1Introduction

I feel that there is much to be gained by defining words as what we normally mean with them in everyday situations and analyzing the consequences of those definitions. I feel that we can find their essential meaning by considering the situations in which we feel that they are the wrong choices.

1.1Target audience, purpose, and how to read

The target audience of this book is myself.

Purpose of the book: To find the ultimate consequences of mind-related concepts defined in English. My plan is:

  • Define the concepts according to how we use them in everyday English.
  • Infer the consequences of those definitions.
  • Relate the concepts with each other.
  • Order the concepts by requirement (which concepts require which concepts).

How to read this book: Read anything you want to. But most parts are unfinished. If you feel that a part is unfinished, feel free to skip it.

Perhaps this book should be like formal concept analysis1?

1.2Fundamental assumptions

We must agree on these before you read further. If we don't agree, no communication can happen between us. I'm not absolutely certain about these assumptions. I'm happy to change my beliefs if there is a reason for that. But I don't know how I can communicate without them.

I assume these axioms.

Objective reality exists.

Logic works.

Every statement has exactly one truth value (somewhere in the continuum between false and true), although we may not always know it.

I assume that these concepts are primitive concepts. I leave them undefined. They are like the concept of "point" in geometry. I don't know how to state them in terms of anything simpler. The primitives are: want, to want, belief, to believe.

I assume these synonyms.

imagination, fantasy. Imagination comes from Latin. Fantasy comes from Greek. Imagination and fantasy have the same meaning. Imagination doesn't have to be visual, although "imagination" and "image" are related.

knowledge, awareness. These are the same: to know X, to be aware of X.

attention, focus.

1.3The concept graph/clusters

How to read this graph. Adjacency list. A paragraph beginning with the sentence "A: B1, B2, …, Bn." declares n edges: A-B1, A-B2, and so on until A-Bn.

want (verb).

cause (verb). Synonyms: force, make.

control: force, want. X controls Y iff X can force Y to do what X wants.

self: control. X's self is the extent of X's control.

2How should we do philosophy?

2.1Philosophers should strive to be understandable

We should clarify words. We may generalize words, but we should not redefine words. We should start from their everyday meaning.

We should avoid inventing a new word if a word already exists for it.

We should use everyday language. People who bend words too much alienate themselves.

Most debates are definition problems. Communication requires that everyone use the same definitions.

2.2Reddit philosophy TLDR challenge: a great time-saver, but is it correct?

https://www.reddit.com/r/askphilosophy/comments/1pdczz/philosophy_tldr_challenge/

2.3<2018-11-06> "Academic philosophy’s wrong turn"?

https://medium.com/the-polymath-project/in-defense-of-philosophy-2ca6ef0aa4a0

2.4Major philosophical issues

2.5List of unsolved problems in philosophy

2.6What Reddit stuffs?

skepticism and epistemology https://www.reddit.com/r/philosophy/comments/66pdk6/reddit_seems_pretty_interested_in_simulation/

https://www.reddit.com/r/philosophy/comments/74nl51/reddit_it_seems_like_youre_interested_in_the/

https://www.reddit.com/r/philosophy/comments/89qful/how_morality_changes_in_a_foreign_language/ "Yeah I saw an old PewDiePie video where he tried to only speak his native Swedish, he was obviously very uncomfortable making the same jokes in our own language. The same thing happens to me, I can say outrageous things much easier in English or Spanish than in Swedish since it feels less real." "Hm my friend from Mexico had no problem swearing up a storm (even at playgrounds..)" I can confirm. I swear more in English than in my native Indonesian. I do swear in both. https://www.theguardian.com/science/blog/2017/mar/27/bad-language-why-being-bilingual-makes-swearing-easier "The scientific term for this is reduced emotional resonance of language."

2.7Fact, judgment, and seeing things as is

People often conflate fact and judgment. Example:

  • Fact: "I don't understand this piece of math."
  • Judgment: "I'm bad at math."

English syntax doesn't distinguish between fact and judgment.

2.8etymology

The origin (the etymology) of a word tells us what it should mean.

3Basic concepts

3.1Ability is the existence of satisfying action

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Ability is the existence of satisfying action.

"S can P" means "There exists an action A such that, after S does A, the statement 'S did P' becomes true." Example: "I can boil an egg" means "There is something I can do to make the statement 'I did boil an egg' true".

"S cannot P" means "It is false that S can P". Thus it means "there is nothing S can do to make 'S did P' true."

Problem: "cannot" is hard to prove, if it's even possible to prove at all. Example: There are several issues with "I can't jump 10 meters high":

  • Am I not able to do that, or do I merely not know how to do that? There is a difference between not being able and not knowing how.
  • Linguistic issue: What does "jump" mean? Must I use my own legs?
  • Proving a universal negative: How do I know that there is nothing I can do to make "I jumped 10 meters high" true?

People sometimes say "can't" when they mean "won't". Example: "I can't wake up earlier." Of course he can; there is a satisfying action: Go to bed earlier, and put the goddamn phone away from bed. But he doesn't want to. He should say "I don't want to wake up earlier." But can doesn't mean should.

People sometimes say "can't" when they mean they don't know how. Example: "I can't start the car." Of course he can; there is a satisfying action: Repair the car, turn the key, and so on. But he doesn't know how. He should say "I don't know how I can start the car" or "The car isn't starting." That satisfying action exists regardless of whether he knows it.

3.2Negated modal

Let M be a modal verb such as "can", "may", "must".

"S M not P" means "It is false that S M P".

Possibility "You may also want this." Permission "You may enter the room now." Ability "You can enter the room." Necessity "S must P in order to C" means that "C is necessary for S to P". "You must fill this in order to be able to get to the next step." Obligation "You must enter the room."

It is incorrect to say "you cannot enter this room"; the correct saying is "you must not enter this room". (You aren't permitted to enter the room; I'm not letting you enter this room.)

"Can you pass the salt?" means "Please pass the salt".

3.3Power is the ability to harm

We mean political power.

Power is the ability to instill fear in others.

Power is the ability to do violence.

Power is potential violence.

4Want

4.1By "want", I mean "will" or "desire", not "lack"

We assume that "want" is a primitive concept.

We assume that everything wants something.

4.2To be animate is to have changing wants

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To be animate is to have changing wants.

To be inanimate is to have unchanging wants. An inanimate thing is a thing whose wants don't change. That inanimate thing always has that same want.

An animate thing is a thing whose want may change.

Problem: Must the wants change? Or is it sufficient to have the possibility of changing wants, without having to actually ever change wants? What is the difference between: one who can do X but never does X, and one who really cannot do X?

4.3Life is a thing that has changing wants

Synonym: An animate thing is a living thing. A living thing lives. Thus the meaning of "to live" is "to have changing wants". Thus the meaning of "life" is, literally, "a thing that has changing wants".

Problem: this definition generalizes "to live" too much?

4.4Science is about finding what each inanimate thing wants

Recall that, by definition, each inanimate thing has an unchanging want. One way of finding those wants is the hypothetico-deductive scientific method.

Remember that we assume that want is a primitive concept. It doesn't assume what can want and what can't want.

What an inanimate thing wants is what it would do if it weren't forced to. Thus we can find what an inanimate thing want by isolating it so that nothing forces it to do anything.

Example. Imagine a weight balance. I put a heavier weight on the left plate. I put a lighter weight on the right plate. Both weights want to fall toward the Earth. The heavier weight forces the lighter weight to rise, against what the lighter weight wants, against what the lighter weight would do if the heavier weight did not force the lighter weight to rise.

Science aims to find what each inanimate thing wants. We isolate inanimate things, so that nothing control them, so that we know how they behave. We isolate atoms so that we can understand their wants.

Nature wants to enforce the law of nature.

A gas wants to fill its container?

We aren't personifying inanimate things. They do want something. It's just that their wants don't change with time.

Every mass wants to attract every other mass. Earth wants a rock to fall toward the Earth.

What does a voltage regulator want?

There is a difference between these statements:

  • Every thing that does not exist wants to continue not-existing.
  • Nothing wants to continue not-existing.

4.5Problem: How do we know that nothing is forcing an inanimate thing to do anything?

Difference of meaning:

  • "Nothing" exists = the English word "nothing" exists
  • Nothing exists = there does not exist anything; it is not true that anything exists

Which one does "Nothing causes its own existence" mean?

