Teaching The Narrow Way

Saturday, September 7, 2024

Vacuous Truth or Vacuous Falsehood

Let's say two days ago, or in other words the day before yesterday, Rob said, "if I do P tomorrow then Q will happen tomorrow"

Now today Samantha says, "Q never occurred yesterday so Rob was lying"

In reply Alexander says, "A statement can only exclusively either be one of two options of true or false but not both and there is no third possibility. P did not happen yesterday so Rob's statement is not false so that only leaves one other option and this makes Rob's statement vacuously true. All statements with counterfactual antecedents also called true protasis have true consequents also called true apodosis"

Samantha replies that if Rob said, "if I do P tomorrow then Q will not happen tomorrow would that also have been vacuously true"

Alexander replied, "yes"

Then Samantha said, "then since we know that Rob said if I do P tomorrow then Q will happen tomorrow but we know that it is vacuously true that Q would not have happened tomorrow, this proves that Rob's statement that Q would have happen tomorrow vacuously false because if it is true that Q did not happen that day then it would be false that Q did happen that day"

Alexander replied, "P did not happen yesterday so there is no evidence that Rob's statement is false and if there is no evidence that it is false then it must be true"

Samantha replied, "The only way for there to be evidence that Rob's statement was true would be if P did happen yesterday and Q also additionally happened yesterday and since there is no evidence that Rob's statement is true then it must be false."

Alexander replied, "Now you got me all confused Samantha. The statement can only be true or false and only one of those two options and those are the two options. But a compelling case can be made that it is true and also a compelling case can be made that it is false."

Samantha replied, "Although you are correct that a statement can not be both true and false simultaneously when measured in the same way, the reason for your confusion is because there are more than two options. You can not know if Rob's statement is true or false because since the claim that P happened yesterday never occurred Robs statement is untested we could try to guess at whether or not Q would have happened if P happened and guess whether the statement would be true or false on that basis but since P never happened his statement would be better described as untested then confirmed to be true or false. Always using the type of logic that limits things to two options of only true or false really does not line up well with the scientific method because some things although they might in reality be only true or false are untested so we should just label them as untested and make the claim that we do not know they are true or false instead of insisting on assigning them a value of being true or false when we do not know which of those two values is correct. Also depending on how you look at things maybe there could be other options then true or false. It is important to keep in mind that being proven true is not the same as being true and being proven false is not the same as being false. Something can not be both true and correctly proven false if you are measuring with a single consistent standard but something can be both true and not proven true at the same time. Likewise something can not be both false and correctly proven true if you are measuring with a single consistent standard but something can be both false and not proven false at the same time. One might argue that under a certain standard there could be two potential values of one kind for a certain statement of either true or false but simultaneously three potential values of another kind of either proven true, untested or proven false. If something is not proven true then it could be true, untested, proven false or false but it could not be proven true. If something is not proven false then it could be false, untested, proven true, or true but it could not be proven false. If something is correctly proven true then it could only be true. If something is correctly proven false then it could only be false. If something is true then it could only be true, proven true, untested but it could not be false nor correctly proven false. If something is false then it could only be false, proven false or untested but it could not be true nor correctly proven true. If something is untested then it could be true or false but could not be proven true nor proven false. Now in this standard if something is proven true then it is both true and proven true. Also in this standard if something is proven false then it is both false and proven false. This is only one standard of looking at things under another standard there could be more nuanced options then true and false, under such a standard something could not be both simultaneously true and not true but being not true would not always mean it is false because there could be a third option. Likewise something could not be both simultaneously false and not false but being not false would not always mean it is true because there could be a third option. It is also important to keep in mind that depending on the view point saying that some object S is not not K is not necessarily the same as saying the object S is object K although it could be the same depending on another view point but maybe one of those two view points might be wrong, but maybe both viewpoints or even additional viewpoints could potentially be right depending on the circumstances. One of these viewpoints is that if an object S is not not the object K then the object S is the same as the object K, I will not go into detail further on this viewpoint because it is a standard viewpoint. Now for an unorthodox viewpoint. Let's say there is a computer programming function where you select a input from a list of three words, spoon, fork or knife and it gives you an output that is one of those three words but is not the word you select. So if you select spoon you will get an object that is not a spoon such as a fork or a knife. But if you run the function a second time with the output that you got from the first time you run it you could end up with a spoon again but you could also end up with a fork or a knife as long as it is not the same object as the output that you got the first time you ran the function. You could say that the function negates your choice, so running it twice is negating your choice then negating it again but you would not necessarily end up with the same choice that you started with even though it is claimed that double negating something ends up where you started. Perhaps double negating only guarantees consistently ending up where you started if you negate something by selecting a list of every object that is not on your list and not having a single object that is on your list each time when you negate the list. To be more technical we could talk about every item in a sample space vs every item even items we are not working with and still have it work so long as we never list items outside the sample space when negating and stick with the same sample space to select from neither adding from it or subtracting from it in all operations although I am not sure this is worded correctly because the language is a bit too technical in definitions for me at this point. I also want to point out that double negating only consistently works this way where you end up with what you originally had if you negate it twice in English when each of the two words that say 'not' are right next to each other with no words in between in a sentence. For example to say let's assume if something is a dog it is an animal is a statement that is always true but to say if something is not a dog it is not an animal is a statement that is not always true even though two negations were added two the sentence, however to say that if something is not not a dog then it is an animal would be a statement that would be always true based on a certain viewpoint because the two times the word "not" is used each 'not' is next to the other 'not' with no words in between"

