Omnipotence 4.2

When responding to the question “can X create a stone that it cannot lift”, another flawed argument is

X can create the stone that it cannot lift but it chooses not to create it. So there is no stone it cannot lift yet. So X has not failed the omnipotence test.

This argument is wrong.

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When we ask “can X choose to create a stone that it cannot lift”, we are discussing whether X has an ability. When we discuss ability, it is always about a potential, a possibility.

Y is able to do action B

always means that

“Y does B” is possible,

which is equivalent to

“Y does B” is not contradictory to any logical laws nor physical laws.

“Whether Y has already done B or will do B” is not the point.

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If we allow such “Y can do B but it chooses not to” argument, then anyone is omnipotent. For example,

Can you fly?

I can fly but I choose not to. So even though you have never seen me flying and will never see me flying, it is not because I cannot fly; it is just because I choose not to.

Can you choose to fly?

I can choose to fly but I choose not to choose to fly.

This type of arguments make the word “can“ meaningless.

— Me@2020-03-30 06:52:58 AM

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2020.04.19 Sunday (c) All rights reserved by ACHK

Omnipotence 4.1

Please read these 2 posts first:

For all, 3 | Omnipotence

For all, 3.2 | Omnipotence 2

You can find them by searching “omnipotence” using this blog’s search box.

— Me@2020-04-08 03:17:34 PM

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If X is omnipotent, X can create a stone that it cannot lift. Then X is not omnipotent, because there is a stone it cannot lift. So omnipotence is a self-contradictory concept.

What if we define omnipotence not as “being able to do anything” but as “being able to do anything except logical self-contradictory ones“?

In order words, omnipotence means that being able to do anything logically possible. Omnipotence does not mean that being able to do also logically impossible things.

This re-definition is not useful, because the original meaning of “being omnipotent” already is “being able to do anything except logical self-contradictory ones“.

There is no re-definition needed. You can only say that the re-definition clarifies the original meaning of “being omnipotent”. However, this clarification cannot eliminate the self-contradictory nature of the meaning of “omnipotence” itself. For example, the following argument is wrong.

If X is omnipotent, “X can create a stone that it cannot lift” is self-contradictory because it is contradictory to “X is omnipotent”.

Since “X can create a stone that it cannot lift” is logically impossible, it should not be a requirement of being omnipotent.

This argument is wrong because:

1. “X can create a stone that it cannot lift” is not SELF-contradictory.

2. “X can create a stone that it cannot lift” is not logically impossible, because, for example, even a human being can create an object that he cannot lift. For example, human beings can create a car that no single person can lift.

Then someone might keep arguing that

But if X is omnipotent, “X can create a stone that it cannot lift” means that “X is omnipotent and X can create a stone it cannot lift”, which is logically impossible. So “X cannot create a stone that it cannot lift” does not make X non-omnipotent.

In other words, “whether X can create a stone that it cannot lift” should not be the requirement of the omnipotence test.

The argument is wrong, because what we are questioning is

Can someone X be omnipotent?

or

Is omnipotence logically possible?

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Remember:

“Being logically possible” means “not self-contradictory”.

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If “X is omnipotent” is true,

then “X can create a stone that it cannot lift” is true.

Then “there is a stone that X cannot lift” is true.

Then “X is not omnipotent” is true.

But “X is not omnipotent” is contradictory to the assumption “X is omnipotent“.

So “X is omnipotent” is self-contradictory.

So the question “whether an entity X can be omnipotent and create a stone that it cannot lift” is illegitimate because “an entity X is omnipotent” is logically impossible in the first place. It should not be placed within a question.

Note that our omnipotent test is

“whether an entity X can create a stone that it cannot lift”,

NOT “whether an entity X can be omnipotent and create a stone that it cannot lift”,

NOR “whether an omnipotent entity X can create a stone that it cannot lift”.

— Me@2020-03-30 06:52:58 AM

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2020.04.10 Friday (c) All rights reserved by ACHK

Two dimensional time 5.2.3

The first time direction is uncontrollable; the second is controlled by making choices, traveling through different realities. Future is a set of parallel universes.

— Me@2017-12-15 10:59:49 AM

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The first time direction, which is along the timeline, is uncontrollable, because one can only travel from the past to the future, not the opposite.

The second direction, which is across different timelines, is controlled by making choices, forming different realities.