  • There isn't anything that causes its own existence.
  • There is a thing that we call "nothing", and it causes its own existence.

Can something cause its own existence? Can something causes itself to exist? Is there such a thing?

Is there something forcing everything else to exist?

Is everything forced to exist? Does anything want to exist?

If we assume that something cannot cause its own existence, then everything must have a cause that is not itself. Thus there is something forcing everything else to exist.

If I don't exist, how can I force myself to exist?

5Cause

5.1Synonyms of the verb "cause": make, force

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These mean the same: "to cause X to do Y", "to make X do Y", "to force X to do Y".

"Force" suggests, but does not require, that X would otherwise not do Y if X was not forced to.

Examples:

  • I made him clean up his room = I forced him to clean up his room = I caused him to clean up his room.
  • I kicked the ball = I made the ball move with my foot = I forced my foot on the ball = I caused the ball to move with my foot.
  • "I gave birth to my child" approximately means "I forced my child to exist".

5.2affect, change, influence, cause/make a difference

These are synonyms: to affect, to cause to differ, to change, to influence, to make a difference.

To affect is to change (to make a difference).

Example: I kick the ball. My existence makes a difference to the ball. The ball moved because I kicked it. The ball wouldn't move if I didn't kick it. I affect the ball.

5.3Cause

"C causes E" means:

  • C precedes E: C happens before E.
  • C is necessary for E: If C doesn't happen, then E doesn't happen.
  • C is sufficient for E: If C happens, then E happens.

Synonyms: to cause, to determine, to ascertain.

A causal factor is not a cause.

5.4Example of updating a causal model: fire, match, and dryness

At first, we believe that Strike causes Fire.

But then we find water.

Now we believe that Strike and Dry causes Fire. Note the verb "causes": "Strike and Dry" is one thing, not two separate "Strike" and "Dry". Strike alone or Dry alone doesn't cause Fire.

But then we find chemistry and vacuum pump.

Now we believe that Strike and Dry and Oyygen causes Fire, and so on.

When we encounter a surprise, we update our causal model.

"The essence of causality is the generation and determination of one phenomenon by another." https://www.marxists.org/reference/archive/spirkin/works/dialectical-materialism/ch02-s06.html

  • That is all that page has to say.
  • That page should have been a sentence instead.

5.5Causality jargon

Suppose that there are a button X, a button Y, and a lamp Z, wired such that Z lights up iff both X and Y are pressed.

Does pressing X cause Z to light up? No, but it contributes. It is a causal factor. Pressing X is necessary, but not sufficient, for lighting up Z.

The cause of Z's lighting up is both pressing X and pressing Y.

Other resources:

5.6Conditional is not causation.

Suppose:

  • L1 lights up iff B1 is pressed.
  • L2 lights up iff B2 is pressed.
  • L3 lights up iff B1 is pressed and B2 is pressed.

Then "if L1 and L2 light up, then L3 lights up" is a true conditional statement, but "both L1 and L2 light up" is not the cause of "L3 lights up".

5.7Causation is not transitive.

See the section "3.1. Counterexamples to Transitivity" in the 2017 article "The Transitivity and Asymmetry of Actual Causation". https://quod.lib.umich.edu/e/ergo/12405314.0004.001/--transitivity-and-asymmetry-of-actual-causation?rgn=main;view=fulltext

5.8Causation increases conditional probability

Suppose that C causes E.

Then P(E|C) exceeds P(E).

What does this mean: "C gives us some information about E"?

The converse isn't always true.

"Causality connotes lawlike necessity, whereas probabilities connote exceptionality, doubt, and lack of regularity" (Pearl 2009 Causality book p. 1).

5.9Suspecting causation from correlation of things that happen almost together

Let C abbreviate Cause.

Let E abbreviate Effect.

"C and E correlate" means that "E happens if C happens, and E doesn't happen if C doesn't happen".

"Immediate" means "within short duration".

If we often see C happen immediately before E, and we often see C and E correlate, then we may come to believe that C causes E. To justify this, we tacitly assume that not much can happen in such short duration; we assume that the immediate future is predictable. We assume the short duration between C and E makes it improbable for anything else to confound the way C causes E. The shorter the duration, the more improbable confounding is.

Consider two drugs: S (Slow) and F (Fast). Suppose that, in reality, F makes the person vomit after 1 hour, and S makes the person vomit after 1 year, but we don't know those yet. It is easier for us to see (and conclude) that F causes vomiting than to see that S causes vomiting, because there are much fewer things that can make the person vomit in 1 hour than in 1 year.

Thus we may define duration as maximum number of possible events. There are more things that may happen in 2 seconds than in 1 second. What does it mean for something to happen?

We may believe that C causes E, but does C really cause E?

I strike a match head. Then it ignites.

I do that three times with other match heads, and find the same thing.

Thus I generalize: Striking a match head causes its ignition.

Modern physics can explicate the chain of causes (I may mistake the details). Friction causes the the heating of the stricken part of the match head. The heat and oxygen causes the ignition of the stricken part. The ignition causes more conversion of chemical bonds into heat. The additional heat causes a chain reaction that spreads the flame into nearby unlit parts.

I wet a match head with drinking water. I strike it. It doesn't ignite. I infer that the wetness causes the match head to fail to ignite. What justifies my inference?

What was causality to early humans?

Can a Hebbian learner learn causality?

5.10Counterfactual reasoning

We justify some counterfactuals by frequentist probability. Suppose that a driver died in a car crash. We assume that the driver would not have died if the car had not crashed. Frequentist probability justifies that assumption. There are many enough car crashes. We have the statistics.

We don't know about other counterfactuals. We don't know what would happen if Hitler won World War 2. We don't know any way of repeating World War 2 many times.

  • How do we justify statements like "If Hitler had never been made a Chancellor, then World War 2 would have never happened."?
    • If Hitler hadn't done it, wouldn't someone else have?
    • If Hitler hadn't done it, wouldn't there be someone else more evil?

What encumbers reasoning is the multitude of probable causes, not the unrepeatability of the event.

When reasoning counterfactually, we tacitly assume that the law of nature doesn't change.

  • We assume that the law of nature is the same 1,000 years ago.
    • It seems that any attempt at justifying this would crash into Hume's induction problem.
      • The law of nature is the same yesterday.
      • The law of nature is the same two days ago.
      • The law of nature has always been the same?
        • We don't know the law of nature before the Big Bang.
      • However, for most practical purposes, the law of nature has always been the same.

5.11Causal inference and causal modeling

Read the 2009 edition of Judea Pearl's 2000 book "Causality: models, reasoning, and inference"?

Can Judea Pearl's theory deal with causal cycles? Things that contribute each other? Such as poverty and homelessness?

https://stats.stackexchange.com/questions/26437/criticism-of-pearls-theory-of-causality

Other resources:

5.11.1Unread

  1. Counterfactual reasoning

5.12Cause, luck, and randomness

Luck is cause that we don't bother to find out.

"Random" means "caused by something we don't know".

6Control

The concept of "control" depends on "cause" and "want".

6.1To control is to force wants

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X controls Y iff X forces (causes) Y to do what X wants Y to do.

Remember that "to force" means "to cause".

Remember that we assume that want is a primitive concept. It doesn't assume what can want and what can't want.

We assume that causation is transitive.

Control is transitive, because causation is transitive. If X controls Y, and Y controls Z, then X controls Z. The contraposition: If X doesn't control Z, then: X doesn't control Y, or Y doesn't control Z, or both.

We can use that contraposition to find who controls whom in a company. Example. Alice, Bob, and Charlie are in the same company. In the hierarchy, Alice commands Bob, and Bob commands Charlie. Alice knows Charlie, but never interacts with Charlie. If Alice tells Bob to make Charlie do what Alice wants Charlie to do, but Charlie doesn't do it, then there are three possibilities: Alice doesn't control Bob, or Bob doesn't control Charlie, or both.

6.2Self is the extent of control

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A system's self is everything that it controls.

The self of X is everything that X controls.

Example. A brain's self is everything that the brain controls. My self is everything I control.

Beware of confusion with reflexive pronouns

Don't conflate "my self" and "myself".

I = myself. Both of them refer to the same thing. "Myself" is an English reflexive pronoun.

