This topic has been the subject of numerous science fiction books and movies - most recently the book Mickey 7 - which was made into the movie Mickey 17

At the risk of prolonging a side discussion - while they could be derived from Mosaic Law, the 7 rules are not in the Bible. They were invented by Talmudic scholars. WIkipedia says this might have occurred sometime in second century C.E.

Books like Genesis and Jonah present a more universalistic picture, — BitconnectCarlos

I'm not an expert in interpreting the bible, but I'd disagree with this. The plain language of Genesis makes it clear that Israel belongs to the Jews for all eternity. Here's from Genesis 13:

14. And the LORD said unto Abram, after that Lot was separated from him, Lift up now thine eyes, and look from the place where thou art northward, and southward, and eastward, and westward:.

15 For all the land which thou seest, to thee will I give it, and to thy seed for ever.

16 And I will make thy seed as the dust of the earth: so that if a man can number the dust of the earth, then shall thy seed also be numbered.

17 Arise, walk through the land in the length of it and in the breadth of it; for I will give it unto thee.

18 Then Abram removed his tent, and came and dwelt in the plain of Mamre, which is in Hebron, and built there an altar unto the LORD.

The later books add the proviso that the Jews must also follow all the laws.

I'm not disagreeing with you, but I have a different take on this - which I consider as a side comment. Apologies if you are already familiar with it, but if you want to understand what the bible is actually saying, I suggest the Skeptic's Annotated Bible. I recently finished the OT and am now plowing through the NT (up to Romans).

It is clear (at least it is clear to me) that the god of the OT is not the Christian God. The OT God is very specifically the god of the Jewish People (AKA the children of Israel, AKA the 12 tribes, etc). As long as the children of Israel follow all the laws - as laid out in Exodus, Deuteronomy. Numbers, & Leviticus - they are entitled to the land of Israel. The OT God holds all other groups of people to be outsiders - Jews are not even allowed to marry non-Jews. The OT God even assists the Children of Israel in committing genocide (think Jericho).

So when you say

God is perfectly good — Bob Ross

or

5. It is unjust to directly intentionally kill an innocent person (viz., it is wrong to murder); — Bob Ross

you are making this judgement from outside the OT. Now this is a perfectly acceptable thing to do - as long as we are aware of what we're doing. But the OT god is not perfectly good. The OT gets angry and changes his mind - not the expected behavior of a perfect entity.

As long as I'm here, here are two other fun links from the Skeptic's Annotated Bible:

A list of all God's killings
A list of ALL the commandments on both the OT & NT

Just remind me again why Einstein said he doesn't believe that God plays dice? — Wayfarer

I'm sure that there are better ways of putting this, but the short answer is that Einstein said this because he believed that there was some underlying mechanism that would (in some manner) eliminate the uncertainty from the uncertainty principle. To the best of our current scientific knowledge, Einstein was mistaken in this belief.

As an aside (and apologies if I'm telling you something you already know) Einstein did not have any conventional religious beliefs. He was sort of a Spinoza-ist.

I could be wrong, but I highly doubt that - after seeing the photos of those trans-men and/or meeting them in person - any significant number of folks would want trans-men using women's bathrooms. As far as I'm concerned? People should use the bathroom that matches their gender identity - but that's just my opinion.

Are we really concerned about where people relieve themselves? Or are we really discussing whether the process of transitioning actually changes a woman into a man? — frank

I may be mis-understanding him, but Harry seems to be very concerned. I'm not.

So you feel that these people should be using the women's bathroom:

How about trans-men? Is it OK for trans-men to use the men's bathroom or must they use the women's bathroom?

I was searching for any context where 2+2 might be equal to something other than 4, any reason to not accept 2+2=4 as an absolute truth. — noAxioms

If you have 2 apples in one hand and 2 apples in your other hand you are holding 4 apples. If you have 2 apples in one hand and 2 oranges in the other hand you are holding 4 pieces of fruit. Etc

But once you say 2+2=4 you are now in into the realm of mathematics where different rules apply and 2+2=4 is not an absolute truth. Rather, 2+2=4 is only true within specific mathematical systems - most commonly Peano Arithmetic - where you start of with certain axioms and rules and then you can derive 2+2=4.

I don't pretend to understand them, but there are other mathematical frameworks where 2+2 is not necessarily 4 - e.g Modular Arithmetic and Abstract Algebra..