— Me@2019-12-21 11:03:23 PM

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2019.12.22 Sunday (c) All rights reserved by ACHK

Two dimensional time 5.2.2

time direction ~ direction of change

multiple time directions ~ multiple directions of change

— Me@2019-12-22 04:38:47 PM

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the first dimension of time ~ direction of change

the second dimension of time ~ direction of change of changes

— Me@2019-12-22 04:46:47 PM

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2019.12.22 Sunday (c) All rights reserved by ACHK

Multiple dimensions of time

Two dimensional time 5.2 | 二次元時間 5.2

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What would be the implications of multiple dimensions of time?

That means the (past) history itself can change, as commonly seen in time travel stories.

But wouldn’t that be the case with one dimension also?

In reality, there is only one dimension of time, meaning that the state of a system keeps changing, forming the timeline. But the timeline itself cannot be changed once formed. In other words, (past) history cannot be changed.

— Me@2019-08-11 04:07:48 PM

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2019.08.11 Sunday (c) All rights reserved by ACHK

Alfred Tarski, 3

The undefinability theorem shows that this encoding cannot be done for semantic concepts such as truth. It shows that no sufficiently rich interpreted language can represent its own semantics. A corollary is that any metalanguage capable of expressing the semantics of some object language must have expressive power exceeding that of the object language. The metalanguage includes primitive notions, axioms, and rules absent from the object language, so that there are theorems provable in the metalanguage not provable in the object language.

— Wikipedia on Tarski’s undefinability theorem

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Tarski’s 1969 “Truth and proof” considered both Gödel’s incompleteness theorems and Tarski’s undefinability theorem, and mulled over their consequences for the axiomatic method in mathematics.

— Wikipedia on Alfred Tarski

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2019.07.20 Saturday ACHK

Confirmation principle

Verification principle, 2.2 | The problem of induction 4

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The statements “statements are meaningless unless they can be empirically verified” and “statements are meaningless unless they can be empirically falsified” are both claimed to be self-refuting on the basis that they can neither be empirically verified nor falsified.

— Wikipedia on Self-refuting idea

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In 1936, Carnap sought a switch from verification to confirmation. Carnap’s confirmability criterion (confirmationism) would not require conclusive verification (thus accommodating for universal generalizations) but allow for partial testability to establish “degrees of confirmation” on a probabilistic basis.

— Wikipedia on Verificationism

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Confirmation principle should not be applied to itself because it is an analytic statement which defines synthetic statements.

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Even if it does, it is not self-defeating, because confirmation principle, unlike verification principle, does not requires a statement to be proven with 100% certainty.

So in a sense, replacing verification principle by confirmation principle can avoid infinite regress.

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Accepting confirmation principle is equivalent to accepting induction.

“This is everything to win but nothing to lose.”

— Me@2012.04.17

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2019.04.06 Saturday (c) All rights reserved by ACHK

The problem of induction 3.3

“Everything has no patterns” (or “there are no laws”) creates a paradox.

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If “there are 100% no first order laws”, then it is itself a second order law (the law of no first-order laws), allowing you to use probability theory.

In this sense, probability theory is a second order law: the law of “there are 100% no first order laws”.

In this sense, probability theory is not for a single event, but statistical, for a meta-event: a collection of events.

Using meta-event patterns to predict the next single event, that is induction.

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Induction is a kind of risk minimization.

— Me@2012-11-05 12:23:24 PM

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2018.12.28 Friday (c) All rights reserved by ACHK

The problem of induction 3.1.2

Square of opposition

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“everything has a pattern”?

“everything follows some pattern” –> no paradox

“everything follows no pattern” –> paradox

— Me@2012.11.05

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My above statements are meaningless, because they lack a precise meaning of the word “pattern”. In other words, whether each statement is correct or not, depends on the meaning of “pattern”.

In common usage, “pattern” has two possible meanings:

1. “X has a pattern” can mean that “X has repeated data“.

Since the data set X has repeated data, we can simplify X’s description.

For example, there is a die. You throw it a thousand times. The result is always 2. Then you do not have to record a thousand 2’s. Instead, you can just record “the result is always 2”.

2. “X has a pattern” can mean that “X’s are totally random, in the sense that individual result cannot be precisely predicted“.

Since the data set X is totally random, we can simplify the description using probabilistic terms.

For example, there is a die. You throw it a thousand times. The die lands on any of the 6 faces 1/6 of the times. Then you do not have to record those thousand results. Instead, you can just record “the result is random” or “the die is fair”.