Alexander replied, "But how do you apply this"

Samantha replied, "If P happens then Q will happen on the same day has been claimed. Since P did not happen it has not been confirmed or proven false that Q will happen if P happens but just because it was not proven false does not mean that it is proven true. Since P did not happen it also has not been confirmed or proven true that Q will happen if P happens. The statement could be true and the statement could be false but the statement could not be both true and false, the statement is untested and neither proven true nor proven false. It is important not to confuse true with proven true nor to confuse false with proven false. It is important to remember that not false does not necessarily mean the same thing as true nor does not true necessarily mean the same thing as false depending on what logic system you are using. And finally depending on how you try to negate something twice it does not necessarily result in ending up where you would have started with zero negations if that also somehow is related to this confusion although I am not sure if it is. If there is a list of three or more options when someone thinks there is a list of only two or more options they might choose something that is not object 1 and assume it is object 2 then choose something that is not object 2 as a second negation and assume they are going back to object 1 and undoing the second negation when they could actually lead to object 3 by choosing something that is not that object a second time. For example if someone says choose something that is not a spoon and they select a knife and then they say now choose something that is not the thing you just selected and they think the only option is a spoon when it could actually mean a fork."

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

https://en.wikipedia.org/wiki/Antecedent_(logic)

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

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

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

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

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

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

https://en.wikipedia.org/wiki/Three-valued_logic

Saturday, August 24, 2024

Calculating sine of average of angles and cosine of average of angles from tangent of average of angles and other proofs for other trigonometric identities

Explaining with a lot of words

It might be technically better to use the term point instead of vertex

This proof is intended to work for real number values and all values plugged in are intended to be real numbers for the way the proof is written but that does not mean whether or not the end result will or will not work if either complex or pure imaginary numbers are used

All angles mentioned in this proof before the second use of the word "solved" refer to angles measured at the origin relative to a horizontal line y = 0 and a second line segment in quadrant 1 of the unit circle

For positive angles between greater than 0 degrees and less than 90 degrees when the angle at the origin is measured. Although this proof will in the end work for any real number angles it is easier to visualize it within quadrant 1

If you take two triangles each on the unit circle with a unit-less radius of 1 and a shared Cartesian origin of (0,0) for one of their vertexes and a second vertex of (1,0) and the third or interesting vertex of (cos(angle), sin(angle))

And convert the interesting vertex of each triangle into Cartesian coordinates

Then if you take the average of the Cartesian coordinates of each interesting vertex with the other interesting vertex for the two angles you will get a new vertex which is not on the unit circle and has a distance other than 1 from the origin