My self = everything that I control.

Don't conflate "itself" and "its self".

6.2.1Supports

  • The definition is not anthropocentric. It does not assume that a self belongs to a human.
  • The definition does not require consciousness.

6.2.2Possibly objectionable consequences

  • A rich person has more self than a poor person because the rich person controls more things than the poor person.
  • If another person B absolutely obeys all my orders, then B is a part of my self.
  • An electrical circuit with feedback has a self.

6.2.3Self-control?

The self-control of X is X's control of X?

My self-control is my control of me?

An example system with self-control is a lithium-ion battery with protection circuit?

"Self-control, an aspect of inhibitory control, is the ability to regulate one's emotions, thoughts, and behavior in the face of temptations and impulses" according to Wikipedia.

6.2.4Further questions

  • What is the relationship between control, intention, and causality?

6.2.5Set-theoretic definition of self

The self of X is the set of everything that X controls. Therefore, because selves are sets, they can intersect and join. This is an ordinary set theory in mathematics.

If there is an overlap between what A controls and what B controls, then they share that overlapping part of their selves. That overlapping part is a joint self.

The size of self may vary over time.

Selves may merge and split. When I'm using a computer, some of the computer's self and some of my self merge into a bigger self. When I'm not using the computer, our selves split.

If I sever my hand, then that hand ceases to be a part of my self, because I can no longer control it. If I reattach it, it becomes a part of my self again, although I may not control it as well as before. https://www.reddit.com/r/NoStupidQuestions/comments/5cu20w/if_your_hand_is_removed_but_reattached_in_time/

6.2.6TODO What is the relationship between control, causality, agency, subject, and subjective experience?

6.2.7TODO For us to determine the size of the self of a system, some its output must feed back into some of its input, so that we can distinguish what it can control and what it can't.

6.2.8TODO Our definition of "self" generalizes its dictionary meaning.

  1. https://en.wikipedia.org/wiki/Self

    • "The self is an individual person as the object of his or her own reflective consciousness. This reference is necessarily subjective, thus self is a reference by a subject to the same subject. The sense of having a self – or self-hood – should, however, not be confused with subjectivity itself."
    • "The first-person perspective distinguishes self-hood from personal identity. Whereas "identity" is sameness, self-hood implies a first-person perspective."

  2. Dictionary definitions of "self" assume too much.

6.3TODO "Causal authority"?

To "control" something is to have "causal authority" over it.

The self of X is the maximum extent of the causal authority of X.

"Causal authority" sounds cool. But what does it mean?

6.4Tools, usage, enlargement of self (boundary of control)

Remember that we defined self as everything that we control.

The essence of tools is the enlargement of self (the boundary of control).

A tool is a thing that extends our self (our boundary of control). A tool is a thing that enables us to control more things than we would without that tool.

"Tool" is a relative concept, like "weed", "good", "bad". Whether something is a tool depends on what use we imagine of it. We can think of a rock as a useless heavy space-occupying thing. We can think of a rock as a tool for crushing things. To 20th century people, a computer is a mind extension tool. To a villager in the Stone Age, a computer might be a heavy weight that can be thrown to kill animals.

Usage is goal-directed control. To use something is to control it for a goal/purpose/intention. "To use X for Y" is to control X in order to achieve Y (to make Y true).

A tool is something we use.

A tool may be animate.

People are tools. Everyone uses everyone else. We use each other. A worker is a capitalist's tool; a capitalist is also a worker's tool. An employee is his employer's tool; an employer is also his employee's tool. Surely employers avoid hiring useless employees, and employees avoid hiring useless employers. A useless employee doesn't work; a useless employer doesn't pay.

How do we use this person? How can we use this person? What does this person help us do? What can this person help us do?

Using other people is not inherently bad. One can use his tools with care, whether animate and inanimate. But this idea may discomfort non-philosophers.

It is only a matter of time before a tool-using animal realizes that it can use other animals as tools.

Are we using others, or are we being used by others?

7Logic, language, ontology

7.1TODO Reading conditionals

7.1.1TODO (Failed attempt) Properly translating material conditional into English "does not preclude"

Remember that the material conditional \( p \to q \) is equivalent to \( \neg (p \wedge \neg q) \) in classical logic.

We can interpret \( p \wedge \neg q \) as "\( p \) precludes \( q \)".

Thus we can interpret the material conditional \( p \to q \) as "\( p \) does not preclude \( q \)". However, we practically pretend that it means "if \( p \) then \( q \)". This lie works because we practically always pick relevant \(p\) and \(q\).

However, there is a difficulty: If \(p\) and \(q\) are irrelevant, \( p \) is true, and \( q \) is false, then what does "\(p\) does not preclude \(q\)" mean?

See also:

7.1.2TODO Belief inference rule in doxastic logic

We can define \( p \Rightarrow q \) as "knowing \( p \) is sufficient to infer \( q \)", that is, "believing \( p \) implies believing \( q \)". \[ (p \Rightarrow q) = (K p \rightarrow K q). \]

But why would we?

7.2TODO Platonism, numbers, ideal existence, and physical existence?

  • Isn't this just Plato's theory of forms?
  • Do we benefit from talking about this?
  • Should we delete this?

"123" is a decimal representation of a number, not the number itself.

A number exists ideally. It doesn't exist physically. Our body can't interact with a number. We can't touch a real number. There is no physical experiment that tests the properties of numbers. Our mind can't interact with a number either. We can't imagine a number. We can only imagine a representation of that number.

But our minds can correlate idea space and physical space.

We use physics experiments to find out physical laws. We use thought experiments to find out ideal laws (such as theorems about real numbers). An eye is a physical sense that enables the brain to probe the space of bodies. A mind is an ideal sense that enables the brain to probe the space of ideas.

8Science, engineering, and technology

8.1Is science knowledge?

How is "social science" and "computer science" science?

"Science" comes from the Latin word "scientia" that means "knowledge".

8.2The meaning of phrases

The phrase head is the most important word. https://en.wikipedia.org/wiki/Head_(linguistics)

Genus-differentia meaning of noun phrases.

A "red car" is a car that is red.

"Natural science" is science about nature.

"Computer science" is science about computers.

"Civil engineering" is engineering about cities.

9TODO Implication (do not read; conversion errors)

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This section contains conversion errors.

Plan: Salvage the parts of this section into the parent document.

9.1Abstract

The implication \(A \to B\) means that \(A\) restricts \(B\).

We introducture an implication system, which involves a metric and a freedom function. We unify (generalizes?) material implication in classical logic and conditional probability in probability theory.

(Need better abstract. Answer "Why should I care?")

9.2What does implication mean?

(This section needs rereading and rewriting.)

We read the sentence \(p \to q\) as "\(p\) implies \(q\)'' or"if \(p\), then \(q\)''.

What does \(p \to q\) mean?

It means that:

  • If we know \(p\), then we can infer \(q\).
  • If we don't know \(p\), then the implication does not say anything at all.
  • Knowing \(p\) allows us to predict \(q\).
  • \(p\) gives information about \(q\).
  • \(p\) determines \(q\).
  • \(p\) restricts \(q\).

We can formalize this constraint by using a metric \(d : [0,1]^2 \to [0,1]\) and a function \(u : [0,1]^2 \to [0,1]\). We can formalize the constraint as the following inequality:

\[\begin{align} d(\tau(p), \tau(q)) \le u(\tau(p), \tau(p \to q)) \end{align} \]

where the function \(u\) must satisfy \(u(0,x) = u(x,0) = 1\) for all \(x \in [0,1]\), and \(u(1,1) = 0\). The right-hand side of the inequality says that the maximum distance depends only on \(\tau(p)\) and \(\tau(p \to q)\). (As we increase our certainty about both the premise and the implication, we become more certain about the conclusion.)

9.2.1Deriving the constraint

If both \(\tau(p)\) and \(\tau(p \to q)\) are high, then the constraint is quite strict, and \(\tau(q)\) should be near \(\tau(p)\).

The modus ponens is "if we are sure about \(p\) and we are sure about \(p \to q\), then we can be sure about \(q\)''. We can say that more formally as "if \(\tau(p)\) is high, and \(\tau(p \to q)\) is high, then \(\tau(q)\) should be high''.