— Me@2018-12-18 12:34:58 PM

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2018.12.18 Tuesday (c) All rights reserved by ACHK

The problem of induction 3.2

The meaning of induction is that

we regard, for example, that

“AAAAA –> the sixth is also A”

is more likely than

“AA –> the second is also A”

 

We use induction to find “patterns”. However, the induced results might not be true. Then, why do we use induction at all?

There is everything to win but nothing to lose.

— Hans Reichenbach

If the universe has some patterns, we can use induction to find those patterns.

But if the universe has no patterns at all, then we cannot use any methods, induction or else, to find any patterns.

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However, to find patterns, besides induction, what are the other methods?

What is meaning of “pattern-finding methods other than induction”?

— Me@2012.11.05

— Me@2018.12.10

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2018.12.10 Monday (c) All rights reserved by ACHK

The problem of induction 3

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In a sense (of the word “pattern”), there is always a pattern.

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Where if there are no patterns, everything is random?

Then we have a meta-pattern; we can use probability laws:

In that case, every (microscopic) case is equally probable. Then by counting the possible number of microstates of each macrostate, we can deduce that which macrostate is the most probable.

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Where if not all microstates are equally probable?

Then it has patterns directly.

For example, we can deduce that which microstate is the most probable.

— Me@2012.11.05

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2018.11.19 Monday (c) All rights reserved by ACHK

defmacro, 2

Defining the defmacro function using only LISP primitives?

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McCarthy’s Elementary S-functions and predicates were

atom, eq, car, cdr, cons

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He then went on to add to his basic notation, to enable writing what he called S-functions:

quote, cond, lambda, label

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On that basis, we’ll call these “the LISP primitives”…

How would you define the defmacro function using only these primitives in the LISP of your choice?

edited Aug 21 ’10 at 2:47
Isaac

asked Aug 21 ’10 at 2:02
hawkeye

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Every macro in Lisp is just a symbol bound to a lambda with a little flag set somewhere, somehow, that eval checks and that, if set, causes eval to call the lambda at macro expansion time and substitute the form with its return value. If you look at the defmacro macro itself, you can see that all it’s doing is rearranging things so you get a def of a var to have a fn as its value, and then a call to .setMacro on that var, just like core.clj is doing on defmacro itself, manually, since it doesn’t have defmacro to use to define defmacro yet.

– dreish Aug 22 ’10 at 1:40

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2018.11.17 Saturday (c) All rights reserved by ACHK