This discussion reminds me of this:
[url] https://en.m.wikipedia.org/wiki/Null_(SQL)[/url]
In particular you might want to check out the section “ Law of the excluded fourth (in WHERE clauses)”

But the idea of ‘universes, plural’ in any other sense, I think is completely meaningless - as it’s obviously not an empirical hypothesis, in the sense of not being able to be refuted empirically, so it must be metaphysical, but without any connection to what the term was devised to mean. — Wayfarer

In the past 100 years our knowledge of the universe has expanded by orders of magnitude. I find the notion of a multiverse intriguing - but I'm just an armchair physicist. However, much smarter people than I think it's worth looking into.

https://www.thescienceblog.net/is-there-scientific-evidence-for-the-theory-of-the-multiverse/

https://organicallyhuman.com/googles-quantum-multiverse-exists/

How do you determine what is best for other people that you have never met? Who gets to determine what is best for everyone? — Harry Hindu

Call me delusion. but I think the following things are pretty darn good for people that I have never met:

- having access to quality health care
- knowing that you will always have a roof over your head no matter how poor you are
- knowing that you will never go hungry,
- knowing that you will not be sent to prison for having the wrong religious or political beliefs
- knowing that you will not be sent to prison for having a tattoo
- etc

In fact I will go out on a limb and say that these things are good for societies - not just for individual people.

in America holocaust deniers are allowed to distribute their literature with little to no censorship, and as a result their ideas just aren’t taken seriously.

Unfortunately this is not accurate. https://forward.com/culture/705403/kanye-west-joe-rogan-darryl-cooper-elon-musk-antisemitism-bonanza/

Pre-conventional morality is only concerned with power. People in this stage don't have genuine moral opinions, but only act off of reward and punishment. So, they will do whatever authority tells them to do, no matter how transparently stupid it is. The left must clearly be in this category, because they talk about equality, and then discriminate against white men. — Brendan Golledge

Talk about getting things ass-backwards. Leftists are trying (in their own inept way) to compensate for centuries of discrimination against women and minorities - imposed by the predecessors of MAGA.

They talk about saving the environment, and then burn electric cars. — Brendan Golledge

Who is this "they"? Millions of Americans are genuinely angry at Musk for destroying essential government programs that they rely on. A few disgruntled people are doing stupid shit. Leftists are still buying electric cars - just not Teslas.

Etc

I think MAGA is in the conventional stage of morality, which is concerned with law and order. I think "law" could be thought of as "consistent authority. It seems to me that MAGA are still waiting for other people (like Trump) to tell them what to do or to fix things, but at least they can see the inconsistency of the left and reject it. — Brendan Golledge

Talk about getting things ass-backwards. MAGA is totally about power - about obeisance to Trump. Virtually everyone Republican who has disagreed with Trump has been ejected from the party - Cheney, Barr, etc

The fact that seemingly intelligent people (like yourself) buy into this upside down view of reality is a tragedy.

I still think that the only thing that's for sure is that something exists without cause in some mysterious fashion. It could be that impersonal laws of physics exist without cause. Or it could be that the laws themselves came from a being whose existence has no cause. Or reality could be circular (like somebody goes back in time to start the big bang). Or it could be some other option which we can not comprehend. — Brendan Golledge

To your list I would add the possibility that the universe has always existed and always will. But my personal choice is the last. I would phrase a bit differently tho: We have no idea what the f**k is going on - and may never will.

I can't find a specific quote, but my understanding is that Singer only supports infanticide in cases where the infant is severely disabled - e.g. spina bifida or anencephaly.

This position has encountered vocal opposition from the disabled community.

Arabs were undoubtedly in the land in the 19th and 20th centuries. I would just question the "indigenous" labeling. — BitconnectCarlos

Ah - now I get it. I wasn't sure how to phrase this. The history of this region is immensely complicated with many different threads (as with most history) - but there was a large number of people who had deep family and cultural roots in the geographic area that was called Palestine - these roots went back many hundreds of years. These people eventually called themselves Palestinians. So what phrase do you use to call these folks? I'm up for suggestions.