The number \(\tau(p \to q)\) should describe how strictly \(\tau(p)\) constrains \(\tau(q)\). Let's consider the corner cases first to gain some intuition for later generalization. The corner cases are:

  • If \(\tau(p) = 0\), then \(\tau(q)\) is not constrained. (If we aren't sure about the premise, we can't make a conclusion, regardless of how sure we are about the implication.)
  • If \(\tau(p \to q) = 0\), then \(\tau(q)\) is not constrained. (If we aren't sure about the implication, we can't make a conclusion, regardless of how sure we are about the premise.)
  • If \(\tau(p) = 1\) and \(\tau(p \to q) = 1\), then \(\tau(q)\) has no freedom at all, and it must be \(\tau(q) = \tau(p) = 1\). (If we are sure about both the premise and the implication, then we can make the conclusion.)
  • If we know that \(\tau(p)\) is low or \(\tau(p \to q)\) is low, then knowing any of those does not enable us to infer anything about \(\tau(q)\).

9.2.2Algebra of metrics

If \(d\) is a metric and \(k\) is a constant, then \(d' = (x,y) \to k \cdot d(x,y)\) is also a metric?

If \(d_1\) and \(d_2\) are metrics then \(d_1 + d_2\) is a metric?

If \(d_1\) and \(d_2\) are metrics then \(d_1 \cdot d_2\) is a metric?

A linear combination of metrics is a metric.

9.2.3Consequent freedom functions

If \(u\) is a consequent freedom function, then so is \(u' = (x,y) \to [u(x,y)]^k\) for all real \(k > 0\).

If each of \(u_1, \ldots, u_n\) is a consequent freedom function, and if \(\sum_{k=1}^n w_k = 1\), then \(u' = (x,y) \to \sum_{k=1}^n w_k \cdot u_k(x,y)\) is also a consequent freedom function.

An example function that satisfies those constraints is \(u(x,y) = 1 - xy\). Indeed, for every real \(k > 0\), the definitions \(u(x,y) = 1 - (xy)^k\) and \(u(x,y) = (1 - xy)^k\) satisfy those constraints. For simplicity, until there is reason for doing otherwise, we pick \(d(x,y) = |x - y|\) (norm-1) and \(u(x,y) = 1 - xy\), and therefore we obtain the following special case:

\[\begin{align} | \tau(p) - \tau(q) | \le 1 - \tau(p) \cdot \tau(p \to q). \end{align} \]

Let \(P = \tau(p)\), \(Q = \tau(q)\), and \(R = \tau(p \to q)\).

\[\begin{align} (P-Q)^2 &\le 1 - PR \\ (P-Q)^2-1 &\le - PR \\ (P-Q+1)(P-Q-1) &\le - PR \\ PR &\le (P-Q+1)(P-Q-1) \\ R &\le \frac{(P-Q+1)(P-Q-1)}{P} \\ R &\le \left(1 - \frac{Q-1}{P}\right) \left( 1 - \frac{Q+1}{P}\right) \end{align} \]

Another example is \(u(x,y) = 1 - \min(x,y)\). Can it be written \(u(x,y) = \neg (x \wedge y)\), as in fuzzy logic?

If we know \(\tau(p)\) and \(\tau(p \to q)\), but we don't know \(\tau(q)\), then we can estimate \(\tau(q)\) as the midpoint. Let \(P = \tau(p)\), let \(Q = \tau(q)\), and let \(R = \tau(p \to q)\).

\[\begin{align} - u(P,R) &\le P - Q \le u(P,R) \\ - P - u(P,R) &\le -Q \le -P + u(P,R) \\ P + u(P,R) &\ge Q \ge P - u(P,R) \\ \hat{Q} &= P \end{align} \]

WTF…

(RAMBLE)

In classical logic, knowing \(\tau(p)\) and \(\tau(q)\) allows us to determine \(\tau(p \to q)\). This does not make sense. It should be the other way around: knowing \(\tau(p \to q)\) should allow us to use \(\tau(p)\) to restrict \(\tau(q)\).

We may know something for sure because we defined it to be true or we experienced it ourselves through our senses.

In classical logic, \(\tau(p)\) is either 0 or 1, and \(\tau(p) = 0\) means that \(p\) is false, and \(\tau(p) = 1\) means that \(p\) is true.

9.2.4Principle of non-contradiction

Principle of non-contradiction: \(\tau(p) = -1\) if we know that \(p\) is false.

Should we accept this principle?

Therefore \(\tau(\neg p) = - \tau(p)\).

Does paraconsistent logic make sense?

9.3Implication system

9.3.1Definition of implication system

A unit metric is a metric whose inputs and output are in the unit real line \([0,1]\). More specifically, a unit metric is a function \(d : [0,1]^2 \to [0,1]\) satisfying the following metric axioms for all \(x,y,z \in [0,1]\):

\[\begin{align} d(x,x) &= 0, \\ d(x,y) &= d(y,x), \\ d(x,z) &\le d(x,y) + d(y,z). \end{align} \]

A consequent freedom function is a function \(u : [0,1]^2 \to [0,1]\) satisfying to for all \(x,y,y' \in [0,1]\), and \(c \in (0,1)\):

\[\begin{align} u(1,1) &= 0, \label{mdf_axiom_1} \\ u(0,x) &= 1, \\ u(x,0) &= 1, \\ y \le y' &\implies u(c,y) \ge u(c,y'), \label{is_mono_1} \\ y \le y' &\implies u(y,c) \ge u(y',c). \label{is_mono_2} \end{align} \]

The constraints and say that \(u\) is monotonically non-increasing with respect to each argument.

An implication system is a tuple \((S,\tau,d,u)\) plus the constraints to .

The set \(S\) is a set of sentences. This set is closed under implication:

\[\begin{align} p \in S \wedge q \in S \implies (p \to q) \in S. \label{is-cstr-begin} \end{align} \]

The function \(\tau : S \to [0,1]\) is a truth value function.

The function \(d\) is a unit metric.

The function \(u\) is a consequent freedom function.

The system must satisfy for all \(p,q \in S\):

\[\begin{align} d(\tau(p), \tau(q)) &\le u(\tau(p), \tau(p \to q)). \label{imp-constr} \end{align} \]

We call the meaningful implication constraint. (Need a better name.) (Simplify this definition.)

9.3.2Known instances

These systems are implication systems: - classical logic - probability theory

Need to find out:

  • possibility theory
  • minimal logic
  • paraconsistent logic
  • Dempster–Shafer theory
  • evidential decision theory

\begin{m:lem} Classical logic is an implication system.

\end{m:lem} \begin{m:lem} Probability theory is an implication system.

\end{m:lem} In probability theory, conditional probability is \(P(A) \cdot P(B|A) = P(A \cap B)\), which can also be written \(\tau(p) \cdot \tau(p \to q) = \tau(p \wedge q)\). If all samples are equiprobable, then the \(P(B|A)\) measures how much of \(B\) is inside \(A\). If the intersection of \(A\) and \(B\) is not empty, then \(0 \le P(B|A) \le 1\). If \(A\) and \(B\) are disjoint, then \(P(B|A) = 0\). If \(A \subseteq B\), then \(P(B|A) = 1\).

9.3.3Probability theory

Probability theory also allows us to compute \(\tau(p \to q)\) by conditional probabilities \(\tau(p) \cdot \tau(p \to q) = \tau(p \wedge q)\).

9.4Induction

9.4.1Justifying induction with probability theory

Let \(X \subseteq \Omega\) be a set of some samples. For every \(x \in X\), we can observe \(x\) and compute \(\tau(x)\).

Induction works because the sample mean is an unbiased esimator of the population mean. If you pick 100 random people, and 55 are male, then it is rational to generalize that to the assumption that 55% of the human population is male. You cannot infer this from your friends because they are not random.

Let \(P(X) = \{ x ~|~ p(x) \}\) where \(p\) is a predicate. Let \(\Omega\) be the universe of discourse. Let \(E \subseteq \Omega\) and \(E' \subseteq \Omega\). Then, states that every additional evidence makes the induction more reasonable.

\[\begin{align} E \subseteq E' \to \tau(P(E) \to P(\Omega)) \le \tau(P(E') \to P(\Omega)) \label{ind} \end{align} \]

9.5Conditionals

9.5.1Types of conditionals according to logic, philosophy, and linguistics

There are several types of conditionals: causal, strict, indicative, counterfactual, strict, material, formal.

