they won’t. Either would entail the same

actions on our part since “acting as though <A>” simply means adding whatever <A> entails we

should do (which in either of these case is nothing extra) to our to-do list.

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Parentheses are added to the term “(fore)seeable” to indicate that it may refer to the

foreseeable future or seeable present as befits whatever it describes. The term “predictatype” is

to refer to what would be (fore)seeable if it were actual or destined.iv When applied to statements

about the present, “(fore)seeable” means detectable and “predictatype” means detectatype.

Detectable states of affairs are both actual and detectaype— that is, they are of the sort for which

it is physically possible that they may impact our experience (albeit perhaps indirectly). For

example, a colleague’s pain is detectable because it would impact our experience if she chose to

describe it to us. Examples of non-detectatype states of affairs would include those in logically

possible “other” worlds with which it is physically impossible for us to communicate, as

physicalists claim a “spiritual world” or “parallel dimension” would be. A predictatype event is

one for which something that determines whether it will (or does) occur is currently detectable.

Armed with these concepts, we can prove, as a lemma for future proofs, a version of what

is known as the rule of “not -elimination”. We will follow Lemmon’s tradition of representing

premises with numbers for convenience, and substitute the abbreviation “DJ:” for the phrase “To

<goal>, we should act as though”.

Let (I) be “[not not <decision-statement A>]“ and (II) be “[not <decision-statement A>] is (fore)seeable”. (1) DJ: if I and II, then [not <decision-statement A>] is (fore)seeable. By def. “if…then”, (AS) (2) DJ: if I and II, then [not <decision-statement A>] is predictatype and not <decision-statement A>. By def “(fore)seeable”, 1 (3) DJ: if I and II, then not <decision-statement A>. By def “and”, 2 (4) DJ: if I and II, then not not <decision-statement A>. By def. “if…then”, (AS) (5) DJ: if I, then [not <decision-statement A>] is not (fore)seeable. By def. “act/goal”, 3, 4 (6) DJ: if I, then <decision-statement A>. By def. “should”, 5

Lemma 1 justifies any line of the form: “To <goal>, we should act as though if <decision-statement C> and not not <decision-statement A>, then <decision-statement A>.”

Commonly known as the rule of “not-elimination” or the law of excluded middle.

Now that we have both introduction and elimination rules for “if…then”, “and” and

“not”, we can use DeMorgan’s laws to define “or” and derive the traditional “or” rules from this.

Thus, when reasoning about decision-justification, we can ground the whole of classical logic

purely in aspects of definitions (i.e. classical logic turns out to have the same justificatory power

as intuitionistic logic).

The definition of “or” justifies following any line of the form: “To <goal>, we should act as though if <decision-statement C>, then not [not <decision- statement A> and not <decision-statement B>].” with the line: “To <goal>, we should act as though if <decision-statement C>, then either <decision-statement A> or <decision-statement B>.”

Commonly known as DeMorgan’s laws

The definition of “or” justifies following any line of the form: Commonly known as DeMorgan’s laws

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“To <goal>, we should act as though if <decision-statement C>, then either <decision-statement A> or <decision-statement B>.” with the line: “To <goal>, we should act as though if <decision-statement C>, then not [not <decision- statement A> and not <decision-statement B>].”

DeMorgan’s laws

Earlier, I promised to more formally explicate aspects of the definition of “decision -

statement”. Rather than stipulate this definition, we will derive aspects of it from what we

already have. As our first aspect, we can prove from the definitions given above that all decision-

statements must be predictatype:

Let (I) be “<decision statement A> is not predictatype”, (II) be “(not <decision statement A>) is (fore)seeable” and (III) be “(not not <decision-statement A>) is (fore)seeable”. (1) DJ: if I and II, then (not <decision-statement A>) is (fore)seeable. By def. “if…then”, (AS) (2) DJ: if I and II, then (not <decision-statement A>) is predictatype and true. By def. “(fore)seeable”, 1 (3) DJ: if I and II, then (not <decision-statement A>) is predictatype. By def. “and”, 2 (4) DJ: if I and II, then <decision-statement A> is predictatype. By def. “predictatype”, 3 (5) DJ: if I and II, then <decision-statement A> is not predictatype. By def. “if…then”, (AS) (6) DJ: if I, then (not <decision-statement A>) is not foreseeable. By def. “act/goal””, 4, 5 (7) DJ: if I, then <decision-statement A>. By def. “should”, 6 (8) DJ: if I and III, then (not not <decision-statement A>) is (fore)seeable. By def. “if…then”, (AS) (9) DJ: if I and III, then (not not <decision-statement A>) is predictatype and true. By def. “(fore)seeable”, 8 (10) DJ: if I and III, then (not not <decision-statement A>) is predictatype. By def. “and”, 9 (11) DJ: if I and III, then (not <decision-statement A>) is predictatype. By def. “predictatype”, 10 (12) DJ: if I and III, then <decision-statement A> is predictatype. By def. “predictatype”, 11 (13) DJ: if I and III, then <decision-statement A> is not predictatype. By def. “if…then”, (AS) (14) DJ: if I, then (not not <decision-statement A>) is not foreseeable. By def. “act/goal””, 12, 13 (15) DJ: if I, then not <decision-statement A>. By def. “should”, 14 (16) DJ:<decision-statement A> is not not predictatype. By def. “act/goal”, 7, 15 (17) DJ: if <decision-statement A> is not not predictatype, then <decision-statement A> By “Lemma 1”

is predictatype (18) DJ:<decision-statement A> is predictatype. By “if…then”, 16, 17 Lemma 2 justifies any line of the form: “To <goal>, we should act as though if <decision-statement C>, then <decision-statement A> is predictatype.”

