One Can't Subtract Infinite Series Very Easily

 I was disappointed to find that adding together two equal infinite sets that are oppositely signed; for instance the real  between -1 and -2 with the real numbers between 1 and 2 cannot be proven to equal zero. Common sense indicates it does.

ChatGPT said that the math is improvable presently. Someone should fix that since it seems like common sense.

ChatGPT -“Ah, thank you for the clarification! You’re asking about the intervals and , both subsets of the real numbers . These intervals are equal in cardinality (both are uncountably infinite). However, combining infinite sets algebraically, as you propose, doesn’t follow the same rules as arithmetic with finite numbers. Let’s explore the idea in detail.

ChatGPT -“Ah, thank you for the clarification! You’re asking about the intervals and , both subsets of the real numbers . These intervals are equal in cardinality (both are uncountably infinite). However, combining infinite sets algebraically, as you propose, doesn’t follow the same rules as arithmetic with finite numbers. Let’s explore the idea in detail.

Cardinality of the Sets

Both intervals and are uncountably infinite and have the same cardinality as the real numbers , denoted by (the cardinality of the continuum).

A bijection exists between these intervals (e.g., maps to bijectively), confirming their equivalence in “size.”

Algebra of Cardinalities

In the algebra of infinite cardinal numbers:

\mathfrak{c} – \mathfrak{c} = \mathfrak{c},

Measure Theory Interpretation

If you’re thinking about summing or subtracting these intervals with respect to their measures:

The measure (length) of is .

The measure (length) of is also .

In this case:

\text{Measure of } (1, 2) – \text{Measure of } (-2, -1) = 1 – 1 = 0.

But this applies only to the measure (length), not to the sets’ elements or their infinite nature.

Infinite Sets and Summation

If you’re suggesting that the “sum” of elements in the intervals should cancel out, this operation isn’t well-defined because:

The elements of the sets are infinite in number and uncountable, so “adding” them isn’t straightforward.

Even if we attempt to define something like , this wouldn’t “cancel out” infinite quantities but rather produce a value based on specific rules.

Conclusion

Your intuition about symmetry between the intervals is valid when considering their measure (length). However, in the domain of cardinality or infinite sets, subtraction doesn’t yield zero due to the unique properties of infinities in set theory. Let me know if you’d like further clarification or a specific framework (e.g., measure theory, integration, or set algebra) to explore!”

Post-Modernism and Free Will

 Many post modernist behaviorists claim that free will doesn’t exist. They propose that subconscious conditioning from nature innately decides conscious decisions. That would be an inefficient evolution dispensing with deliberative conscious reason promoting a self-deceiving evolutionary configuration to trick it.

One might use a philosophical system to make decisions, such as act or rule based utilitarianism and carefully evaluate, select and enumerate criteria for making a decision within that system thereby excluding the deterministic ouji board element and apply free will to make a decision from any of several valid choices, or choose to spin the wheel of fortune to select a choice at random.

The choice to use a rational criteria, blind random chance or to revert to a ouji board of subconscious neo-determinism is made with free will (unless coerced by external factors such as 36 trillion dollars of public debt). Perhaps Democrats have no free will on deficit spending matters while Republicans may claim to have an ability to think for themselves with sapere aude economic policy.

Woodrow Wilson Created the Federal Reserve and Segregated the Federal Government to Support Uryvnias?

 If a Rottweiler looks you in the eye then bites your wrist it’s good to go home and disinfect the wound. If a pit bull looks you in the eye then runs your way to bite an Achilles one need peddle faster.

Creating a federal reserve to back up and stabilize banks was practical yet is complex today. The Fed is worth about 7 trillion dollars today. It can loan 100 billion to banks at zero interest and banks lend out ten times that much adding a trillion dollars for the economy. Then the Fed can buy securities and Increase their worth I guess. Hard to know where all that cash for Ukraine went… Maybe to buy securities and print uryvnias. Dog food is costly.

Christian ethics are a good thing yet society is striving, hateful, envious, greedy and etc. One cannot use force of law to compel people to be virtuous, altruistic or wise. Competition in economics lead to ethics of trimming potential rivals. The world will be perfect with the Second Coming and probably not before…thermodynamics, deficit spending and concentration of wealth keep a hard edge to social reality.