9.5.2Eight types of conditionals by the truth values of the parts

If \(\tau(p) = 1\) means that all swans are white, then \(\tau(p) = 0.99\) should mean that almost all swans are white, and \(\tau(p) = 0\) should mean that we don't have any particular belief about whether swans are white. Should \(\tau(p) = -1\) mean that no swans are white?

There are eight combinations of antecedent, consequent, and implication:

  • total nonsense (UUU): If X had been born in a Muslim family, then X would be a Christian now.
  • counterfactual (UUR): If X had been born in a Muslim family, then X would be a Muslim now.
  • non-sequitur (URU): If X had been born in a Muslim family, I'll get a million dollars.
  • ? ransom (URR): If you give me a million dollars, I'll keep working as usual.
  • wishful thinking (RUU): If I keep working as usual, I'll get a million dollars.
  • paradox (RUR): (Quantum mechanics?)
  • irrelevant (RRU): If John is a man, then Mary is a woman.
  • law (RRR): reasonable antecedent, reasonable consequent, reasonable implication: Theorems in mathematics.

An implication should become more reasonable as its antecedent becomes more reasonable? An implication should become more reasonable as its consequent becomes more reasonable?

The function \(\tau\) takes a sentence (a belief) and gives a real number in \([0,1]\). The value \(\tau(p \to q)\) describes how justified we are when we infer \(q\) just by knowing \(p\).

If \(p\) causes \(q\), then removing \(p\) should also remove \(q\). Formally, \((p \to q) \vdash (\neg p \to \neg q)\).

Correlation is a necessary but not sufficient for causation.

Finding common cause: Find \(p\) such that \(p \to q\) and \(p \to r\).

Should \(p \to \top\) be equally true to \(p\)?

Example: John pressed the button, and a light blinked. It is rational for John to reason that if the button were not pressed, the light would not blink. But why is that rational? What is the mathematical justification? The implicit belief that the system always behaves the same way. The implicit belief is that the button behaves the same at all times. \(\forall t \in \Real, press(t) \to blink(t + 1)\)

Every counterfactual reasoning implicitly makes a ceteris paribus (everything else being equal) assumption. When we make a counterfactual implication, we assume that everything else other than the premise stays the same in the past we are imagining. "If the driver was driving more slowly, the driver would have had enough time to brake, and therefore the crash would have been avoided."

Suppose that two cars crashed at an intersection. What causes the crash?

If we have that axiom, then by \(\forall\)-elimination we can prove the following, given \(t_0 \in \Real\):

\(press(t_0) \to blink(t_0 + 1)\)

What should \(\tau(p \to q)\) be?

Spurious correlation, confounding factor

Is there an example of counterfactual that does not involve time?

\(\tau (\forall x \in [0,1], x \in [0,1/2]) = 1/2\) depends on the distribution?

9.6The axioms

In this section, we list the axioms that \(\tau\) has to satisfy.

9.6.1Equations

The equations allow us to rewrite sentences without changing their reasonability.

and describe idempotence or contraction. and describe commutativity. and describe associativity. I thought everybody would accept these axioms, but I was wrong, as these axioms do not hold in linear logic, but for everyday reasoning, I think these axioms should hold.

\[\begin{align} \tau(p \wedge p) &= \tau(p) \label{and_idem} \\ \tau(p \vee p) &= \tau(p) \label{or_idem} \\ \tau(p \wedge q) &= \tau(q \wedge p) \label{and_comm} \\ \tau(p \vee q) &= \tau(q \vee p) \label{or_comm} \\ \tau((p \wedge q) \wedge r) &= \tau(p \wedge (q \wedge r)) \label{and_assoc} \\ \tau((p \vee q) \vee r) &= \tau(p \vee (q \vee r)) \label{or_assoc} \end{align} \]

The following axioms are less obvious. and state that implication distributes conjunction and disjunction on the right side. states that every sufficient cause is a necessary cause.

\[\begin{align} \tau(p \to (q \wedge q')) &= \tau((p \to q) \wedge (p \to q')) \label{imp_dist_and} \\ \tau(p \to (q \vee q')) &= \tau((p \to q) \vee (p \to q')) \label{imp_dist_or} \\ \tau((p \vee p') \to q) &= \tau((p \to q) \wedge (p' \to q)) \label{imp_suf} \end{align} \]

is currying, which may be obvious if you know functional programming.

\[\begin{align} \tau((p \wedge p') \to q) &= \tau(p \to (p' \to q)) \label{curry} \end{align} \]

9.6.2Tautologies

is self-inference. is conjunction elimination. is disjunction introduction. is modus ponens or implication elimination. is relaxing the consequent. is syllogism. These forms are always valid regardless of the sentences.

\[\begin{align} 1 &= \tau(p \to p) \label{nowhere} \\ 1 &= \tau((p \wedge q) \to p) \label{and_elim} \\ 1 &= \tau(p \to (p \vee q)) \label{or_intro} \\ 1 &= \tau((p \wedge (p \to q)) \to q) \label{mp} \\ 1 &= \tau((p \to (q \wedge r)) \to (p \to q)) \label{imp_and_elim} \\ 1 &= \tau((p \to q) \wedge (q \to r)) \to (p \to r)) \label{syl} \end{align} \]

If we accept the law of excluded middle \(p \wedge \neg p = \bot\), then we must also accept the principle of explosion \(\bot \to p\), which is obtained by replacing \(q = \bot\) in .

9.6.3Inequalities

and describe dominance: satisfying two sentences are harder than satisfying either of them. and are the axioms of prudence that say that restricting the antecedent or relaxing the consequent strengthens the implication. \((p \wedge p') \to q\) should not be less reasonable than \(p \to q\) because both \(p\) and \(p'\) are necessary but not sufficient causes of \(q\).

\[\begin{align} \tau(p \wedge q) &\le \tau(p) \label{and_dom} \\ \tau(p \vee q) &\ge \tau(p) \label{or_dom} \\ \tau((p \wedge p') \to q) &\ge \tau(p \to q) \label{prud_ante} \\ \tau(p \to (q \wedge q')) &\le \tau(p \to q) \label{prud_cons} \end{align} \]

The /axiom of precedence of knowledge over inference} (or just a /language* if there is no ambiguity) is a set of strings, and this set can be described by rules.

From a set \(S\) and a language \(L\), several questions arise:

(RAMBLE)

Sometimes we write \(P(x,y)\) to mean \((x,y) \in P\). But this conflates a set and a predicate that describes the set.

What?

What?

Ontologies and Knowledge-Based Systems http://artint.info/2e/html/ArtInt2e.Ch14.html

Find implication and conditional in arxiv, arxiv math, arxiv logic, google scholar, and logic journals

Types of conditionals: causal, indicative, counterfactual, subjunctive, material, formal.

Metric Spaces, Generalized Logic, and Closed Categories https://golem.ph.utexas.edu/category/2014/02/metric_spaces_generalized_logi.html

Axioms of probabilistic propositional calculus?

  • Boolean truth value \(\{ 0,1 \}\) generalizes to real number probability \([0,1]\).
  • Sentence generalizes to event (subset of sample space).
  • \(t(p \wedge q) = \min(t(p),t(q))\)
  • Find \(t\) such that \(t\) is a probability measure and \(t(p) \le t(p \wedge q)\), \(t(p \vee q) \le t(p)\).
  • A logical predicate becomes an event family (input: sample; output: set of samples).
  • Does it make sense to define \(t(p \to q) = \Pr (q|p)\) (Bayes's law)?
  • What is \(t(\forall x \in A, p(x))\)? It is \(\Pr (x \in A \to p(x))\).
  • The truth value function takes a logical sentence (it cannot contain any free variables) and outputs a real number.
  • The statement "every swan is white" is not entirely wrong.

10TODO Delete these drafts?

10.1Objective reality

10.1.1My inability to manipulate everything implies the existence of reality outside my mind

What is wrong with this argument?

If my mind is all there is, then I should be omniscient and omnipotent: I should be able to do anything I want with the law of nature.

My will does not change reality. A green elephant does not appear even though I will it to appear.

10.1.2Is "objective reality" redundant? How does "objective reality" differ from "reality"?