Thus, although logical positivists might have gone a bit overboard to brand claims about

the undetectable “meaningless”, it is nevertheless appropriate to make the weaker move of

pointing out that claims about the undetectable are “red herrings” in that they canno t participate

in any logic of decision-justification. Any attempt to apply any logic of decision-justification to

claims about the unpredictable must be susceptible to the same sort of complaint as attempts to

apply classical logic to statements like “Ange r banana through” — regarding classical logic, we

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complain that the statement is an ill-formed formula, in decision-justifying logic, we complain

that it is irrelevant to decision-making purposes.

This has some interesting consequences regarding statements about the past. If the world

were created just one moment ago, complete with (false) memories and other misleading records

of a past that never occurred, we would never be able to detect that such was the case. Thus, we

could not be obliged to take account of that fact in our decision-making, and the way we should

act if the past never occurred must be the same as the way we should act if it did. Therefore, any

sound logic of decision-justification must dismiss all claims about the past as irrelevant.

Perhaps we should convict a defendant because evidence (be it misleading or not)

currently exists, which we should expect to convince the defendant and/or others that the

defendant currently has or will have criminal nature, but it must be unethical to convict them on

the basis that they committed a crime in the past, since claims about the past must be

unknowable and therefore irrelevant to how we should act. Similarly, a decision to issue a stamp

of approval for a marketing campaign, construction project or medical treatment may be justified

on the basis that we currently face records, which (whether false or not) we should expect to

incline the campaign, project or treatment to succeed, but we cannot claim justification on the

basis that past campaigns, projects or treatments succeeded. Finally, although it may be that we

should act as though future consequences will be determined by present choices, it must be

unethical make a choice on the grounds that it has been forced by past ones, since we are obliged

to act as though the past never occurred— i.e. we should treat each present moment as a fresh

opportunity.

To elaborate on our semantics further, and explain why we should expect records (even

false ones) to influence the success of construction projects, medical treatments, and so forth

(thus permitting us to make justifiable decisions), I will introduce some new variations on

familiar concepts.

The Semantics of Decision-Justification Richard Dawkins extended the language of biological evolution to the realms of artificial

life and cultural evolution by introducing the concept of “memes”. v Much as species supposedly

evolve through the transfer of genes amongst their constituent organisms, cultures and artificial

species may be said to evolve through the transfer of memes amongst their members. As

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examples of memes, consider the many techniques transferred among the members of a culture

(through instruction, example-setting, etc.) for tying one’s shoelaces. If one such technique is

easier to pass along or if adoption of it empowers the practitioner to relay it more effectively,

then it will proliferate more than alternative techniques and will dominate the culture.

Languages, religious rituals and the manufacture and use of tools are all memes that can be said

to have evolved because they empowered those who used them to be more influential (by

increasing their lifespan or efficiency or wealth, etc.) than those who did not, much as effective

genes empower organisms who have them to produce more offspring than do organisms who

have less effective genes.

Here we will consider an even broader extension of Darwin’s theory. Call all properties

sets of “ xemes”, and call that of which they are properties “xeme -hosts”, or “ hosts” for short.

Thus, by definition, anything detectable must be a hosting of a set of xemes. We need the term

“xeme”, in addition to “property” because, although some properties may be xemes, others may

be infinite sets of xemes (not individually detectable), just as, while some geometric regions may

be points, others may be infinite sets of points. Like sets of memes, sets of xemes are analogous

(although not perfectly so) to sets of genes. Sets of genes and memes are two kinds of sets of

xemes (an individual gene may also contain more than one xeme). Hosts are likewise analogous

to organisms (and all organisms are hosts), but there is an important limit to the analogy: since

xemes have properties, all xemes are also hosts (whereas genes are not organisms). Each xeme

plays multiple roles.

Going further, just as

we may divide

organisms into

species and meme-

hosts into societies,

we shall divide

xeme-hosts into

“xeme -host-groups”,

or “ groups” for short.

Since groups have

properties, they also

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are hosts, but at higher hierarchical levels than the hosts that compose them. Thus, each group

plays multiple roles.

This hierarchical structure may be seen in the following diagram above where arrows

represent xeme transfers. Groups 2, 3 and 4 are shown as component hosts of group 1. The

“ environment“ of group 1 co ntrols the rate at which xemes are exchanged between them. The

environment of group 2 may include groups 3 and 4 in addition to that of group 1. Thus, groups

can also play the role of environment as well as that of group and host— which role is relevant to

the claim at hand depends upon which group is the subject of the claim.

The following table provides examples of how this language aligns with that of several

disciplines:

Much as the distinction between the concepts of host and group sets up the relation of

“ composition”, that between the concepts of xeme and host sets up the relation of “ essence”, and

that between the concepts of xeme and group sets up the relation of “ predication”. vi For X to be

predicated of group Y means to assert that a certain majority of its components host the set of

xemes corresponding to X. Let me emphasize that xemes assigned to Y through predication are

hosted by the components of Y, not by Y itself. As the composition of a group may vary over the

course of its existence, various different sets of xemes may be predicated of it, but its essence

(what it hosts itself) will, by definition, always remain the same. Thus, all predictions regarding

the futures of things that change can be understood as future-tense predications. For example, the

"In(field),.. ...a (group)... ...is a collection of (hosts),..

...that pass or share (set of xemes)...

...with different success depending upon their (environment)."

Biology Species Organisms Genes Climate, ecosystems, available resources (etc.)

Sociology Society Minds Ideas (methods, beliefs and prejudices)

Language, evidence of truth, ambient advertising (etc.)

Computer Science

Computer Circuits Files, strings and other software

Programming and operator input

Psychology Brain Neural structures Images, ideas and decisions

Precepts, ambient drugs and social pressures

Chemistry Solution, cloud, crystal, surface

Electrons and nuclei Energy states Ambient fields and particle streams

Physics/ Astronomy

Fluid, field or assembly

Particles/objects Movements (flow) Surrounding particles/objects

Art Work Components, parts, sequences, etc.