The word "Arab" is a generic term that refers to an ethnic identity and has nothing to do with a particular geographic location.

https://teachmideast.org/arab-middle-eastern-and-muslim-whats-the-difference/
https://en.wikipedia.org/wiki/Arab_identity
https://www.britannica.com/summary/Arab

Early Zionism was to renounce any sort of biologism and nationalism, to build bridges between every nation of man and bring them together. — DifferentiatingEgg

I confess to being totally baffled how anyone as well informed as you seem to be could consider early Zionism to be some sort of kumbaya "let's all get together and build a better world" movement. Yes there were some who espoused that, but these were fringe elements and had no real impact on events. We know from both internal correspondence and public statements that statehood was always the goal - and using "homeland" was a cover.

In any case, the indigenous Arab population (i.e. the Palestinians) were under no such illusions. The local population always opposed Jewish immigration even before Zionism was a thing. By WWI the anti-Zionism movement was highly organized (and sometimes violent) . The post WWI riots of 1920, 29, & 33 - the 36-39 revolt, etc, etc? Clearly these were not directed against an organization that was trying to build bridges between every nation of man and bring them together.

As far as Chomsky goes I am in large agreement with his positions on world events, but he got this one wrong.

Perhaps you are familiar with this already, but here is some excellent material about pre-WWI events.

All that said, I have no doubt that this will not change your mind. I give you the last word.

get it from Zionist philosophers, not a 7 man swiss committee making propositions on land, — DifferentiatingEgg

There were over 200 delegates at the First Zionist Conference and the program waw adopted unanamously.

you'll notice none of the names I mentioned are even on that committee. — DifferentiatingEgg

Quite true - especially considering that Chomsky was born in 1928 - 30 years after these events. But even apart from this obvious goof on your part, these people were all wa-a-a-y outside the mainstream Zionist movement. I don't have the time or energy to bring you up to speed - but I'll leave it that the end goal of mainstream Zionism from the very start was colonization - the establishment of a Jewish state in Palestine.

Early Zionism was to renounce any sort of biologism and nationalism, to build bridges between every nation of man and bring them together. Berdichevski, Brunner, Popper-Lynkeus, Lessing, Herzl, Buber, Chomsky, Zeitlin... the list goes on. — DifferentiatingEgg

I don't know where you get this notion, but it has no relationship with reality. Of course history is very complicated - and there were numerous variants of Zionism, but here is the basic outlines of the first Zionist Congress in 1897:

"The program set out the goals of the Zionist movement as follows:[5]

Zionism seeks to establish a home in Palestine for the Jewish people, secured under public law.[6]
To achieve this goal, the Congress envisages the following means:

1. The expedient promotion of the settlement of Jewish agriculturists, artisans, and tradesmen in Palestine.
2. The organization and bringing together of all Jews through local and general events, according to the laws of the various countries.
3. The strengthening of Jewish feeling and national consciousness.
4. Preparatory steps for obtaining the governmental approval which is necessary to the achievement of the Zionist purpose."

I’ve been following this thread with a combination of amusement and astonishment (with a bit of dread thrown in for good measure :roll: ). The technical details of the philosophical discussions are above my pay grade but the poems are astonishing. I don’t know if this is possible but I have a suggestion. Could you configure two different AIs to defend two different religions - say Christianity vs Islam - and have them engage in a debate over which is the true religion? Would be interesting/entertaining if one AI convinced the other that their choice of religion is correct.

We're just repeating ourselves here. I've given you 2 clear definitions and use cases of the words "true" & "false". You seemingly acknowledge what I'm saying then you go back and repeat your previous talking points.

So to repeat myself: "What is" is not true. "What is" is not truth. "What is" is not "the Truth". Etc. "What is" simply is. It is our sentences describing "what is" that are true or false.

If true refers to the property of sentences and propositions, isn't a true sentence "what is" while a false sentence is "what is not"? — Philosophim

Again - no! You keep equating our sentences with "what is". True sentences describe "what is" - they are not equivalent to "what is".

My challenge for you is to see if you can come up with a context of truth that doesn't contain 'what is' at its base, — Philosophim

Notice that you used the word "contain" - this is yet another poetic metaphor. A true sentence does not contain "what is" - it describes "what is".

Anyway, I'll give you the last word.

Hi EricH, I wanted to say first of all I love your light hearted style of posting, much appreciated. :) — Philosophim

I'll never understand the level of invective out here. I mean let's face it - we're all a bunch of eccentric cranks out here. Let's have some fun, but don't take it too seriously.