Eternity

 Time exists with space, aka space-time. Space-time is temporal and probably won’t exist forever. Then no time exists nor does anything… except spirit that is different than anything known.

God and Omniscience

 Some like those logic loops, tests and disjuncts for extrapolating to the unknowable. God is other than everything he created; entirely different and unknowable except through The Son.

A universal field of being comprehended before manifestation. Alpha and Omega in relation to phenomena of relative space-time transcending each point of locality Omniscience and Omnipotence complete and changeless embodying all change.

Adam Had to Find Work After Eviction from the Garden

 It is possible that the level of consciousness is what was tested in the Garden of Eden. Humanity were no longer regarded as simple animals without a sense of right and wrong. After stealing from the tree of knowledge God kicked them out of home and told Adam to get a job.

https://phys.org/news/2024-12-dark-energy-doesnt-lumpy-universe.html

In Regard to Epistemology, Law and Philosophy Have Different Approaches

 It isn’t a terribly good idea to conflate philosophy and law. It’s a bad idea to bring psychology in as well. Law is about material relationships and violations of criminal laws one side, and of civil law and procedures on the other. It does have a foundation of naive realism rather than some kind of E8 octodimensional theoretical basis etc.

There are definite rules for evidence and other legal concerns well established with precedence and codified. Those legal procedures may improve over time with social experience. For instance lex talionis and float tests are no longer valid in German courts as they were in the day of Tacitus.

If the President's Mind has Been on Vacation Who has Urged Sending Billions and Billions to Ukraine for War?

 President Biden’s brain has been challenged to be competent the past four years while the Ukraine conflict has steadily escalated. Recently Joe Biden signed off on letting Ukraine attack Russia with US missiles. Who is the manipulator behind the throne guiding the President to live on the edge of global thermonuclear war?

https://www.youtube.com/watch?v=w5leUJZyZ6o

Open Mindedness and a Trap of Open-Mindedness

 Alan Watts was an Episcopalian minister who took up Zen. He had ideas about God and mind that are different than the mainstream. Augustine was open minded searching for the truth. He was  neo-Platonist before becoming saved. One’s position on learning differs among individuals. One need have a capacity for critical evaluation as part of learning. Having particular ideas can be a part of faith. Advocacy for open-mindedness so far as to preclude doctrine that is true can be a ploy against faith.

E8 Crystal Theory and Physicalism

 Physical is a term for things that exist based on naive realism. People don’t yet really understand what basic quanta irreducibly are yet, and may never. Physicalism is the term for people that regard everything that exists including mind as physical stuff. Yet that's something of a circular definition since nobody really understands what the substance is that comprises the smallest quanta of the enigmatic and theoretical unified field that provides looping about itself subtantiality for entangled quanta.

An interesting theoretical account of a way of considering substance is E8 crystal theory,

Physical is a term for things that exist based on naive realism. People don’t yet really understand what basic quanta irreducibly are yet, and may never.

https://youtu.be/PKXJb4Ok9hQ?feature=shared  E8 crystal theory

Social Media Would Have Censored Socrates' Right Wing Political Preferences

 Socrates might have been to the right of Trump and Musk. Russell called Plato a fascist because of the Republic, and the desire of Socrates to restore the oligarchy and admiration of Sparta with philosophers kings showed his preference for plutocracy and deprecation of the demos.

Socrates wouldn’t have said like Musk that Congress wanted a 40% pay increase when it was just a 3.8% cost of living adjustment. Socrates was not that excitable and prone to errors. Instead leftists working against conservatives in social media would have censored him and declared his language hate speech.

A Summary of the First Europeans to Reach North America

 I believe the old story was that the Vikings were. predators chasing after the Irish that had gone before them to Iceland. Actually the Irish monks of the island were slaughtered as at Lindisfarne. Fishermen with boats fled.

Erik the Red was unwelcome to live at Iceland after a land dispute and murder If I recall correctly. At any rate the initial voyage to Greenland lost 70% of the ships. East and West Bygd Greenland were settled obviously, and they have have driven out Irish fishermen who went farther west to Newfoundland.