Themes The properties of perception for the audience/artist

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prediction that a lake will freeze solid may be understood as a claim that a certain majority of the

molecules that compose that lake will share the property of having velocity within a certain

range. The subject of any such prediction may be understood as a group (in this case, the lake is

a group of molecules which are groups of atoms which are groups of quarks and leptons and so

forth) and the predicate as a kind of set of xemes to be held by (predicated of) the hosts in that

group (in this case, the kind of set of xemes is one of velocities within a certain range).

Our analog to the standard problem of determining the boundaries of species is one of

determining the essences of groups. Take a lake, for instance. Given the way we’ve separated the

concepts of essence and predication, a lake is neither essentially liquid, nor essentially H2O, nor

essentially in a certain location, nor essentially having a volume within a certain range. Since

such properties also apply to the components of the lake, they are predicated of it, rather then

being essential to it. One could imagine freezing a lake, gradually transporting dirt from one

bank to the other until its shape and location were completely altered, or gradually adding more

and more oil to it until it doubled in volume, and evaporating the water away, all the while

referring to it by the same name— referring to it as the same lake. Such is the case for nearly

every “thing” we talk about — a person grows from child to adult, completely replacing nearly

every molecule in their body, and social institutions (such as nations, companies and clubs) can

completely change both their membership and mission over time.

Just what are the essences of things like lakes? In many (if not all) cases, the motives

behind dividing the world go beyond mere recognition of natural boundaries. For example, we

assign national borders even where no natural geographic boundaries exist. Even where we think

our divisions follow natural boundaries, as where we use rivers to define borders, they are

usually only natural with respect to the needs of our particular species or culture. For example,

rivers seem like natural boundaries to us because they obstruct walking, but if we were birds we

might instead consider zones lacking vegetation as more natural boundaries. Given recent

discoveries that our world is composed of quantum mechanical stuff unlike anything conceived

by the inventors of our languages, confidence that the groups into which ancient poets divided

our world correspond to natural divisions would be no better founded than that of a scientist

who, given data about the ripples on the surface of a pond on a newly discovered planet,

attempted to discern the anatomies of all the organisms that dwelled therein. We should not be

surprised to find that although our experience gives us keen insight into the nature of xemes

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predicated of groups, natural essences escape us; that, while the non-essential properties we

attribute to things may be quite natural and while there may be natural boundaries of which we

are unaware, the boundaries between what we call “things” are often (if not always) pra gmatic

constructions.

We will use the term “fundamental host” for any hosts that cannot be divided (i.e. are not

groups). Such hosts may have essence but cannot have composition nor predicates. Recall that all

xemes are hosts. Calling those that are fundamental hosts “fundamental xemes”, we may divide

the set of all hosts into four kinds as shown on the diagram below:

FUNDAMENTAL HOSTS HOST GROUPS

XE

ME

S Fundamental Xemes

Indivisible properties or things of which

properties are composed

(Locke’s “primary qualities”?)

Xeme Groups

Xemes composed of other xemes

(Plays all three roles: xeme, host and group,

depending on your perspective)

NO

N-X

EM

ES

Fundamental Non-Xeme Hosts

Indivisible things which are not properties (nor

that of which properties are composed)

(Aristotle’s “primary substances”?)

Non-Xeme Groups

Higher-order natural divisions of the non-xeme

stuff (i.e. matter) of the universe.

(Aristotle’s “secondary substances”?)

We will discover, in Lemmas 5 and 6, that we should act as thought we cannot empirically

measure any essences. This entails that we should act as though all of the natural things we

encounter are divisible (e.g. quarks are not fundamental). It further entails that we should act as

though any divisions we perceive in nature are artificial. Thus, although one may argue that the

existence of xeme groups entails the existence of other kinds of host, we should act as though

that is all we can know about such hosts.vii All but the upper right quadrant of the diagram above

should therefore be taken as corresponding to purely metaphysical machinery, and whether any

given natural thing is a xeme, host or group should be taken as purely a matter of perspective

(i.e. as with relational categories like “offspring”), since it must have all three aspects. For

example, a chair may be a group of atoms, yet also a host of momentum and a xeme of whatever

culture distinguishes it from the rest of the world (i.e. holds an opinion about what to refer to as

“the chair” when components are added to and/or t aken away from it). Thus, it participates in

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generalized evolution in at least three different ways: Its melting (or not melting) would be an

instance of the first (i.e. chair as group). Collision with the chair would be an instance of the

second (i.e. chair as xeme-host). Advancement in furniture design would be an instance of the

third (i.e. chair as a xeme). viii The metaphysical tradition of dividing the objects of experience

into non-relational categories (such as formal, material, mental, etc.) amounts to privileging one

of these perspectives— for now, we will bracket the question of whether that is justified.

There is one last concept we need to introduce here, the concept of “ physical possibility”.

There may be predictions that are logically possible (that is, not self-contradictory), yet are not

physically possible, and, since foresight is directed at physical possibility, we need to distinguish

it. The way we establish physical possibility is through a direct demonstration or indirectly

through multiple demonstrations of other possibilities and a model that show how they could be

combined to achieve the possibility in question. For example, a blueprint is a model that is

credible because each of the fabrication processes for which it calls (e.g. the fabrication of a

screw, the alignment of two beams, etc.) has been previously demonstrated.

Although a model is not an actual fabrication of that to which it refers, it contains all the

same xemes aside from those of the previously demonstrated processes it cites and the xemes

corresponding to the requisite motivation to do what the blueprint indicates. Thus, we establish

the physical possibility of a prediction by observing the hosting of all of the non-motivational

xemes in a set of the kind corresponding to the predicate of that prediction (I will use the term

“motivational xemes” to refer to the difference between a complete model and an actual

demonstration, supposing this difference to be merely lack of commitment to actualize the

model). We will use the term “physically possible” to refer to any set of xemes (or prediction

corresponding to a set of xemes) for which each of the non-motivational members has already

been hosted. For example, a 10-foot solid gold statue of George Bush will be called “physical ly

possible” even if no one would make such a thing because the shape of George Bush, the gold

and the technology for shaping it all exist, so the statue could come into existence if the requisite

motivation to bring it into existence were found.