10.1.3<2018-11-06> Example difference between statements about objective reality and statements of subjective reality

There is this difference:

  • "I can fly." is a statement about objective reality.
  • "I believe I can fly." is a statement about my subjective reality.

10.1.4TODO A thing is real iff …

  • … it has material existence?
  • … it interacts with our senses?
  • … it influences us?
  • … we can think about it?

10.1.5TODO We can know some of objective reality.

https://medium.com/the-polymath-project/so-you-think-humans-cant-know-objective-reality-e609346c2682

10.2Solipsism unnecessarily assumes that one person's point of view is special.

Let there be three people P, Q, and R.

  • P states SP: P exists, and Q does not exist.
  • Q states SQ: P does not exist, and Q exists.
  • R sees that SP is the negation of SQ, and, assuming the law of non-contradiction, infers that SP and SQ cannot be both true.
    • What if R rejects the law of non-contradiction?
      • Does it make sense to reject the law of non-contradiction?

10.3TODO Delete this section? Maybe we don't have to define these terms.

  • Define: A model is a representation or approximation.
  • Define: The self-model of X is X's model of X.
  • Define: awake and asleep
    • Define: Something is asleep iff it is not awake.
  • Define: think, feel
  • Define: thought, feeling, qualia, perception, mental state
  • Define: percept
  • Define: To recall something is to reproduce a model of it.
  • Define: To remember something is to be able to recall it.
  • Define: Memory is something affected by the past.
  • Define: Soul is what animates a thing?

10.3.1<2018-11-05> A system is a reflex system iff it is memoryless.

10.4TODO <2018-11-04> Summarize current research

10.4.1Neuropsychology

  1. 2017 article "The Status and Future of Consciousness Research" https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5641373/

    • This article makes me sure that I'm not interested in how to measure consciousness, I'm not interested in neural correlates of consciousness, and I'm not interested in neuroscience.
    • Consciousness research is multidisciplinary.
      • "Cognitive scientists and neuroscientists agreed that the philosophical problems of why and how there is consciousness are also their problems. Philosophers agreed that empirical evidence may resolve or at least influence this debate. Scientists across disciplines generally agree that consciousness is subjective, characterized by a kind of privileged first-person access."
    • Challenges
      • "One major obstacle for consciousness research is the lacking consensus of how to optimally measure consciousness empirically."
      • "Another major challenge is how to identify neural correlates of consciousness."
    • "The future challenges"
      • "One major future challenge will be how to measure consciousness 'from the outside'."
      • "One possibly even greater challenge will be to reintegrate the philosophical metaphysical debate into the scientific work."
    • "Future directions"
      • "Currently, consciousness research is often considered a 'topic'—or even 'niche'—under the umbrella of cognitive neuroscience."

  2. 2011 article "Understanding Brain, Mind and Soul: Contributions from Neurology and Neurosurgery" https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3115284/

    • The section "The Mind" correlates brain damage and behavior change.
    • The section "Where is the Mind Located?" says "The brain is the organ of the mind just as the lungs are the organs for respiration."
    • "How does the Mind Function?"
      • "Krishnamoorthy (2009) uses an analogy based on computers to explain the workings of the mind: […]"
      • "The mind cannot be localised to particular areas within the brain, […]"
    • "The Soul"; "The search and some conclusions"
      • "In 1907, Dr. Duncan MacDougall of Haverhill, Massachusetts, decided to weigh the soul by weighing a human being in the act of death."
      • "If there be a soul, where is it located? Views of neuroscientists"
        • "If we accept the existence of the soul and its localisation in the brain, we must focus on the brainstem."
    • "Take home message"
      • "The study of the brain, mind and soul has engaged some of the finest intellects of yesteryears. It remains an ennobling and inspiring pursuit, worthy of all those who are dedicated votaries of science."
    • "Questions That This Paper Raises"
      • "2. Do you agree with the author’s conclusions on the mind in the brain?"
        • My objections to the article
          • <2018-11-04> I doubt "The brain is the organ of the mind […]"; near-death experience research suggests that the mind can function without brain activity.

  1. 2013 article "Distinguishing Brain From Mind" https://www.theatlantic.com/health/archive/2013/05/distinguishing-brain-from-mind/276380/

    • "In coming years, neuroscience will answer questions we don't even yet know to ask. Sometimes, though, focus on the brain is misleading."
    • Neurocentric/reductionistic/materialistic approach to addiction theory, that focuses on the brain but ignores the mind, is wrong.

  2. 2013 article "Why are top scientists […] interested in researching human consciousness?" https://www.mindscience.org/index.php/research/the-scientific-study-of-consciousness.html

    • "modern brain imaging seems to indicate that it is Spinoza's concept of an integrated mind-body that is closer to reality."
    • "psychologist William James' great work on consciousness in the late 1800s is slowly regaining the pivotal position it deserves in understanding and interpreting human behavior."
    • "technological advances in brain imaging have given scientists a new range of tools to more accurately observe and measure the apparent causes and manifestations of consciousness."

10.4.3Nonlocality

  1. 2016 Pim van Lommel interview "Continuity of non-local consciousness" https://www.landelijkexpertisecentrumsterven.nl/inspiratie/continuity-of-non-local-consciousness/

    • Which experiment of continuity of nonlocal consciousness convinces you the most?
      • "the studies of near-death experience (NDE) in survivors of cardiac arrest"
      • "Based on these NDE-studies one can conclude that there are good reasons to assume that our consciousness does not always coincide with the functioning of our brain"
      • "most likely the brain must have a facilitating and not a producing function to experience consciousness"
      • "Also cases of after-death communication (ADC), with communication with the consciousness of deceased loved ones, and sometimes information was shared that was not yet known"
      • "Like the NDE there is also a huge taboo to talk about ADCs, because they cannot be 'objectively proven'."
    • How did you contribute?
      • "our prospective study in survivors of cardiac arrest"
      • "after the temporary loss of all functions of the brain during clinical death (= cardiac arrest) the experience of enhanced consciousness was still possible in 18% of those patients"
    • "How close do you feel we are in establishing without a doubt that there is life after death?"
      • "it will never be possible to 'prove' this idea because consciousness is subjective, and (materialist) science uses only objective methodology"
      • "The scientific study of NDE pushes us to the limits of our medical and neurophysiological ideas about the range of human consciousness and mind-brain relation."

  2. 2016 article https://explore.scimednet.org/index.php/all-physics-is-nonlocal/

    • "there is no agreement among physicists on what nonlocality means"
    • "Bohmian mechanics is different from traditional quantum mechanics, in that particles follow definite trajectories, and possess both a definite position and momentum. This doesn’t violate the uncertainty principle, because that principle only places limits to what we can know about position and momentum. What Bohm said is that a quantum particle has a real as opposed to statistical existence, […]"
    • "Nonlocal behavior is seen most plainly in the behavior of entangled particles as described by Bell’s Theorem."

  3. 2017 article https://bigthink.com/robby-berman/is-consciousness-in-the-physical-world-we-may-be-about-to-find-out

    • Lucien Hardy "has an experiment to see if the mind operates on a quantum level."
    • "I am currently working with the group of Jian-Wei Pan to realize this experiment using their satellite source that can distribute entanglement over 1200km." https://www.perimeterinstitute.ca/people/lucien-hardy
    • TU Delft – The Bell test explained https://www.youtube.com/watch?v=z1twSZF4fLM
    • "It’s a Bell test that Hardy is interested in running, with an added wrinkle of his own. Instead of varying the properties to be observed using random number generators, he proposes observing entangled particles with A and B detection units positioned 100 kilometers apart, and whose settings are controlled by EEG signals from headsets on 100 human volunteers."

  4. 2015 article "Does consciousness go beyond the brain?" https://noetic.org/blog/arnaud-delorme/does-consciousness-go-beyond

    • "What is the evidence so far?"
    • "Currently consciousness is considered by mainstream science as an epiphenomenon often with no causal consequence that emerges from this structure in a sort of magical way. The prevailing view is that consciousness an illusion created by the brain."
    • "One of our main approach […] is to perform scientific experiments which attempt to show the non locality of consciousness."
    • "If consciousness is non-local, then certainly the 'consciousness in the brain' hypothesis must be revised."
    • https://noetic.org/research/projects

10.4.4TODO Summarize Wikipedia

10.5TODO Tidy up these ramblings

10.5.1TODO Intension (actual) vs extension (apparent)? What are we trying to say?