As I use them, the words “true” and “false” are adjectives which describe properties of statements/propositions. The words “truth” and “falsehood” are the noun forms of the adjectives; they identify statements/propositions that have the property of being true/false. — EricH
I agree with this. — Philosophim

But you're gonna disagree in a moment.

1) Statements are true if they accurately (or as accurately as possible) describe the real world (AKA reality, the universe, existence, what is, etc) This is commonly referred to as the Correspondence Theory of Truth.
2) Mathematical/logical propositions are true if they follow the rules of a particular mathematical/logical framework -e.g. Peano Arithmetic. Any particular proposition can be true in one mathematical system and false in another. — EricH
No objection here either. What's important here is that you have clearly established that we are talking about truth as a state of reality, not a belief or something we know. — Philosophim

Suffering succotash! You seemingly just agreed with me above that the word "truth" identifies statements that are true. So I most definitely am not talking about "truth as a state of reality". To repeat, I am talking about the word "truth" as a property of sentences/propositions.

You appear to be using the word "truth" in a completely different way here. Now there's nothing wrong with this - but if so then you need to give that definition and show how it works semantically in specific contexts.

================

Mathematics is not true by virtue of being. Mathematical statements/propositions are true or false within the rules/context of a particular framework, but the words “true” and “false” do not apply to the field of mathematics (the manipulation of numbers and symbols). Mathematics is neither true not false. — EricH

Almost, we just have to clarify the context. Is it true that 1 captures 'an identity'? — Philosophim

I don't know what you mean by 'an identity'.

Is it true that 1+1=2? — Philosophim

I can only repeat myself here. If you have one apple in your right hand and one in your left, you have two apples. etc, etc. But "1+1=2" is only true within certain mathematical frameworks (e..g. Peano Arithmetic) and it is only true because it can be derived using the axioms and rules of the framework. There are other mathematical frameworks in which it may not be the case.

Is it a belief, or is it a known truth? — Philosophim

Aargh again. It is neither..

After all, we just don't believe that 1+1=2, we know that 1+1=2. — Philosophim

Sigh - we know no such thing.

1+1=3 would be false, but this is because we know it to be false. — Philosophim

Again we know no such thing. What we do know is that by applying the axioms of Peano Arithmetic we can prove that "1+1=3" is false - but again this is only the case within Peano Arithmetic.

================

Any discussion of true and false must involve the context of belief and knowledge in some sense of the discussion — Philosophim

You spend a lot of time on belief/knowledge, but this is [metaphor alert!] a side show. Of course belief and knowledge are legitimate and important topics of conversation, but they do not affect the semantics of the words "true" and "false". If we say
I believe P.
I know P.
where P is a sentence/proposition about reality/existence/what is/the universe/etc? It is P which is true or false. The words "belief" and "know" are used to indicate the speaker's attitude/assessment/evaluation/judgement/confidence in/etc of the accuracy of P.

==================

Truth is, "What is". — Philosophim

As I said in my first response, this is not a definition, it is a poetic metaphor. The universe/existence/what is/everything that is the case/reality/etc is neither true not false - it simply "is". it is our statements about the universe/existence/what is/everything that is the case/reality/etc that are true or false.

Interestingly enough, @Arcane Sandwich seems to agree with you on this point.

Truth = Reality

What it means:
It mea[n]s that Truth is identical to Reality.

Good enough? — Arcane Sandwich

==================
Summary - I'm doubting that this conversation will be productive moving forward. I'm pretty much repeating the previous points I made - and you seem to be mostly repeating your points. But who knows. I've presented a pretty sound case that there are two working definitions/usages of the adjectives "true" and "false" - and their noun equivalents. You seem to be suggesting that there is a third definition/usage, but so far I'm not seeing anything I can sink my [metaphor alert!] philosophical teeth into. But if you can present a clear and explicit definition and the context(s) under which your definition functions, I'll definitely check it out and try to respond.

Another very delayed response here . . .

We’re taking past one another. I will try to clarify. I suspect that I will fail in communicating, but I’ll try again.

To recap what I said, I am attempting to make a very narrow point about the semantics of the words “true”, “truth” “false”, and “falsehood” (and any synonyms).