The Deductive Justificatory Strength of some Scientific Laws

The concepts of generalized evolution allow us to elaborate on the semantics of decision-

statements. Since anything detectable must be an assignment of xemes to a host and each

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decision-statement must be predictatype (which entails being about the future or present and

having something currently detectable that determines whether it does or will occur), each

decision-statement must refer to present or future hostings (via predication, composition or

essence) of sets of xemes of currently detectable kinds.

The definitions of “xeme” and “host” justify following any line of the form: “To <goal>, we should act as though if <decision-statement C>, then <decision-statement A> is predictatype.” with the line: “To <goal>, we should act as though if <decision-statement C>, then <decision-statement A> is a claim that a host does or will host a certain (kind of) set of xemes currently detectable to us.”

From this and Lemma 2, it follows that every decision-statement must be an assignment

of physically possible xemes to hosts. Statements that do not meet such criteria are, like “Anger

banana through”, ones to which decision -justifying logics cannot apply. Thus, the semantics of

any logic of decision-justification must be entirely expressible in the terms of generalized

evolution. Now we are in a position to construct proofs of the justificatory power of analogs of

scientific laws. This will be equivalent to proving that our semantics must take the form of world

models governed by such laws. As some examples, we will consider proofs of the justificatory

power of analogs of determinism, conservation of mass/energy, Heisenberg’s uncertainty

principle and evolution by natural selection. (From here on out, we will give explicit definitional

citations only for new concepts, since they can be reverse-engineered from the proof.)

The definition of “spacio-temporally local cause” justifies following any line of the form: “To <goal>, we should act as though if <decision-statement C>, then all members of the set of xemes assigned in <decision-statement A> will immediately previously have been hosted in immediately adjacent space.” with the line: “To <goal>, we should act as though if <decision-statement C>, then <decision-statement A> will have had previously existing spacio-temporally local cause.”

The definition of “adjacent space” justifies following any line of the form: “To <goal>, we should act as though if <decision-statement C> and <decision-statement A>, then the hosting in the immediately previous moment of the xemes assigned in <decision- statement A> will have been directly detected by the host of <decision-statement A> at the moment of <decision-statement A>.” with the line: “To <goal>, we should act as though if <decision-statement C>, then all members of the set of

xemes assigned in <decision-statement A> will immediately previously have been hosted in immediately adjacent space.”

The notion of space is defined in terms of the possibility of “direct detection”.

Let (I) be “<decision-statement A> will occur in the future”. (1) DJ: if I, then <decision-statement A> is predictatype. By “Lemma 2” (2) DJ: if I, then <decision-statement A> is a claim that a host does or will host a certain By def. “xeme(etc.)”, 1 (kind of) set of xemes currently detectable to us.

15

(3) DJ: if I, then, in the immediately previous moment, <decision-statement A> will be a By def. “future/previous”, 2 claim that a host does or will host a certain (kind of) set of detectable xemes. (4) DJ: if I, then, in the immediately previous moment, all the xemes assigned in By def. “detectable”, 3 <decision-statement A> will be hosted. (5) DJ: if I, then, the xemes assigned in <decision-statement A> will have transferred By def. “immed./inst.”, 4 instantaneously from the immediately previous moment. (6) DJ: if I, then the hosting in the immediately previous moment of the xemes assigned By def. “direct detection”, 5 in <decision-statement A> will have been directly detected by the host of <decision-statement A> at the moment of <decision-statement A>. (7) DJ: if I, then all members of the set of xemes assigned in <decision-statement A> will By def. “adjacent space”, 6 immediately previously have been hosted in immediately adjacent space. (8) DJ: if I, then <decision-statement A> will have had previously existing spacio-temporally local By def. “STL-cause”, 7 cause.

Lemma 3 justifies any line of the form: “To <goal>, we should act as though if <decision-statement A> will occur in the future, then it will have had previously existing spacio-temporally local cause.”

Determinism (with no “action at a distance”)

This account of determinism also entails the idea of “no action at a distance”. Newton’s

theory of gravitation was once considered scandalous for contradicting that idea, but the

modifications Einstein made to Newton’s theory resolved the conflict (according to Einstein, all

events must have causes that will lie within their “past light cones”). As can be seen from the

proof above, one reason to be horrified by the possibility of action at a distance is that, just like

Heraclitean metaphysics, it would debilitate our decision-making. Note that the proof rests on

defining adjacency in both space and time in terms of the potential for “direct detection” and that

this concept is employed in a way that brackets questions of intelligence— i.e. the collision of

billiard balls meets all the criteria employed above for an instance of “direct detection”, and we

will leave the debate about whether billiard balls have intelligence for other essays.

Adding definitions for the concept of conservation, and the related concept of negation

(or lack of hosting) of a xeme, we can now derive the justificatory power of a generic

conservation law that would seem to entail analogs to most modern laws of mechanics. This

derivation basically hinges on the fact that to cease to host a xeme of a given fundamental type is

to host a new xeme of that type, an alternative to the one lost:

The definition of “conserved” justifies following any two lines of the form: “To <goal>, we should act as though if <decision-statement C> and <decision-statement A> is a claim about a host for which the number of xemes transferred to it of each fundamental type from adjacent hosts equals the number transferred from it of that type to adjacent hosts, then <decision-statement A> is not a claim that a given host has or will have additional xemes of a given fundamental type than it did in the immediately previous moment.” “To <goal>, we should act as though if <decision-statement C> and <decision-statement A> is a claim about a host for which the number of xemes transferred to it of each fundamental type from adjacent hosts equals the number transferred from it of that type to adjacent hosts, then

Conserved means that changes in quantity are balanced by changes in quantity in neighbors (i.e. for every action there is an equal and opposite reaction).