  • Intension: actually having a mind
  • Extension: apparently having a mind (behaving like something having a mind)
  • We are interested in the intension.
  • Is it even possible to test the intension?
  • WP:Hard problem of consciousness
    • intension is "hard" problem
    • extension is "easy" problem

  1. Examples of intensional consciousness vs extensional consciousness?

    • Intensional but not extensional: a person playing dead.
    • Extensional but not intensionally: a rule-based system with very many rules but never changes (doesn't have memory, doesn't learn).
      • Why isn't it intensionally conscious? It displays complex behavior.
        • Also, for every test it fails, we can always add a rule.
        • We can also add rules to make it behave as if it were self-aware.

    1. Locked-in syndrome: The sensors work but the actuators don't work.

10.5.2TODO Problem with idealism? If reality is an illusion, why is it consistent?

10.5.3TODO Identity continuity problem

What is the relationship between my old self and my present self?

10.5.4TODO Blind protocol?

The blind protocol and its place in consciousness research

10.5.5Things I'm no longer interested in

  1. Memory is unreliable.

    1. Observe: There exists things I experienced but don't remember.

      • Example: What I ate some long time ago.

    2. How far back does our memory extend?

      • Human memory is unreliable.
      • I don't remember being a fetus in the womb.
      • I don't remember being a baby.
      • I vaguely remember my kindergarten when I was 3 years old. I'm not sure I remember it correctly. I don't remember anything that happened before I was 3 years old.
      • I don't remember what I ate two days ago. I rarely even remember what I ate yesterday.
      • I don't exactly remember what I wrote yesterday.
      • I only remember a very tiny amount of everything that I perceive (everything that interacts with my senses).

    3. What does it mean to remember?

      • If one does not remember a thing, it does not mean that he does not have any memory about that thing.

    4. How do we remember things?

  2. What?

    • Thought is the brain's perception of itself. Does consciousness arise in a body, or attach to a body?

  3. What?

    • Sentence S is true.
    • Proof P proves sentence S in formal system F.
    • Agent A knows the truth of sentence S.

10.5.6TODO Ruminations about control

Example. A feedback system controls its output? I don't control what you say but I control my emotion. Who is in control? The situation is getting out of control? I control the character's motions using this controller.

"Control […] is a word with diverse meanings and applications, ranging from those found in control theory regarding dynamical systems, self-control of one's own behavior, social control of processes and political mechanisms that regulate individual and group behaviour, including security controls against perceived or unperceived dangers, mind control, in which groups or individuals systematically use unethically manipulative methods to direct others, and scientific control to isolate variables in experiments." https://en.wikiquote.org/wiki/Control

Control is going against nature? How can we go against nature if we are part of nature? How can nature go against nature?

Control is making something go against what it would go when left alone.

Control is limit.

Control is giving commands.

"To control" means "To exercise influence over; to suggest or dictate the behavior of" according to Wiktionary. Thus X controls Y iff X influences Y's behavior.

What is "influence"?

  1. Failed ruminations

    1. X controls Y iff X does what Y wants X to do.

      I control something iff it does what I want.

      Problematic consequence of that definition: If, by luck, Y happens to be already doing what X wants, then the definition says that X controls Y. Example: If I want you to do what you do, the definition says I control you.

10.6TODO What is the relationship between first-person view, consciousness, imagination, and reality?

10.7<2018-11-06> If I can imagine something, does it exist?

10.8<2018-11-06> Imagination is not real, because saying otherwise bends words too much.

11Correspondences?

11.1Contemporary philosophers that perhaps I should work with?

11.2Steve Patterson

11.2.1<2018-11-17> compression

The algorithm you're looking for may be similar to Huffman coding. "a Huffman code is a particular type of optimal prefix code that is commonly used for lossless data compression" (emphasis mine) https://en.wikipedia.org/wiki/Huffman_coding

Arithmetic coding may even compress better, but it is patent-encumbered. https://en.wikipedia.org/wiki/Arithmetic_coding

12Known problems

12.1Unfixed spelling errors

  • "master's thesis", not "master thesis"
  • "law of non-contradiction", not "law of no contradiction"

13Mess

13.1Judea Pearl, causality

"Deep Probabilistic Logic: A Unifying Framework for Indirect Supervision" https://arxiv.org/abs/1808.08485

bunch of links http://bactra.org/notebooks/causality.html

This looks readable "Causal inference in statistics: An overview" https://projecteuclid.org/euclid.ssu/1255440554 https://projecteuclid.org/download/pdfview_1/euclid.ssu/1255440554

Judea Pearl annotated bibliography https://amturing.acm.org/bib/pearl_2658896.cfm

Judea Pearl won 2011 Turing award https://amturing.acm.org/award_winners/pearl_2658896.cfm

2011 article "The algorithmization of counterfactuals" http://ftp.cs.ucla.edu/pub/stat_ser/r360.pdf

I wanted to read "Book of why", but I changed my mind.

This book narrates Judea Pearl's hard-won war against anti-causality statisticians. Most of it is history of 21st century statistics. A little part describes causal model.

It's too long (400 pages). It should take at most 20 pages.

Is Pearl 2000 a better book?

Human interprets data.

Science requires philosophy.

To intervene is to control.

To control a variable is to fix its value.

How to read it:

  • Read page 111 about junctions: mediators, colliders, forks
    • page 113: "We will now see that this collider pattern works in exactly

the opposite way from chains or forks when we condition on the variable in the middle."

The collider is counterintuitive. What does it mean to control for an output variable?

There is no input/output variable in statistics.

  • Read page 149 "The do-operator and the back-door criterion"

"I like to think of the links as pipes that convey information from a starting point X to a finish Y."

13.2Cyclic subgraphs in causal graphs

Example cyclic cause: Accident -> Poverty <-> Homeless

https://math.stackexchange.com/questions/276591/what-is-the-extension-of-bayesian-network-into-cyclic-graph

Infinite unfolding: X <-> Y X0 -> Y0 -> X1 -> Y1 -> … Cyclic Bayesian network

A <-> B A means X attacks Y B means Y attacks X Never-ending retaliation.

What does a Bayesian network (a conditional independence network) represents?

13.3Geometry

Finitism:

Finitism and geometry, from Steve Patterson https://plato.stanford.edu/entries/geometry-finitism/ https://en.wikipedia.org/wiki/Finitism https://en.wikipedia.org/wiki/Rational_trigonometry

Google scholar "finitism in geometry" https://scholar.google.co.id/scholar?hl=en&as_sdt=0%2C5&q=finitism+in+geometry&btnG=

Geometrical Models of the Locally Anisotropic Space-Time

https://en.m.wikipedia.org/wiki/Incidence_geometry

Essence of geometry Minimal geometry Finitist analytic geometry Geometry vs topology Birkhoff axioms History of geometry, semantics of geometry Solomon Feferman?

2004 "Minkowski space-time: a glorious non-entity" https://arxiv.org/pdf/physics/0403088.pdf

2008 "Why Constructive Relativity Fails" https://www.pitt.edu/~jdnorton/papers/Constructive_Relativity_BJPS.pdf

https://www.quora.com/Does-the-universe-wrap-around-so-that-Earth-could-see-itself-far-away-were-it-not-for-the-speed-of-light "We now know that the universe is flat with only a 0.5% margin of error." What?

2002 master's thesis; Axiomatic Discrete Geometry by Nils Anders Danielsson http://www.cse.chalmers.se/~nad/publications/danielsson-msc.pdf

Reread this? "A universe tiled with points", Akinbo Ojo http://www.rxiv.org/pdf/1211.0154v1.pdf

https://www.reddit.com/r/badmathematics/comments/4gjs5n/some_notes_on_ultrafinitism_and_badmathematics/

https://www.google.co.id/amp/s/amp.reddit.com/r/badmathematics/comments/4gjs5n/some_notes_on_ultrafinitism_and_badmathematics/

https://www.reddit.com/r/math/comments/1uhj1a/what_do_you_mathematicians_think_about_finitism/

2011 Geometrical Models of the Locally Anisotropic Space-Time

13.4Philo of CS

2018 William J. Rapaport draft "Philosophy of Computer Science" https://cse.buffalo.edu/~rapaport/Papers/phics.pdf

Read and understand https://plato.stanford.edu/entries/computer-science/ They say "technical artifact", I say "tool".