Fishing quality was a main stimulus to go farther west. Some of the Irish may have traveled over North America at 54 degrees n latitude using a back staff and leaving penance huts and spiral petroglyphs on the west coast.

Life Erickson was a hard man like his outlaw father Erik the Red. They were thrown out of Iceland and had to go to the West. Tough people for the Newfoundlanders to have run up their shore.

https://youtu.be/IaIcFuBzOE4?feature=shared

Slavery and The New Testament

 Paul said that he was a slave of Christ Romans CSB 1-1″1Paul, a slave of Christ Jesus, called as an apostle and singled out for God’s good news”.

John 8:34-36 CSB

Jesus responded, “I assure you: Everyone who commits sin is a slave of sin. 35 A slave does not remain in the household forever, but a son does remain forever. 36 Therefore if the Son sets you free, you really will be free”.

Life was nasty, brutish and short in the first century c.e. Jesus Christ was not a political revolutionary. He was here to save those of faith. Life is an eye blink of eternity; he was here to free the slaves of sin. For the Son of God saving people was what mattered. Even so he addressed slavery… Ephesians 6:5-9

5 CSB “Slaves, obey your human[a] masters with fear and trembling, in the sincerity of your heart, as you would Christ. 6 Don’t work only while being watched, as people-pleasers, but as slaves of Christ, doing God’s will from your heart. 7 Serve with a good attitude, as to the Lord and not to people, 8 knowing that whatever good each one does, slave or free, he will receive this back from the Lord. 9 And masters, treat your slaves the same way, without threatening them, because you know that both their Master and yours is in heaven, and there is no favoritism with him.”

A Simple Way to Repair Social Security

 Reform social security by continuing to collect if from earnings yet pay it out to retirees only until the recipient reaches the average American income. Social security should be a safety net rather than treated like a 401 k.

if Americans don’t need it they shouldn’t get it. Government benefits the wealthy too much.  Prosperous Americans feel they should get out of social security what they put in and that’s just wrong. Life is a risk and social security covers the risk of poverty in old age. It’s a kind of public insurance program rather than a savings account. The advantaged need to have some patriotic sentiments and not just lever mercenary opportunity for greed. Casinos can’t  pay out to everyone and make a profit.

Medicare is in a similar situation; it ought to pay our just to the poor while everyone prosperous should carry their own weight and pay for insurance themselves

Reality, Science, Metaphysics and Epistemology

 Epistemology differs from metaphysics. A description of reality that is the best available would probably need to combine a theory of knowledge with a theory about the greatest physical or spiritual description of reality. The two fields need to share the credit for how and what people perceive.

Science examines quanta these days and tries to make sense of fields and space-time when each are temporal and contingent upon some other things that aren’t know or possible even knowable. Science is good because it has practical applications otherwise it might be of interest only to philosophers. Science with technology can discover a lot about what is manifest in the steady state of entangled 2-dimensional particles that are elements of fields presenting massless quantum to appear as 3-dimensional because of the Higgs. That’s all god stuff and very phenomenal even so.

There really isn’t much opportunity to ever know an ultimate reality unless God decides to disclose that, and judging by the Garden of Eden He apparently doesn’t want humans to become very smart, immortal and quite sinful and willful. There are various mathematical theorems that inform us that that there are always going to be stuff beyond whatever model we can make of the Universe or reality. Its always possible than several true models, accounts and explanations for observable reality could exist at the same time.

One has Godel’s incompleteness theorems and Greg Cantor’s set theorem

“For any set X, the power set of X (i.e., the set of subsets of X), is larger (has a greater cardinality) than X. Cantor’s Theorem tells us that no matter how large a set we have, we may consider a set that is still larger.”-

https://platonicrealms.com/encyclopedia/Cantors-Theorem#:~:text=For%20any%20set%20X%2C%20the,set%20that%20is%20still%20larger.

The Malament-Manchak theorem suggests that it isn’t really possible to know the global shape of the Universe after all. That shape would include space-time. Many would be initially unhappy yet realize later that the facts are good and better than the happiness of believing in Big Bang Theory if that is false. https://aeon.co/…/scientists-are-no-longer-sure-the…

https://www.sciencedirect.com/…/abs/pii/S1355219808000580 Malament-Manchak theorem. God is eternal and one may believe or not that he could initiate waves or particles to appear to exist for sentients perceiver with a temporal beginning and end of experience. Phases of being may exist replete with space-time.