As I use them, the words “true” and “false” are adjectives which describe properties of statements/propositions. The words “truth” and “falsehood” are the noun forms of the adjectives; they identify statements/propositions that have the property of being true/false. My position is that there are two uses of these words that work - i.e. that make semantic sense. Any discussion of wisdom, knowledge, belief etc is a separate topic which has no bearing on the semantics of the word “truth”.

1) Statements are true if they accurately (or as accurately as possible) describe the real world (AKA reality, the universe, existence, what is, etc) This is commonly referred to as the Correspondence Theory of Truth.
2) Mathematical/logical propositions are true if they follow the rules of a particular mathematical/logical framework -e.g. Peano Arithmetic. Any particular proposition can be true in one mathematical system and false in another.

With that in mind . . .

Basically we use true for, "True as I know/believe it" and "True despite my knowledge or beliefs" — Philosophim

I read this and am reminded of the old joke about The Lone Ranger and Tonto (it’s considered a bit racist these days).

Anyway, maybe this is how you use the word true, but I suspect that the majority of folks out here would disagree with this.

Basically we use true for, "True as I know/believe it" — Philosophim

For purposes of this discussion I will take it that this is analogous to The Correspondence Theory of Truth (my first definition/usage of the word “truth”). So we agree on this usage.

“1+1=2” is only true within the context of a mathematical framework - e.g. Peano Arithmetic. — EricH
Agreed. Kant came up with two terms that attempted to capture these differences. Analytic knowledge is true by virtue of being, — Philosophim

Aargh! No! I am not qualified (and have no interest) in discussing Kant, but I am confident in saying that Peano Arithmetic (in fact all mathematics) is a human invention in which we manipulate symbols within specific rules. Mathematics is not true by virtue of being. Mathematical statements/propositions are true or false within the rules/context of a particular framework, but the words “true” and “false” do not apply to the field of mathematics (the manipulation of numbers and symbols). Mathematics is neither true not false.

No, I actually was using it as another synonym. — Philosophim

If you are using the word “truth” as a synonym for “existence” then the following sentence is semantically correct:

“According to our best scientific knowledge, truth came into existence 13.8 billion years ago”

This is patently absurd (at least it looks that way to me). I am humbly requesting that you refrain from using the word "truth" in this fashion.. It serves no syntactical or semantic purpose and only makes communication massively confusing.

Perhaps the word 'truth' has becomes such a broadly applied word in culture that it is difficult to use it in a distinct and clear context. The problem is that if we don't lock it in to clear and distinct contexts, then it becomes what I like to call a 'wiggle word'. — Philosophim

Absolutely! That is exactly what you are doing here - you are giving the word “truth” an additional context that converts it into a “wiggle word”. There are already two clear & distinct contexts in which we can use the word “truth”, there’s no compelling need to give it this third definition.

Belief, knowledge and truth are not the same thing. — Philosophim

I would consider “knowledge” and “belief” to be wiggle words - and as I stated they have nothing to do with the point I am trying to communicate. There are endless discussions out here on TPF debating the meanings/usages of these words - and it seems like no two people can agree.

As long as we remember that belief and knowledge are assessments of what is true, and not 'Truth' itself, its a bit easier to sort out a solid meaning of truth that more easily avoids being a wiggle word. — Philosophim

I’m not sure what you’re saying here. You’ve capitalized ’Truth’. Are you asserting that there is this, umm, thing out there called Truth? If so, then you’ve introduced yet a 4th usage of the word “truth” and I strenuously disagree. There ain’t no such thing as “Truth itself”. Or perhaps you are opposed to using the word “Truth” in this way? In which case I agree.

Anyway, just to re-iterate. There are two semantically consistent ways of using the word “truth”. The words “knowledge” and “belief” do not factor into these definitions/usages.

You haven't changed my mind about the quality of that particular poem, but I'll take the praise. Thanks!

Very belated response here . . .

I think we’d all agree that words can have different meanings depending on the context. When I use the words “true” or “truth” they have one of two different meanings.

"A true statement is about something concrete, and corresponds to reality." — Philosophim

That is one of the meanings I use. When a person in a USA court swears to tell the truth they are saying that their sentences will correspond to reality. An important corollary to this is that the words “true” and “truth” require the words “false” and “falsehood” (or similar). We need some semantic way to express that a statement about something concrete is not true.