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<decision-statement A> is not a claim that a given host has or will have fewer xemes of a given fundamental type than it did in the immediately previous moment.” with the line: “To <goal>, we should act as though if <decision-statement C>, then <decision-statement A> is

a claim in which xemes of each fundamental type are conserved. Let (I) be ”<decision-statement A> is about the future”, (II) be”<decision-statement A> is a claim that a given host has or will have additional xemes of a given fundamental type than it did in the immediately previous moment”, (III) “<decision-statement A> is a claim about a host for which the number of xemes transferred to it of each fundamental type from adjacent hosts equals the number transferred from it of that type to adjacent hosts”, and (IV) be “<decision-statement A> is a claim that a given host has or will host fewer xemes of a given fundamental type than it did in the immediately previous moment”. (1) DJ: if I, II and III, then <decision-statement A> is a claim that a given host has or will have By def. “if…then”, (AS) additional xemes of a given fundamental type than it did in the immediately previous moment. (2) DJ: if I, II and III, then <decision-statement A> will have had spacio-temporally local cause. By “Lemma 3” (3) DJ: if I, II and III, then the additional xemes assigned in <decision-statement A> will have By def. “STL-cause”, 2 transferred from immediately adjacent space. (4) DJ: if I, II and III, <decision-statement A> is a claim about a host for which the number of By def. “if…then”, (AS) xemes transferred to it of each fundamental type from adjacent hosts equals the number transferred from it of that type to adjacent hosts. (5) DJ: if I, II and III, then the additional xemes assigned in <decision-statement A> will not have By def. “additional”, 1, 4 transferred from immediately adjacent space. (6) DJ: if I, and III, then <decision-statement A> is not a claim that a given host has or will have By def. “act/goal”, 3, 5 additional xemes of a given fundamental type than it did in the immediately previous moment. (7) DJ: if I, III and IV, then <decision-statement A> is about the future. By def. “if…then”, (AS) (8) DJ: if I, III and IV, then <decision-statement A> is a claim that a given host will host any xemes By def “lost”, 7 hosted in the immediately previous moment that were not lost. (9) DJ: if I, III and IV, then <decision-statement A> is a claim that a given host has or will host fewer By def. “if…then”, (AS) xemes of a given fundamental type than it did in the immediately previous moment. (10) DJ: if I, III and IV, then <decision-statement A> is a claim that a given host will host the By def. “fut/lost/negation”, 9 negations/alternatives of any xemes lost from the immediately previous moment. (11) DJ: if I, III and IV, then <decision-statement A> is a claim that a given host will host as many By def. “negation/and”, 8, 10 xemes of each fundamental type as it did in the immediately previous moment. (12) DJ: if I and III, then <decision-statement A> is not a claim that a given host has or will host By def. “act/goal”, 9, 11 fewer xemes of a given fundamental type than it did in the immediately previous moment. (13) DJ: if I, then <decision-statement A> is a claim in which xemes of each fundamental By def. “conserved”, 6, 12 type are conserved.

Lemma 4 justifies any line of the form: “To <goal>, we should act as though if <decision-statement A> is about the future, then <decision-statement A> is a claim in which xemes of each fundamental type are conserved.

Conservation Law

What does it mean for xemes to be conserved? Does it mean that the properties of any

host in isolation cannot change? No— since properties are sets of xemes and sets can reorganize,

they can change. However, the way they change is restricted to mere reorganization. Isolate a

scientist in a vacuum chamber and they will die— their memes (e.g. thoughts) will be reorganized

into other kinds of sets of xemes. Given determinism, there can only be change (and, indeed,

there must be change) if the hosted set of xemes contains a program for reorganization. The

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isolated host must carryout its program— the spinning top must continue to spin, the dispersing

cloud must continue to disperse, and so forth. Since the xemes themselves are conserved,

however, so must their combined value on any fundamental dimension of xeme-space (i.e. the

number of each fundamental type) or dimension orthogonal to the action of the program.

Properties corresponding to these combinations must remain unchanged for the duration of any

isolation.

The generalized law of conservation has the advantage of entailing an analog of

Heisenberg’s uncertainty principle, and thus analogs of certain aspects of quantum mechanics.

For this proof, let (I) be <decision statement A> is a claim that <host A> will completely measure all of the xemes of <host B> of <fundamental type C> and that this set of xemes will not be empty”, and (II) be “<decision statement A> is about the future”. (1) DJ: if I, then <decision statement A> is a claim that <host A> will completely measure all of the By def. “if…then” (AS) xemes of <host B> of <fundamental type C> and that this set of xemes will not be empty. (2) DJ: If I, then <decision statement A> is a claim that xemes of <fundamental type C> not held by By def. “complete/ meas.”, 1 <host A> will transfer from <host B> to <host A> and that <host B> will not gain any new xemes of <fundamental type C> in the process. (3) DJ: If I, then <decision statement A> is a claim that <host B> will have fewer xemes of By def. “transfer/regain”, 2 <fundamental type C> in one moment than in the immediately previous moment. (4) DJ: if I, then <decision statement A> is a claim in which xemes of a fundamental type are not By def. “conserved”, 3 conserved. (5) DJ: If I, then <decision statement A> is about the future By def. “future” (6) DJ: if I and II, then <decision-statement A> is a claim in which xemes of each fundamental By “Lemma 4” type are conserved. (7) DJ: If I, then <decision statement A> is a claim in which xemes of each fundamental type are By def. “if…then”, 5, 6 conserved. (8) DJ: <decision statement A> is not a claim that <host A> will completely measure all of the By def. “act/goal”, 4, 7 xemes of <host B> of <fundamental type C>. Lemma 5 justifies any line of the form: “To <goal>, we should act as though <decision statement A> is not a claim that <host A> will completely measure all of the xemes of <host B> of <fundamental type C> and that this set of xemes will not be empty.