13.5Simplicity?

1996 "A Simplification of the Theory of Simplicity" https://www.jstor.org/stable/20117522?seq=1#page_scan_tab_contents

2001 "Simplifying complexity: a review of complexity theory" https://www.sciencedirect.com/science/article/pii/S001671850000035X

https://www.google.co.id/amp/s/phys.org/news/2017-06-gaining-knowledge-simplification.amp

https://en.m.wikipedia.org/wiki/Simplicity_theory

Simple, Multiple = many-fold Ply, plier?

Complexity theory inspired by paper folding

Group complexity theory

Simplicity theory

Simpler to prove (having shorter proof)? Adding an axiom. Simpler to write (shorter to write)?

A simplifying assumption is an axiom added to a formal system. This axiom shortens proofs, but reduces correctness.

Smaller doesn't always mean simpler.

13.6Total mess

The -ness suffix can denote degree/grade/amount/extent. The brightness is 50%. His agreeableness is 90%.

It is hot. There is much hotness. The hotness is high.

The house is big. The house has bigness.

Calmness

By "his calmness"

This well is deep. The deepness of this well is high.

-ness turns an adjective (a predicate) into a continuous property.

Dodgy. Dodginess. Tangible Tangibility Red Redness Friendly Friendliness Indebtedness A chicken is two-legged. The two-leggedness of chicken is true.

I met a person I didn't know. I-didn't-know-ness?

That car is desirable. The desirability of that car is high.

He is handsome. The handsomeness of him is high. He has much handsomeness?

The water is boiling. The boilingness of the water is true.

S is Adj. Adj(S) Adjness(S,true)

Maybe I can ask some of my questions to https://www.reddit.com/r/philosophy/.

Example of causality

A chips breaks a vase. A mom gets angry.

A man is angry. He throws dishes.

A man eats a poisonous mushroom. He dies.

Examples of coincidence

I came to office. My coworkers came to office a few seconds after I did. My coming does not cause their coming.

What makes some explanations plausible?

https://en.wikipedia.org/wiki/Causality

Buying the lottery is a necessary cause for winning the lottery.

X causes Y iff X raises the probability of Y?

X causes Y iff the absence of X causes the absence of Y?

Personification or shortening

"The author claims X."

"This document claims X."

Causality is the direction of effect? C causes E means C affects E.

These people should collaborate: Judea Pearl, J\"urgen Schmidhuber, Marcus Hutter, Shane Legg:

  • Counterfactual reasoning is the about constructing a causal model.
  • Algorithmic probability can compute the feasibility of a causal model.

This is a somewhat helpful summary. It has a link to his talk. Should I watch him talk? https://www.quora.com/What-is-Judea-Pearls-work-on-causality-in-a-nutshell

Is this the same talk? "Keynote: The Mathematics of Causal Inference: with Reflections on Machine Learning" https://www.youtube.com/watch?v=bcRl7sXR1hE

https://en.wikipedia.org/wiki/Involuntary_memory

https://www.reddit.com/r/philosophy/comments/9u4tx1/an_example_of_how_to_tackle_and_highlight_logical/

I can't reduce "Want" cannot be broken into parts. "Want" is an undefined term, like "point" in geometry.

Suppose that cause C causes effect E.

The "causality lag" is the time after C has ended but before E begins.

https://writingcooperative.com/why-every-serious-writer-should-study-philosophy-cf058563ba81

13.7What is the relationship between ability, logic, semantics, time?

13.7.1Problems

Do inanimate objects have abilities? How do we make sense of "This rock can crush me"? Can a rock do anything? When a rock falls, does the rock do the falling?

13.8Machine, engine, software

A machine is either programmable or non-programmable.

An engine requires energy and does work.

An engine transforms energy into work.

Defining software is related to solving the hard problem of consciousness.

13.9software?

A software is an executable model.

Software is hardware configuration.

13.10chance, random, hazard, ignorance

13.11what

https://www.realsimple.com/work-life/life-strategies/inspiration-motivation/philosophy-101

https://philosophy.hku.hk/think/phil/101q.php

13.12model?

Model of an axiomatic system https://en.wikipedia.org/wiki/Axiomatic_system#Models

If X models Y and Y models X, then X and Y are the same thing, and the model doesn't have any simplifying assumptions.

"Model" https://en.wikipedia.org/wiki/Non-Euclidean_geometry

Euclidean geometry locally models a manifold.

Non-Euclidean geometry removes an axiom from Euclidean geometry. Thus Euclidean-geometry models non-Euclidean geometry, by adding an axiom

The formula p to q models the formula q

The set of all theorems of a formal systema

A formal system F models a formal system G iff every theorem of F is also a theorem of G.

F has axioms A G has axioms A,B Same inference rules Thus every theorem in F is a theorem in G Is formal system inference rule monotonic? G is a model of F. The simplifying assumption is the extra axiom B. More axioms mean simpler formal system.

Elliptic geometry has fewer axioms than Euclidean geometry, and thus the former is objectively simpler than the latter, but why does the later feels simpler?

Two lines are parallel if and only if they are the same or they don't intersect.

Absolute geometry is a model of Euclidean geometry https://en.m.wikipedia.org/wiki/Absolute_geometry

Adding axioms make it easier to prove theorems. Adding axioms simplifies (shortens) proofs.

p and q models p with the simplifying assumption q.

A set models a group, by forgetting the group operation.

https://en.wikipedia.org/wiki/Conceptual_model

Rewriting system formulation of Turing machine model

A state is S A H Z where S is the program, A is the string to the left of the head, H is the string on the head, and Z is the string to the right of the head.

0 e 1 00 1 1 0 0 1 10 0 e 2 10 1 e

https://www.youtube.com/watch?v=coFpDOsvfLY Wilfrid Hodges "Games to solve problems - LMS 1987" 5:44 An algorithm is a "general method for solving a class of problems"

13.13Sometimes we need to bait people into education

2

14Ethics

14.1Making happen vs letting happen?

If X causes Y, and Y is bad, then X is bad?

Can inaction (absence, non-existence) cause anything at all? Does it make sense? For example, "your inaction causes the house to burn down and kill the child inside."

Ethics answers "What is good?" and "Is X good?" objective ethics (ethics without intentions)?

Self-preservationism? Survivism?

egoism: What benefits X is good for X. species egoism: What benefits X's species is good for X. nihilism: 'Good' doesn't exist. utilitarianism: What is good is what maximizes the sum of happiness of people. evolutionary: What is good is what we feel according to how we have evolved.

good, desirable, pain, masochist

X has power over Y iff X makes Y do what X want Y to do

Power and control is the same thing.

Agency; control; causality

14.2Trolley problem?

My position on the original 1-vs-5 trolley problem: Never switch. If your existence does not make any difference, then you cannot be at fault. The objection "But you could have saved 4 more people" comes from misunderstanding causality.

  • If you switch, you cause the death of 1 person, and you cause the survival of 5 people.
  • If you do nothing, you can't cause the death of 5 people, and you can't cause the survival of 1 people. If you do nothing, your existence does not make any difference, and you don't alter the natural course of events.

If your existence does not make any difference, then you cannot be at fault. If the outcome does not depend on you, then you are not the cause of the outcome. Is it wrong to deliberately not use an ability?

The 1-vs-0 trolley problem:

  • Two branches. 1 person on left branch. 0 people on right branch. Train is going to the left branch unless you switch the train. You know how many people on each branch.
  • If you switch, you cause the survival of 1 person.
  • If you don't switch, you don't cause the death of 1 person.

If you don't know how many people are on each branch, should you switch?

Can we cause something that we don't know? Yes. Suppose you don't know that a bomb explodes when you kick it. You kick the bomb. It explodes. You caused the bomb to explode, although you did not intend to.

The trolley problem really asks these questions:

  • Can inaction cause anything, by definition?
  • Does it make sense for inaction to cause anything?
  • When should we change the course of natural events?

  1. https://en.wikipedia.org/wiki/Formal_concept_analysis↩

  2. Why do we ask questions? Michael "Vsauce" Stevens at TEDxVienna https://www.youtube.com/watch?v=u9hauSrihYQ↩