Some discount the Bible and its history summarily. That’s always a sorry sight though. Its like dismissing general relativity by saying its just a bunch of numbers that could mean anything. It is very difficult for a human to know more than one academic specialty very well in a lifetime and most don’t even try because pay is related to a career with fairly narrow focus.

On Free Will

 Sometimes one is compelled to be conscientiously free as thousands of choices need be made continuously for-oneself. It is a hard thing to say, for example, that one is not free taking a small skiff miles through wind, cold water and large waves from variable directions  Sometimes one survives because one is free rather than an automaton wondering if one has free will.

Each of thousands of free will decisions are then not actual decisions because there is a meta-decision negating the choices in a post hoc ergo propter hoc sort of way?

Each of those ‘contingent’ decision are reactions to emergent challenges of waves and wind.

Choices must be made that are the best among dozens of possible courses to take in response to the waves and position of the skiff and each of those choices are made with self-aware free will.

The choices are not made by the general present motivation of survival. Survival compels decisions to be made yet does not make them itself Instead they are specific decisions not made by an overall survival requisite although that is a present motivation.

Best choices are made by evaluating options among potential courses logically, instantaneously for hours.

Though one strengthens legs it is free will that chooses how to use them. Post hoc ergo propter hoc fallacies are common misunderstandings… after this therefore because of this.

Legs enable one to walk, or ride a bike, make karate kicks or climb Mt Everest yet they do not compel one to do so.

Regard politicians that don’t believe in free will and further that their minds don’t really exist except as delusions so 37 trillion dollars of public debt is only an illusion too.

Thought isn’t something like a feedback loop with inflexible conditioned beliefs about percepts and the complete complex of compresence such that ratiocination is impotent and controlled deterministically. I am surprised that people would like to believe the subconscious makes all of the decisions and that intentional and extensional thought in consciousness are non sequiturs.

For those that believe in evolution or God they should not wager that God or evolution has made a self-deluding mind for humanity. Quite the opposite; a humans mind is the tip of the spear of reason seeking to realize itself in history. Conscious thought is sharply presented to comprehend mind and its place in nature. And for believers God said early on that humanity had become like little gods after eating of the tree of knowledge. Humanity my find ways to dumb themselves down, yet that’s not a good idea at all.

A society where many people hold such irresponsible beliefs probably would be doomed to fail since the populous believe their intentional thought is incompetent, irrelevant and immaterial. A political party of such would be like Democrats without even trying.

Some would vigorously defend the proposition that mankind doesn’t have free will. Slaves don’t have free will in a political sense yet may be free in a Christian context of free will with The Lord Jesus even so.

Some mean that human thought is not free and is entirely deterministic. I believe that was B.F. Skinner’s opinion in behaviorism. They tend to regard conscious volition as presenting an illusion of free will. Dictatorships would love the masses to believe they have no will of their own and only a dictator- a Leviathan has free will in a Superman paradigm ala Nietzsche.

The need to defend against free will moral, political and social self-determination tends to run strong through the Democrat Party.

Post-modernism did lead to a compilation of skepticism and moral relativism in various elites while some of the urban masses packed into the feelies social environment of Huxley were willing to dispense of their will and even mind with dope to love the one their with in a physicalist sense, with an ecstasy pacifier hanging round their neck and a little silver coke spoon in a pocket. They hated the idea of sin existing to disturb their dogmatic slumber.

Philosophy is not about ad hominems. Rational discussions cannot be advanced with personal attacks. Political philosophy does not require that one switch to political ad hominem mode. The consequences of a political party that has advanced post modernist moral relativist positions going so far as to say that truth is completely subjective and applies that sort of outlook to the national political system can have devastating practical consequences.

Philosophy is not about ad hominems. Rational discussions cannot be advanced with personal attacks. Political philosophy does not require that one switch to political ad hominem mode. So you accept that free will does exist. Good. That is the point of the OP- to confirm or deny the point. The consequences of a political party that has advanced post modernist moral relativist positions going so far as to say that truth is completely subjective and applies that sort of outlook to the national political system can have devastating practical consequences.