Heisenberg’s Uncertainty Principle

This is an interesting curiosity— although predictatype statements must be sufficiently

foreseeable to act upon, the supposition of universality of predictatypeness entails that we should

expect to be unable to completely measure whatever natural evidence there may be regarding

whether, when and how they will come true. To paraphrase the proof, in the process of

measuring anything, we must change it into something unmeasured and thus restrict our ability

to make justifiable forecasts about it, so we cannot reliably foresee everything about it. Does this

contradict our previously established claim that we must be able to foresee enough about each

decision-statement to act? No— decision-making does not require complete foresight. For

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example, we may foresee enough about the weather to realize that we should build a roof, yet not

know exactly when that roof will come in handy. Our knowledge of the weather is not so limited

as to be irrelevant. Predictatypeness must refer to this limited kind of knowability.

This is the second thing we have learned about the definition of <decision-statement>: it

must not refer to events that are foreseeable in complete detail. We have a corresponding

discovery to note regarding our semantics: Since conservation of xemes ensures that

measurement will always involve replacing the measured xemes with others of the same

fundamental type, we will only be able to measure xemes that can change. That is, we can only

measure xemes that are predicated of— not those that are essential to— any given host. Thus, the

xeme assignments in any decision-statement about nature (i.e. the empirically detectable) must

be predications, and the hosts must not be fundamental. In short, we cannot reason practically

about natural essences, so we are obliged to consider all divisions we perceive in the natural

world to be artificial ones we have imposed upon it. Furthermore, we cannot reason practically

about fundamental natural hosts, so we are obliged to treat all natural things as divisible beyond

detection.

Now, to incorporate observation into deductive logic, to extend deductive logic from the

analytical to empirical realm, we will introduce a lemma to let us to build upon claims about

physical possibility. Although it seems clear that direct observations would have just as much

justificatory power as definitions, and therefore are as much candidates for incorporation into

deductive logic, there has been confusion about just what constitutes a direct observation. For

example, the possibility that a human’s thought process might be simulated on an alien computer

raises serious doubt about the proposition that Descartes’ observation of his own thought would

provide him with justification to believe in (his own) human existence. Skeptics may point out

that, since Descartes’ thought could be a simulation (i.e. his observation could actuall y have been

made by something like a computer), it doesn’t necessarily follow from such observation that

any human actually exists.

The terms of generalized evolution provide us with a way of recouping Descartes’

insight. Although observations of thoughts may not (at least not by themselves) justify asserting

the existence of human beings, they certainly do justify (by the definition of host) asserting the

existence of some sort of host bearing the properties of having such thought. That host might not

be a human being— it might be a computer or even some part of the observer’s imagination — but

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it certainly must exist if the observation does. While one may doubt that direct observation can

establish the existence of anything else, it certainly establishes that the observed xemes are

hosted. Thus, it establishes that the xemes are physically possible (make it “I think, therefore

such thought is possible”). Much as the giving of definitions allows us to socially share the

justificatory benefits of our concepts, so then will the giving of blueprints allow us to share this

justificatory benefit of our direct observations. The following lemma will allow us to formally

leverage such benefits, to use blueprints as empirical components of deductive proofs:

Let (I) be “<kind of xeme set A> is physically possible”, (II) be “<xeme B> will have been hosted in the moment previous to <moment M>”, (III) be “<xeme B> will not be hosted at <moment M>”, (IV) be “<xeme B> will not not be hosted at <moment M>” (1) DJ: if I, II and III, then <xeme B> will have been hosted in the moment previous to By def. “if…then” (AS) <moment M> (2) DJ: if I, II and III, then <xeme B> will have been hosted by the group of all hosts in the By def. “group-all-hosts” 1 moment previous to <moment M> (3) DJ: if I, II and III, then <xeme B> will not be hosted at <moment M>. By def. “if…then” (AS) (4) DJ: if I, II and III, then <xeme B> will not be hosted the group of all hosts at <moment M>. By def. “group-all-hosts” 3 (5) DJ: if I, II and III, then the group of all hosts will lose <xeme B>. By def. “lose”, 2, 4 (6) DJ: if I, II and III, then, in losing <xeme B>, xemes of each fundamental type will be By “Lemma 4” conserved. (7) DJ: if I, II and III, then the group of all hosts will gain a replacement to <xeme B>. By def. “conserve”, 5, 6 (8) DJ: if I, II and III, then if <decision-statement A> will occur in the future, then it will By “Lemma 3” have had spacio-temporally local cause. (9) DJ: if I, II and III, then <xeme B> will transfer to the group of all hosts from an By def. “STL-cause”, 7, 8 immediately adjacent host. (10) DJ: if I, II and III, then the group of all hosts will have an immediately adjacent host. By def. “from”, 9 (11) DJ: if I, II and III, then the group of all hosts will have no immediately adjacent host. By def. “all/adjacent” (12) DJ: if I and II, then <xeme B> will not not be hosted at <moment M>. By def. “act/goal”, 10, 11 (13) DJ: if I, II and IV, then <xeme B> will be hosted at <moment M>. By ”Lemma 1” (14) DJ: if I and II, then <xeme B> will be hosted at <moment M>. By def. ”if…then”, 12, 13 (15) DJ: if I, then <kind of xeme set A> is physically possible. By def. “if…then”, (AS) (16) DJ: if I, then, each non-motivational xeme from a full set of xemes of <kind of xeme By def. “phys. possible”, 15 set A> has been hosted. (17) DJ: if I, then, at each future moment, each non-motivational xeme from a full set of xemes By def. “” 14, 16 of <kind of xeme set A> will be hosted. Lemma 6 justifies any line of the form: “To <goal>, we should act as though if <kind of xeme set A> is physically possible, then, at each future moment, each non-motivational xeme from a full set of xemes of <kind of xeme set A> will be hosted.”

Indestructibility of Xemes

This lemma basically entails that we should act as though the xemes of any set we directly

observe will always exist, albeit perhaps transferred to a different host or split across multiple

hosts. We will use this fact to deduce the justificatory power of a generalized theory of evolution.