If you draw a line segment from the origin to the new vertex created by the average already mentioned then that line will have a slope that is the same as a triangle with an angle equal to the average of the two original angles and the length of the line segment will not be 1

Thus you can use the coordinates of that new point to calculate the tangent of the average of the two angles for the original triangles on the unit circle even thought that point is not on the unit circle so it's coordinates can not directly be used to calculate the sine or cosine

If you multiply both horizontal or X and vertical or Y Caartesian coordinates of the new vertex already mentioned by the same constant and select the correct constant you can get coordinates which form a line segment with a length of 1 from the origin with the same slope as the tangent of the average of the two original triangles angles that can be used to form a third triangle on the unit circle. With this third triangle the sine and cosine can be calculated. The cosine of the average of the two angles will be the X coordinates of this newest line segment with a length of 1 and the sine will be the Y coordinates of this newest line segment with a length of 1 that has the same slope as that for the average of the two angles in the original triangles.

Explaining using more algebra and less words if you can not understand why what is being done go to the wordy section above or to the diagram if I add it later

Given

tangent(0.5A+0.5B) = ( N * [ 0.5sin(A) + 0.5sin(B) ] ) / ( N * [ 0.5*cos(A) + 0.5*cos(B) ] )

sin(0.5A+0.5B) = N * [ 0.5sin(A) + 0.5sin(B) ]

cos(0.5A+0.5B) = N * [ 0.5cos(A) + 0.5cos(B) ]

Solve for both

sin(0.5A+0.5B)

cos(0.5A+0.5B)

as functions of these four functions

cos(A), cos(B), sin(A), sin(B)

Solution

This value of N when multiplied by the coordinates of ( 0.5cos(A) + 0.5cos(B), 0.5sin(A) + 0.5sin(B) ) creates coordinates of a vertex which can form a line segment with a length of 1 from the origin (0, 0)

This line segment has a slope that is equivalent to the angle of ( 0.5A + 0.5B ). N is calculated using the Pythagorean theorem to calculate the distance from the origin (0,0) to ( 0.5cos(A) + 0.5cos(B), 0.5sin(A) + 0.5sin(B) ) and then taking the reciprocal of that distance

N= 1 / ( [ 0.5sin(A) + 0.5sin(B) ] ^ 2 + [ 0.5cos(A) + 0.5cos(B) ] ^ 2 ) ^ 0.5

sin(0.5A+0.5B) = [ 0.5sin(A) + 0.5sin(B) ] * N

cos(0.5A+0.5B) = [ 0.5sin(A) + 0.5sin(B) ] * N

Solved but needs to be simplified to get other trigonometric identities in simplified form

Solving for the square of the sine of a half angle by letting B = 0

sin(0)=0

cos(0)=1

sin(0.5A+ 0 ) ^ 2 = [ 0.5sin(A) + 0.5sin(0) ] ^ 2 * N ^2

[sin(0.5A) ]^2= [0.5sin(A)]^2 / ( [ 0.5sin(A) + 0.5sin(0) ] ^ 2 + [ 0.5cos(A) + 0.5cos(0) ] ^ 2 )

[sin(0.5A) ]^2= [0.5sin(A)]^2 / ( [ 0.5sin(A) ] ^ 2 + [ 0.5cos(A) + 0.5 ] ^ 2 )

[ 1 + cos(A) ] ^ 2 = 1 + 2cos(A) + cos(A)^2 = 2 + 2cos(A) - [sin(A)]^2

[ 0.5cos(A) + 0.5 ] ^ 2 = 0.25 * [ 1 + cos(A) ] ^ 2 = 0.5 + 0.5cos(A) - 0.25[sin(A)]^2

[ 0.5sin(A) ] ^ 2 = 0.25[sin(A)]^2

[sin(0.5A) ]^2= [0.5sin(A)]^2 / ( [ 0.5sin(A) ] ^ 2 + 0.5 + 0.5cos(A) - 0.25[sin(A)]^2 )