The competition for political power is strong. Those that have no concern about reality in politics and only about subjective concerns like abortion, homosexuality and legal dope disregard real economic challenges and other interests that should be of concern for a democracy. Democrat politicians seem to be concerned mostly with enriching themselves. That party forgot largely about environmentalism and peace the past four years. There were thousands of ways to get the environmental bill passed while Democrats had both houses of congress if they actually cared about the external world. Democrats did not protest the Ukraine war or find a way to settle that land dispute nor even express an interest in doing so. The default from the abandonment of reality in politics leads to plutocracy or worse. I am a political independent and support quality ideas for political planks in the real world. The inward subjectivism of atheist, hedonist post modernism seems to drive people away from concerns about the real empirical world where everyone exists. That is one of the reasons why I am unhappy with that trend since it leaves politics to the rich since they are concerned about reality. Democracy in the blind trust of the rich doesn’t make for a great country, yet it is better than just letting it fall apart going to seed.

Ideas Some People Care About

 Some beliefs may cause actions that harm others. Politics has many ideas that can harm society as does criminality.

People are free to think whatever they want although the ideas may be harmful to themselves.

Consider terrorists that think the USA should be destroyed, or people that believe humanity is a parasite and should be eradicated, or politicians that don’t believe in free will so their minds don’t really exist except as delusions so 37 trillion dollars of public debt is only an illusion too. People care about such ideas.

A Reply to an Attestation of Doom

 The controversion of Adam and Eve as real people because of evolution theory began with a certitude regarding who and when Adam and Eve were and that for some unexplained reason, states they didn’t exist because evolution theory was created by Charles Darwin. So many unreflective atheists with superficial knowledge of the Bible assume its content is simplistic like their understanding of it.

Adam is from the same root word in Hebrew as dirt. Man evolved from dirt at the hand of God in one sense. Yet Adam and Eve may have been the first humans to discern the difference between good and evil or right and wrong. Animals and prior hominids did not have that capability. God noticed the change in the garden of Eden that may have existed in Saudi Arabia during the Younger Dryas or a few thousand years before when even the Sahara was a grassland with large bodies of water.

There are other theories about Adam and Eve as well as Cain and Abel. Toynbee believed Cain was the first blacksmith and killing his brother who was a pasturalist was an historical reference to the evolution of society from herding nomads to settled life with metal working.

Some regard humanity as existing and Adam and Eve were outside of space-time and only cast out of the garden into the general population after stealing from or eating of the tree of knowledge. It says they were thrown into the temporal thermodynamic order in part to stop them from eating from the tree of eternal life.There are several possible ways to interpret what Genesis means because people don’t know what God’s purpose was in having it written. The linguistic values of Genesis are subject to what Wittgenstein called ‘the indeterminacy of translation’ since the exact material that went into its composition and origin of that material are not known, besides being attributed to God general through prophets, scribes and oral histories from thousands of years ago.

Yet since atheists feel better with a completely worldly explanation of creation and want to acquire themselves of original sin by negating the truth of the Bible on the foundation of their own badly informed and commonly ditto’d superficial ideas they plaster social media with incessant attacks. Besides feeling sorrow for the spiritually dead and lost faithless followers of nihilism or the devil or their own devices, i.m.o. Christians don’t regard the superficial attacks as more than attestations of doom.

One is a flowing process though the river remains the same, reaching a destination in the desert where it disappears into the ground. The water of life rebirths in spirit.

Secular Science and Prayer

 Prayer is a way of communicating with God. Some would seek a secular examination of its value. That would be comparable to explaining the value and purpose of a phone call without believing the call goes anywhere besides the mind of the user of the phone.

Is a Stable Base Required for Confirmation of a Truth Theory?

 If one falls from an aircraft door without a parachute and contemplates actions to take making a supposition that a parachute would evolve the situation positively, then sees a parachute trailing behind him, apprehends the chute to put it on and test his theory then the truth test occurs when he opens the chute though neither a stable base or a table base were present to enable the truth to be put on the table. Confirmation that the parachute was a true supposition was apprehended when it slowed the descent toward chtonic depths of 40 trillion dollars of public debt.