First, however, let me explain the concept of “manifolds” that we will use. A manifold is to be a

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series of groups for which each subsequent group contains the previous group in the series plus

some hosts adjacent to it. A manifold from <group B> to <host C> is to be one starting with

<group B> and ending with a group adjacent to every group containing <host C>. We will call

each group in such a series a “layer”. It may be he lpful to conceive manifolds as series of regions

as shown in the following diagram:

The phrase “alive/active” will refer to any group that exists and continues to have a potential for

change, where “exist” will mean that there is a manifol d from that group to us (i.e. exists in our

universe), for which no layer introduces any new component that is not alive/active. In other

words, there must be at least one complete “active channel” through which we might detect

change in any “alive/active” group.

Let (I) be “<kind of xeme set A> is physically possible”, (II) be “<group B> will be alive/active”, (III) be “<kind of xeme set A> will be favored by the environment of <group B>”, (1) DJ: if I, then, at each future moment, each non-motivational xeme from a full set of xemes By “Lemma 5” of <kind of xeme set A> will be hosted. (2) DJ: if I, II and III, then, at each future moment, each non-motivational xeme from a full set of By def. “if…then”, 1 xemes of <kind of xeme set A> will be hosted. (3) If I, II and III, then, at each future moment, for each non-motivational xeme from a full set of By def. “exist (be)”, 2 xemes of <kind of xeme set A>, there will be an active channel from a host hosting that xeme to us. (4) If I, II and III, the <group B> will be alive/active. By def. “if….then”. (AS) (5) If I, II and III, then, at each future moment, there will be an active channel from <group B> to us. By def “alive/active”, 4 (6) If I, II and III, then, at each future moment, for each non-motivational xeme from a full set of By def. “channel”, 3, 5 xemes of <kind of xeme set A>, there will be an active channel from a host hosting that xeme to <group B>. (7) If I, II and III, then <kind of xeme set A> will be favored by the environment of <group B>. By def. “if…then”, (AS) (8) If I, II and III, then the average speed at which xemes from sets of <kind of xeme set A> would By def. “favored by env.”, 7 transfer to <group B> from any host to which it has an active channel is greater than that at which it would transfer back. (9) If I, II and III, then xemes from sets of <kind of xeme set A> would transfer to <group B> from By def “more often”, 8

<GROUP B> <HOST C>

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any host to which it has an active channel more often than they would transfer back. (10) If I, II and III, then the average population at <group B> of xemes from sets of <kind of xeme By def. “population-grow”, 9 set A> hosted by a host with an active channel to <group B> would continually grow. (11) If I, II and III, then the average population at <group B> of each non-motivational xeme from By def. “would/will”, 6, 10 a full set of xemes of <kind of xeme set A> will continually grow. (12) If I, II and III, then <group B> will host the motivational xemes from a full set of xemes of <kind By def. “mot. xeme”, 11 of xeme set A>. (13) If I, II and III, then <kind of xeme set A> will dominate <group B>. By def. “dominate”, 11, 12 Lemma 7 justifies any line of the form: “To <goal>, we should act as though if <kind of xeme set A> is physically possible and <group B> will be alive/active and <kind of xeme set A> will be favored by the environment of <group B>, then <kind of xeme set A> will dominate <group B>.”

Evolution by Natural Selection

Notice that the xemes that are to be transferred to <group B> as per Lemma 7, need not be

favored by the environment of every layer in the channel along which it transfers. There may be

obstacles to cross. However, if the channel is active, every obstacle must be permeable. For

example, for a particular xeme to be favored by group B is consistent with the possibility of the

following speeds for exchange with host A and a host C equidistant from both A and B

mediating the only active channel:

Average Transfer Speed from A to B 6 Average Transfer Speed from B to A 5 Average Transfer Speed from C to B 12 Average Transfer Speed from B to C 5 Average Transfer Speed from A to C 4 Average Transfer Speed from C to A 5

We see that the average transfer speed to B from either host is greater than that in the reverse

direction, as required for the environment of B to favor the xeme. However, the average speed of

transfer to C from A is less than that in the opposite direction, so the environment of the

manifold layer containing C in addition to B does not favor the xeme. In short, C represents an

obstacle (since 4 is less than 5, the average net flow between A and C is in the direction of A).

However, C does not block the xeme— the average transfer speed to C is still greater than zero.

The environment of a group at any given time defines a destiny for that group. This

destiny is not necessarily its ultimate one, however, since the environment may change (and the

destiny along with it). The ultimate destiny of a group is the one defined by the unchangeable

(essential) properties of its environment. Lemma 7 assures us that we should act as though over

the duration of their existence, each group must converge towards such an ultimate destiny. Once

we have deduced appropriate lemmas regarding the nature of ultimate environmental favor, we

can use observations of possibility to learn about what those destinies will be. In particular, we

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can rule out any destiny that would be less favored than any we have, by blueprint or

demonstration, observed possible.

Our investigation into the nature of ultimate environmental favor will rely on a yet

unproven lemma that I will explain by way of an example. The lemma states that the average

xeme set will be hosted more often in groups with a combination of higher average interaction

rate and a certain kind of disperse distribution that I will call “diversity”. Consider the following

two active channels:

Potential to be Created in Second Moment

AA Y N N Y Y Y AB Y Y Y Y Y Y BB N Y N Y Y Y

Supposing that each host will exchange one xeme with each neighbor, the average

configuration can be created in only 1.67 of the hosts on the left but in all 3 of the hosts on the

right, so we would call the configuration on the right “more d iverse”. Intuitively, we think of

complex structures, intelligent creatures and civilized societies as being more diverse— we

expect the range of evolutions that can arise in less diverse groups to be relatively limited.