(0.5)^2/ 0.5=0.5 = 1 / 2

[sin(0.5A) ]^2= [0.5sin(A)]^2 / [ 0.5 + 0.5cos(A) ] = [sin(A)]^2 / [ 2 + 2cos(A) ]

https://www.geogebra.org/graphing

Monday, July 29, 2024

Getting something for nothing of value through money

I am publishing this in 2024. This was in my drafts from an unknown date

Below is all that was in this draft other than the title, "Getting something for nothing of value through money"

Ponzi scheme

money made out of dung

I will add the following comments

Imagine if someone gave you a piece of dung that was even less valuable than normal dung and you did not want to eat or touch or use for tools and you did not even want to burn it or use it for fertilizer. But they said this piece of dung had value because you could trade it for other things that had value. They would get something that is valuable to you through you in exchange for something that has no value in terms of use to you. You could only trade this worthless dung if you convinced other people that this worthless dung has value and by recruiting new members to believe this worthless dung has value or maintaining the belief of the current members in the value of this worthless dung. This dung would be a ponzi scheme just like money is a ponzi scheme if you can not use it for anything other than trading it. The first person to give away this dung got something of value from someone else in exchange for losing nothing of value to them and every person after them lost the value of whatever they traded to get the dung in exchange for a piece of dung that is of no value to them. Each person could recover their loss by giving the piece of dung to trade with the next person but they gained nothing of value by giving away their prized possession for getting the piece of dung in return in the first place. Money is like a game of hot potato where people throw a potato from one person to another and the last person to hold the hot potato loses when the time runs out loses instead of throwing a potato you are throwing around dung that infects the minds of people who have not developed the mental immune system to see through the lie.

Involuntary taxation forbidden in Catholic Catechism

Copyright Carl Janssen - This will be published right now in 2024 - This was written at an unknown date - It was in my drafts

The Catechism of the Ultramontane Roman Catholic Church approved by "pope" John Paul 2 clearly forbids involuntary taxation which shall be referred to as taxation for short.

Most people say taxation is ok because it is for a greater good but to paraphrase the catechism it is a sin to do an evil action even if it is done to achieve a good result specifically listing murder, theft and lying. Taxation is lying to claim someone owes a debt for something they did not agree to and did not owe on account of causing harm to a individual or their possession of property. Taxation is also theft since it is taken something that rightfully belongs to someone else and not you without their properly informed consent as they were lied to and coerced with the threat of violence being done to you possibly resulting in murder if you do not comply. Taxation involved three cardinal or mortal sins that are still sins even if a good is promised in return such as creating roads, feeding the poor, providing infrastructure, paying for research education or healthcare or hiring people to defend people from violence, etc.

Furthermore taxation involves an absence of the four cardinal virtues of prudence, fortitude, temperance and justice.

Taxation is an absence of prudence because it is a choice not to exercise your conscience to realize Taxation is a violation of the commands not to murdrr, lie and steal.

Taxation is an absence of fortitude because it involves quitting before using the prudence to figure out how to get the good you want without resorting to sin or a lack of perseverance in exercising temperance if you must deny gratification of achieving a good you want in order to avoid evil.

Taxation is an absence of justice because it involves hearing false witness, stealing from the rightful owners to give to those who do not rightfully own something and murdering or threatening to murder people who should not be executed.

Taxation is a failure to implement the grace to live a more virtuous life.

Taxation is also an absence of the theological virtues of faith, hope and charity

It is an absence of faith as it is a failure to profess and witness to God's moral teachings and involves a lifestyle of dead faith.

Taxation is an absence of the virtue of hope because it is a failure to imagine the possibility that things could work for good if one is obedient to God's moral teachings.

Taxation is an absence of charity because murder, lying and theft are opposed to love.

Taxation involves a boastful arrogance and lack of generosity because it is worse than giving all you have to the poor that you may boast but lacking love. Taxation is giving what belongs to someone else that you may boast of feign generosity instead of giving what belongs to you.

Taxation is a violation of the fruits of charity of joy, peace and mercy.