defmacro

SLIME, 2

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Alt + Up/Down

Switch between the editor and the REPL

— Me@2018-11-07 05:57:54 AM

~~~

defmacro

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(defmacro our-expander (name) `(get ,name 'expander))

(defmacro our-defmacro (name parms &body body)
  (let ((g (gensym)))
    `(progn
       (setf (our-expander ',name)
	     #'(lambda (,g)
		 (block ,name
		   (destructuring-bind ,parms (cdr ,g)
		     ,@body))))
       ',name)))

(defun our-macroexpand-1 (expr)
  (if (and (consp expr) (our-expander (car expr)))
      (funcall (our-expander (car expr)) expr)
      expr))

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A formal description of what macros do would be long and confusing. Experienced programmers do not carry such a description in their heads anyway. It’s more convenient to remember what defmacro does by imagining how it would be defined.

The definition in Figure 7.6 gives a fairly accurate impression of what macros do, but like any sketch it is incomplete. It wouldn’t handle the &whole keyword properly. And what defmacro really stores as the macro-function of its first argument is a function of two arguments: the macro call, and the lexical environment in which it occurs.

— p.95

— A MODEL OF MACROS

— On Lisp

— Paul Graham

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(our-defmacro sq (x)
  `(* ,x ,x))

After using our-defmacro to define the macro sq, if we use it directly,


(sq 2)

we will get an error.

The function COMMON-LISP-USER::SQ is undefined.
[Condition of type UNDEFINED-FUNCTION]

Instead, we should use (eval (our-macroexpand-1 ':


(eval (our-macroexpand-1 '(sq 2)))

— Me@2018-11-07 02:12:47 PM

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2018.11.07 Wednesday (c) All rights reserved by ACHK

Existence and Description

Bertrand Russell, “Existence and Description”

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§1 General Propositions and Existence

“Now when you come to ask what really is asserted in a general proposition, such as ‘All Greeks are men’ for instance, you find that what is asserted is the truth of all values of what I call a propositional function. A propositional function is simply any expression containing an undetermined constituent, or several undetermined constituents, and becoming a proposition as soon as the undetermined constituents are determined.” (24a)

“Much false philosophy has arisen out of confusing propositional functions and propositions.” (24b)

A propositional function can be necessary (when it is always true), possible (when it is sometimes true), and impossible (when it is never true).

“Propositions can only be true or false, but propositional functions have these three possibilities.” (24b)

“When you take any propositional function and assert of it that it is possible, that it is sometimes true, that gives you the fundamental meaning ‘existence’…. Existence is essentially a property of a propositional function. It means that the propositional function is true in at least one instance.” (25a)

— Brandon C. Look

— University Research Professor and Chair

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2018.10.07 Sunday ACHK

The Sixth Sense, 3

Mirror selves, 2 | Anatta 3.2 | 無我 3.2

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You cannot feel your own existence or non-existence. You can feel the existence or non-existence of (such as) your hair, your hands, etc.

But you cannot feel the existence or non-existence of _you_.

— Me@2018-03-17 5:12 PM

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Only OTHER people or beings can feel your existence or non-existence.

— Me@2018-04-30 11:29:08 AM

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2018.04.30 Monday (c) All rights reserved by ACHK