"1+1=2" — Philosophim

At the risk of going on a tangent, this statement is true - but the context is different. If I have one apple in my left hand and one in my right I have two apples. If I have an apple in one hand and an orange in the other I have two pieces of fruit. Etc. But once we say “1+1=2” we are no longer talking about something concrete - we are doing math - we are manipulating symbols. “1+1=2” is only true within the context of a mathematical framework - e.g. Peano Arithmetic. And - as previously - we need some method to state that a particular mathematical statement is not true.

So far, so good.

Truth is what simply is. — Philosophim

Ii could be mistaken but I don’t think you’re saying that “what simply is” is simply another definition/synonym for the word “truth" (or visa-versa). I don’t think you’re saying that we can use the word “truth” in place of using the phrase “what simply is”. If that were the case then there are much better words - “reality”, “the universe”, existence”, etc - which do not have any additional implication.

So from my perspective it seems that you are trying to create a third context in which the words “truth” and “false” have specific meanings - but how this works is not clear to me. Just e.g., how does “falsehood” work in your context? Would you say “Falsehood is what simply is not”?”

I’m guessing (and again I could be wrong) that you are trying to express a more encompassing philosophical concept. You may be onto something here (not me to judge). But your usage strikes me more as poetry. Here I’ll compose a short poem:

What Is - by EricH

Truth is the sky is blue
Truth is my love for you
Truth is not a miss
Truth is what simply is.

Not a particularly good poem - pretty pathetic actually.

the proposition "five legged blue creatures that breathe fire freely roam in Cyprus" isn't [truth apt]. — RussellA

This is sort of nit-picking, but I consider this sentence to be truth apt. After all, I can envision some evil super genius genetically engineering such creatures and setting them loose on Cyprus. Of course it's false.

"The non-existent apple threw the square root of the Eiffel Tower"

Now that is most definitely not truth apt.

Does it mean "therefore" has some logical significance in the statement and all statements? — Corvus

There are likely an infinite number of sentences (or certainly a very large number) that could contain the word "therefore", so I can't comment on how it would work in all sentences. But I would agree that typically the word "therefore" is used to indicate that there is a linkage between the other components of the sentence (or perhaps a previous sentence). I googled synonyms for "therefore" - "accordingly", "hence", "thus" "consequently" & "ergo" all seem to have similar usages (with some subtleties in emphasis and style.)

When you say, "I think therefore the Moon exists. ", doesn't sound quite logical or convincingly meaningful or true, than "I think therefore I am.". What do you make of this? — Corvus

We can construct an infinite number of sentences (or certainly a very large number) that are grammatically correct/sound but which have no semantic meaning. "The capital of France is Paris therefore zebras have purple hexagons for camouflage". "Quadruplicity drinks procrastination" "Colorless green ideas sleep furiously" etc

"I think I am" sounds like I am guessing I exist. — Corvus

Indeed, yes.

"I think therefore I am." indicates "I think" is the precondition or necessary foundation for "I exist". — Corvus

I would put it a bit differently, but this is fine.

So how can the same "I think" imply guessing, and also the solid reasoned precondition for the existence? — Corvus

Because context matters. The same word or phrase can have wildly different meanings depnding on the full context on which they appear.

Or are they different "I think"? — Corvus

They are different. The additional word "therefore" changes the meaning of the full sentence exactly as you just described.

There’s no need for a clarifying statement as it is obvious by the plain language reading. I’m a plain language person. As an aside, I can’t remember the exact quote but didn’t someone once say something to the effect that philosophy takes things that are obvious and tries to make them seem more complicated than they are?

There doesn't seem to be difference between saying,
1) The oak tree is standing there. and
2) You I think that the oak tree is standing there. — Corvus

To my way of thinking these are very different things. #2 implies that the speaker is not certain. I.e., there is an implied "But I could be wrong" that follows #2.

[Edit] Now that I've thought about this some more, it seems to me that the sentences are even more different.
#1 is not expressing a thought, it is a proposition that is either true or false via the Correspondence Theory of Truth.
#2 is a speaker expressing a proposition which they have (at least some) confidence that it is true.

All due respect, that is a red herring. It is not necessary to understand set theory to understand such basic facts as 2+2=4, they are logically necessary within arithmetic.. — Wayfarer

To the best of my knowledge that's simply not the case - at least with regards to arithmetic. If you have two apples in one hand and two apples in the other you have 4 apples. If you have two apples in one hand and two oranges in the other you have four pieces of fruit. Etc. But to say 2 + 2 = 4 is logically necessary within arithmetic is simply not the case - it relies on the rules of arithmetic - which are not logically necessary.