Taxation is a violation of joy because coveting is a killjoy

Taxation is a violation of mercy because how much less mercy is there not to harm someone who has done you no wrong then to harm someone who has done you wrong. Taxation of all white people or all males, or the Germans, for alleged sins of their ancestors as some people have suggested is a unjust vengeful attitude that lacks mercy.

Taxation is an absence of peace as it involves the threat of violence. Taxation also stems from anxiety of what will happen if one can not use taxation to get the goods desired.

Taxation is oppositional to beneficence, friendship and communion as it involves reaching out to a third party bureaucratic system for receiving help instead of developing friendships and using a third party bureaucracy as an excuse not to exercise beneficence towards your neighbor.

Taxation is an absence of benevolence as there is nothing kind about it

Taxation is a violation of the seven gifts of the spirit

Does Ayn rand endorse a lack of empathy?

This was an old draft, all that was in it was the title, "Does Ayn rand endorse a lack of empathy?"

It was written at a unknown date at or prior to 2024. I do not remember what I was going to say about that but it is probably a question a lot of people have. For me right now the question of if Ayn Rand endorsed a lack of empathy in the past, I do not really currently feel I have an answer to, I do not know if I thought I had a answer to that question when I wrote the title.

Optimizing violence according to political maps of reality.

The following was in drafts with the exact wording as follows.

"Graph as ordinal data violence imposed by the state vs violence imposed by other sources and danger, suffering and reduced pleasure imposed by lack of state services and bribes"

The following is new content that I am adding in 2024

I think I was going to do a graph of how much different worldviews believe a level of violence from the State would be versus how much violence from non state sources they believe would happen with that level of State violence

The monarchists might believe that once State violence goes below a certain minimum amount that violence from non state sources would increase thus to optimize the minimum amount of total violence from both state and non state sources a particular non zero level of State violence is needed. The minarchists might believe state violence must be set just right, setting it above or below a certain number would increase the violence from state sources plus non state sources

Some Anarcho capitalists might believe that decreasing State violence to zero will not increase violence from non state sources compared to a higher level of violence. They would not believe that lowering state violence below a certain amount would guarentee an increase from non state sources of violence. Thus some anarcho capitalists might believe that in order to minimize the sources of violence from state sources plus non state sources the total amount of violence from state sources should be set to 0

Other people might not care about the level of violence and simply want to maximize the amount of pleasure , comfort and or happiness they have right now and or minimize the amount of pain, suffering and or inconvenience they have right now. They might be willing to increase the total amount of state and non state violence they receive in order to get better service from government and non government sources

Money oreates economic calculation problems

The following is in drafts I thought I wrote about this somewhere else in more detail but I am publishing it. I am publishing this in the year 2024 but I do not know what year it was written. It has at least one typo. This is exactly how it was written below.

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

https://en.m.wikipedia.org/wiki/Lange_model
Obsfuscates

You primarily need to know what items you want and which elements (as in the periodic table) form them and then how much energy the physical or chemical changes require. Most of the things required for day to day living are water, calories, vitamins, protein and dietary elements as well as simple tools or shelter. The goal is to use something similar in concept to Maslow's ladder

It would not be exponentially increasing unless you want or need an exponentially increasing number of things.although it would be potentially large if you look at the periodic table but many elements are only needed in trace amounts.

Feminist flat shaming skinny women's bodies

https://www.chess.com/forum/view/off-topic/flat-shaming

https://web.archive.org/web/20240729201730/https://www.chess.com/forum/view/off-topic/flat-shaming

https://web.archive.org/web/20180713104703/http://theweek.com/articles/497091/australias-small-breast-ban

Government human experiments

https://m.youtube.com/watch?v=18_ixbpmXOQ

the link above was in drafts, the link above no longer works, the link below is the archived version

https://web.archive.org/web/20170627181259/https://www.youtube.com/watch?v=18_ixbpmXOQ&app=desktop

Money the unsung weapon of mass destruction

https://m.youtube.com/watch?v=l6uLUaqgWY0

The following above was in drafts with the title, "Money the unsung weapon of mass destruction"