機遇再生論 1.6

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所以,「同情地理解」,亦可稱為「意念淘金術」。

機遇再生論,可以同情地理解為,有以下的意思:

(而這個意思,亦在「機遇再生論」的原文中,用作其理據。)

假設,你現在手中,有一副樸克牌,存在於某一個排列 A 。洗牌一次之後,排列仍然是 A 的機會極微。

一副完整的撲克牌,共有 N = 52! \approx 8.07 \times 10^{67} 個,可能的排列。亦即是話,洗牌後仍然是排列 A 的機會率,只有 \frac{1}{N}

由於分母 N 太大(相當於 8 之後,還有 67 個位),洗牌後,理應變成另外一個排列 B 。

P(A) = \frac{1}{N}

P(\text{not} A) = 1 - \frac{1}{N}

洗了一次牌後,發覺排列是 B 不是 A 後,我們可以再問,如果再洗一次牌,「是 A」和「不是 A」的機會,分別是多少?

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由於,機會率只是與未知的事情有關,或者說,已知的事件,發生的機會率必為 1;所以,如果發生了第一次洗牌,而你又知道其結果的情況下,問「如果再洗一次牌,『是 A』和『不是 A』的機會,分別是多少」,第二次洗牌各個可能結果,發生的機會率,與第一次洗牌的結果無關。

第二次洗牌結果為組合 A 的機會率,仍然是

P(A) = \frac{1}{N}

不是組合 A 的機會率,仍然是

P(\text{not} A) = 1 - \frac{1}{N}

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(問:那樣,為什麼要問多一次呢?)

我是想釐清,我真正想問的是,並不是這個問題,而是另一個:

如果在第一次洗牌之前,亦即是話,一次牌都未洗的話,問:

「如果洗牌兩次,起碼一次洗到原本排列 A 的機會率是多少?」

把該事件標示為 A_2

A_2 = 兩次洗牌的結果,起碼一次洗到原本排列 A

再把該事件的機會率,標示為 P(A_2)

由於 P(A_2) 相對麻煩,我們可以先行運算其「互補事件」的機會率。

A_2 的互補事件為「不是 A_2」:

不是 A_2

= 兩次洗牌的結果,不是起碼一次洗到原本排列 A

= 兩次洗牌的結果,都不是排列 A

其機會率為

P(\text{not} A_2) = (1 - \frac{1}{N})^2

那樣,我們就可推斷,

P(A_2)
= 1 - P(\text{not} A_2)
= 1 - (1 - \frac{1}{N})^2

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同理,在一次牌都未洗的時候,問:

如果洗牌 m 次,起碼一次洗到原本排列 A 的機會率是多少?

答案將會是

P(A_m)= 1 - (1 - \frac{1}{N})^m

留意,N = 52! \approx 8.07 \times 10^{67},非常之大,導致 (1 - \frac{1}{N}) 極端接近 1。在一般情況,m 的數值還是正常時, P(A_m) 會仍然極端接近 0。

例如,你將會連續洗一千萬次牌(m = 10,000,000),起碼有一次,回到原本排列 A 的機會是:

P(A_m)
= 1 - (1 - \frac{1}{N})^m
= 1 - (1 - \frac{1}{52!})^{10,000,000}

你用一般手提計算機的話,它會給你 0。你用電腦的話,它會給你

1.239799930857148592 \times 10^{-61}

— Me@2018-01-25 12:38:39 PM

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2018.02.13 Tuesday (c) All rights reserved by ACHK

機遇再生論 1.5

例如,

甲在過身之後,一千億年內會重生。

是句「科學句」(經驗句),因為你知道在什麼情境下,可以否證到它 —— 如果你在甲過身後,等了一千億年,甲還未重生的話,那句就為之錯。

但是,

甲在過身之後,只要等足夠長的時間,必會重生。

則沒有任何科學意義,只是一句「重言句」;因為,沒有人可以講得出,它在什麼情況下,為之錯。

如果你等了一千億年,甲還未重生的話,這個「機遇再生論」,仍然不算錯;因為,那只代表了,那一千億年,還未「足夠長」。

把「重言句」假扮成「經驗句」,就為之「空廢命題」。

(請參閱本網誌,有關「重言句」、「經驗句」和「印證原則」的文章。)

但是,那不代表我們,應該立刻放棄,機遇再生論。反而,我們可以試行「同情地理解」。

「同情地理解」的意思是,有些理論,雖然在第一層次的分析之後,有明顯的漏洞,但是,我們可以試試,代入作者發表該理論時的,心理狀態和時空情境;研究作者發表該理論的,緣起和動機;從而看看,該理論不行的原因,會不會只是因為,作者的語文或思考不夠清晰,表達不佳而已?

其實,該理論的「真身」,可能充滿著新知洞見。那樣的話,我們就有機會把「機遇再生論」,翻譯成有意義,不空廢的版本。

所以,「同情地理解」亦可稱為「意念淘金術」。

機遇再生論,可以同情地理解為,有以下的意思:

(而這個意思,亦在「機遇再生論」的原文中,用作其理據。)

假設,你現在手中,有一副樸克牌,存在於某一個排列 A 。洗牌一次之後,排列仍然是 A 的機會極微。

一副完整的撲克牌,共有 N = 54! = 2.3 \times 10^{71} 個,可能的排列。亦即是話,洗牌後仍然是排列 A 的機會率,只有 \frac{1}{N}

由於分母 N 太大(相當於 2 之後,還有 71 個位),洗牌後,理應變成另外一個排列 B 。

P(A) = \frac{1}{N}

P(not A) = 1 - \frac{1}{N}

— Me@2017-12-18 02:51:11 PM
 
 
 
2017.12.18 Monday (c) All rights reserved by ACHK

Determined by what?

If you say “an event is determined”, in order to be meaningful, you have to specify, explicitly or by context, that the event is determined by whom.

Similarly, if you say something is free, you have to specify “free from what” or “free with respect to what”. 

free ~ independent of

Without a grammatical object, the phrase “independent of” is meaningless, unless the context has implied what that grammatical object is.

— Me@2015-05-23

free [without an object] ~ free from everything

is meaningless, because the word “everything” is meaningful only if it has a context.

— Me@2017-07-20

2017.07.29 Saturday (c) All rights reserved by ACHK

馬後炮

注定外傳 2.3.4 | Can it be Otherwise? 2.3.4

或者說,到頭來,你也是要根據「有沒有道理」這個原則,去判別一個想法,是不是「神的旨意」。

如果沒有「神的旨意」,你就要靠自己,判斷是非明白,決定行事策略。如果有「神的旨意」,你也要靠自己,判斷哪些意念想法,真的是「神的旨意」,應該跟隨執行。

換言之,即使有「神的旨意」,你並不會在一件事發生之前,(在毋須自己判斷的情況下,)就知道那是不是「神的旨意」。

你至多只可以在,該件事件發生後,根據它的結果好壞,把它歸類為「神的旨意」或否。

但是,那又會令我們回到,今天討論的起點:

以往的事是注定的;未來之事不完全注定。

即使有些未來之事是注定的,你也不會在事前,百分之百肯定地知道,那注定的結果是,眾多可能性的哪一個。

既然就算有注定,你也不知注定為何;事情注定與否,對你又怎會有影響呢? 

— Me@2017-02-03 04:15:54 PM

2017.02.03 Friday (c) All rights reserved by ACHK