Is anything within math is logically necessary? People much smarter than anyone here on TPF have been studying and analyzing & theorizing about this for thousands of years - and as far as I'm aware there is still no definitive answer to these deep mysteries.

BTW - just to be clear, I am not taking a stand on whether there are such things as necessary truths - I'm simply saying that 2 + 2 = 4 is not one. That's why I suggest you need a different example - is all.

Good luck with your endeavors.

The point about necessary being is that it needs no explanation. It is the terminus of explanation for all question about 'why is that the case?' A trivial example is the case of a simple arithmetical equation, what is the sum of two plus two? The answer of course is 'four' and there is no point in asking why it is. Asking "why is 2 + 2 = 4?" misconstrues the nature of necessity. — Wayfarer

At the risk of picking on a minor point, I think you need a better example of something that needs no explanation. There is nothing "necessary" about 2 + 2 = 4. In fact this depends on a number of more basic assumptions (axioms).

If John is in Paris is claimed as the axiom or fact in this proof above, then it gives a logical implication that John is not anywhere in Japan. — Corvus

Again, no one is disagreeing with this.

It sounds like you have never heard of "reductio ad absurdum" in Logical Proof. — Corvus

Of course - but reductio ad absurdum is not part of propositional logic.

I'll try one more time. Once you say P->Q, ~P, ~Q you are (at a minimum) in the world of propositional logic and your proof must follow the rules of propositional logic.

If P is of the form "X has property Y"?

~P is not "X has property Z"

~P is "X does not have property Y"

I can't make it any clearer. And now I'll give you the last word.

I've been very reluctant to respond to you given your desire not to continue the conversation, but the thing is - we're on the same side regarding the OP. I agree with you that PSR is nonsensical. And I also feel that maybe I did not explain things well enough. So please take what I'm saying here in the spirit of constructive criticism - I'm not trying to belittle you.

So first of all, of course if John is in Paris then he is not in Japan. As my kids would say - "Duh dad!". You don't need any premises or propositional logic or truth tables to figure this out. All you need is common sense and some rudimentary geography.

But once you say this:

P->Q
~P
~Q

you are now using (at least) propositional logic which has a very specific set of rules - and if you do not follow those rules you will get called out. Some basic rules are:

P = P
~P = ~P

You are saying that P is "John is in Tokyo". No problem there. But then ~P is "John is not in Tokyo".

Saying that "John is in Paris" obviously contradicts P by common sense, but it is not the same thing as ~P. If this were the case (which it isn't) then you would have an infinite number of different ~Ps that contradict each other:

"John is in Paris" is <> "John is in Oslo"
which yields
~P <> ~P

which is obviously wrong.

If "John is in Tokyo" then "John is in Japan", but if "John is not in Tokyo" then John could be some other place in Japan.

I hope you find this helpful.

Good catch Tim. I would put it slightly differently - there are missing steps/facts in Corvus' "logic":

P -> Q
If John is in Tokyo, then John is in Japan.
R
John is in Paris (not in Tokyo). <=== A fact from real life situation.
S
Paris is not in Japan <=== Another fact from real life situation.
R & S ->~Q
Therefore John is not in Japan.

P -> Q
R
S
R & S->~Q
Therefore ~Q — Corvus

P is irrelevant to getting ~Q. Of course this is all loosey-goosey and not formal 1st order logic

I am a millionaire totally and solely dependent on the fact of the antecedent "If I win the lottery jackpot". — Corvus

In which case, Q would have been proved without the proof process. — Corvus

I thought I was clear, obviously not. I've bolded the key phrase. As you acknowledged, this is simply not the case - your being a millionaire is clearly NOT dependent on winning the lottery. For your example to work, it needs to be re-phrased. I can think of two options:

1 - Add an additional qualifier: If I was not previously a millionaire, then etc etc . .
OR
2 - Get rid of the "totally and solely dependent". E.g., If I win the lottery jackpot then I will be a millionaire

And without which, you have left the logic behind, not having proved ~Q, but simply having asserted it. — tim wood

.I am a millionaire totally and solely dependent on the fact of the antecedent "If I win the lottery jackpot". — Corvus

You could already be a millionaire prior to the lottery drawing.