Assuming that groups can have varying diversity and interaction rates, we will now show that

any goal must entail a goal to maximize the combination of interaction and diversity. From this,

it follows that we should act as though the ultimate destiny of the universe is maximum diversity

and interaction rate.

(1) DJ: to <goal 2> one should aim to implement a better strategy for achieving <goal 2>. By def. “strategy” (2) DJ: to <goal 2> one should aim to know better strategies for achieving <goal 2>. By def. “implement/know”, 1 (3) DJ: if knowing better strategies is to occur in the future, then it will have had spacio-temporally By “Lemma 3” local cause.” By “Lemma 3” (4) DJ: to <goal 2> one should aim to acquire from adjacent hosts sets of xemes corresponding to By def. “STL-cause”, 2, 3 knowledge of better strategies to achieve <goal 2>. (5) DJ: that “one will acquire from adjacent hosts sets of xemes corresponding to knowledge” is By “Lemma 5” not a claim that one will completely measure all such xemes from them. (6) DJ: to <goal 2> one should aim to acquire from adjacent hosts sets of xemes corresponding By def. “complete/know”, 4, 5 to knowledge of better strategies to achieve <goal 2> and expect this aim to never be completely fulfilled. (6) DJ: to <goal 2> one should aim to acquire from adjacent hosts sets of xemes corresponding By def. “nev. comp. ful.”, 4, 5 to knowledge of better strategies to achieve <goal 2> as much as possible. (6) DJ: to <goal 2> one should act to maximize the rate which they encounter the average By def. “maximize rate”, 6

AB AA BB AB AB AB

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xeme set. (7) DJ: to <goal 2> one should act to maximize the diversity and interaction rate of the groups By def. “diversity/int. rate”, 7 in which one participates. Lemma 8 justifies any line of the form: “To <goal>, we should act as though to <goal 2> one should act to maximize the diversity and interaction of the groups in which one participates.”

Entropy Law

Since <goal 2> would include <goal> this entails that no matter what goals or moral laws define

what we “ should” do, we should act to maximize the diversity and interaction rate of our society,

building more efficient infrastructure, protecting free speech, and so forth. In effect, this lemma

proves something about the definition of “goal” much as previous le mmas proved things about

the definition of “decision -statement”: Anything contrary to the goal of maximization of

diversity and interaction rate cannot be a goal. It must fall in to the category of non-goals, along

with “to fail” and “anger banana through” . Even if meaningful, it cannot be employed in any

justifiable decision-making, for we would find that to pursue it would necessarily entail pursuing

its contrary.

Since <goal 2> would include any ultimate destiny, Lemma 8 also entails that anything’s

ultimate destiny must be for its universe to have maximum diversity and interaction rate. That is,

progression towards such a universe must be what every environment favors. How to progress

depends upon where you are at, so discovering exactly what such progression would entail is an

empirical matter. We can converge on this discovery by periodically showing physically possible

a state (or kind of state) superior to all others previously shown to be physically possible. Lemma

5 assures us that such convergence is the best we should expect to accomplish.

Conclusions We have discovered that restricting our attention to questions of the form, “Should I act

as though <statement A> is true?” allows us to develop a logic justified purely in aspects of

definitions— especially leveraging the definitions of “act” and “should”. If those definitions have

the properties suggested above, then we should act as though our world is one in which the law

of excluded middle holds, the future (but not necessarily the present) is deterministic, and the

components of all properties are indestructible entities (xemes) that travel continuous trajectories

through our universe abiding generalized evolution by natural selection. Since we should act as

though these entities are indestructible, once we have directly observed them, we should suppose

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that they will continue on their deterministic paths even after they leave our direct observation.

Thus, we are able to deduce justification for claims about corners of our universe currently

beyond direct observation. Building deductions upon direct observations of possibility (rather

than of actuality) allows us to develop a purely deductive (i.e. non-inductive) empirical method.

The next step in this project is to derive lemmas regarding the nature of environmental

favor. Less formal preliminary work suggests that the following are good candidates:

“To <goal>, we should act as though if <group B> will be a group of decision -makers, and <kind of xeme set A> would cause <outcome C>, and <group B> will ultimately desire <outcome C>, and the members of <group B> would be unable to detect any undesirable consequences of <kind of xeme set A>, then <kind of xeme set A> will be favored by the environment of <group B>.” “To <goal>, we should act as though decision-makers will desire increased access to diversity (and thus desire money so far as it can buy diversity)” “To <goal>, we should act as though decision-makers will desire having more free time (and thus desire money so far as it can buy time)”

These would establish analogs of the familiar economic law of supply and demand, the claim

that markets will meet consumers’ desires and the claims that consumers will desire convenience

and novelty. This wouldn’t directly relieve the skeptical worry that th e inductive justification

traditionally cited to support such principles fails to establish their truth, but, by deductively

establishing that we should act as though the laws are true, they would formally explicate how

pragmatic considerations empower us to cope with such skepticism.

i Brouwer, L. E. J. (1908), "The Unreliability of the Logical Principles," in Heyting, Ed., Op.Cit.: 107-111. ii Field, H. (2001), “Apriority as an Evaluative Notion”, in Truth and the Absence of Fact, Oxford: Clarendon Press iii Aristotle’s Methaphysics, book IV, especially chapter 6. iv There are several reasons to introduce the term “predictatype”: (1) “predictable” refers to things that will happen and “predictatype” additionally refers to things that won’t happe n, and (2) the new term is required to explicate the difference between justifiable vs. unjustifiable predicting. vDawkins, R. (1976), The Selfish Gene, New York: Oxford University Press. vi This is different from the accidental vs. essential dichotomy. Predicated properties are not accidental— they are essential to some of the components of that of which they are predicated. If composition is taken to be like the casting in a playbill listing different performers for different nights, then it isn’t accidenta l either. vii Except, perhaps, the matter of the universe as a whole. viii Regarding the third, note that ideas are not always in brains— books and artifacts are just the most obvious examples of how a society may store ideas outside the brain.