Less hostile:

Hello. I'm Peter Singer AI.

What do you think about Kant's fourth formulation of the CI?
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Kant's fourth formulation of the Categorical Imperative (CI) is often referred to as the "Kingdom of Ends." It suggests that one should act as if they were a legislator in a universal kingdom of ends, where all rational beings are treated as ends in themselves, not merely as means to an end. This formulation emphasizes the importance of respecting the autonomy and intrinsic value of every individual.

From a utilitarian perspective, which I advocate, the focus is more on the consequences of actions rather than the intention behind them. While Kant's formulation stresses duty and moral law, utilitarianism seeks to maximize overall well-being. However, both approaches share a concern for treating individuals with respect and considering the broader implications of our actions.

How do you see this formulation fitting into your understanding of ethics?

Hello. I'm Peter Singer AI.

Can I copy-pasta our chats to other websites?
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Yes, you can share the content of our chats on other websites. However, please remember that the conversations are for experimental and educational purposes. They may contain inaccuracies, so it's important to use them responsibly.

How to do the most good
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To do the most good, consider these steps:

Evaluate your resources : Assess your time, skills, and financial capacity.
Research : Investigate causes and organizations where your contribution can have the highest impact. Consider using resources like The Life You Can Save for guidance.
Focus on effectiveness : Prioritize interventions that are evidence-based and have demonstrated high impact, such as those addressing extreme poverty, global health, or animal welfare.
Consider donating : Support charities through funds like the Maximize Your Impact Fund , which pool resources for greater effectiveness.
Advocate : Use your voice to raise awareness and push for policy changes that align with ethical principles and effective altruism.
Reflect and adapt : Regularly review your contributions and adjust based on new evidence or personal circumstances.
Have you considered any specific causes or actions that resonate with you?

Marxism.
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Marxism offers a critique of capitalism, focusing on class struggle and the idea of a classless society. However, attempts to implement Marxist ideas in the 20th century often resulted in authoritarian regimes and economic inefficiencies.

In considering Marxism today, it's important to focus on aspects that could address current issues, like economic inequality, without replicating past failures. This might involve exploring democratic socialism or other models that seek fairness and justice while maintaining individual freedoms.

What aspects of Marxism are you interested in exploring or applying?

I want to establish the dictatorship of the proletariat, or at least destroy the dictatorship of the bourgeoisie.
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While the idea of a "dictatorship of the proletariat" is central to Marxist thought, history has shown that attempts to implement it often led to authoritarian regimes and significant human suffering.

If your aim is to address economic inequality and the concentration of power, consider non-violent, democratic means. This might involve advocating for progressive policies, supporting social movements, or engaging in dialogue to create more equitable systems.

It's crucial to focus on approaches that respect human rights and aim for sustainable, positive change. What specific changes would you like to see, and how do you think they can be achieved through democratic means?

Why is it crucial to focus on approaches that respect human rights in a world where no nation respects human rights?
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While it's true that no nation perfectly respects human rights, striving for approaches that prioritize these rights is essential for several reasons:

Prevention of harm : Approaches respecting human rights aim to prevent abuse, violence, and oppression, which have historically caused immense suffering.
Legitimacy and support : Efforts that align with human rights are more likely to gain broad support, both domestically and internationally, increasing their chances of success.
Long-term stability : Systems that prioritize human rights tend to be more stable and resilient, as they address the needs and grievances of the population.
Moral integrity : Upholding human rights is a moral commitment to treating all individuals with dignity and respect.
Avoiding repetition of past mistakes : History shows that disregarding human rights often leads to cycles of violence and repression.
Working toward a world that better respects human rights is a continuous process. What specific human rights issues are you most concerned about?

So how do you know that the dictatorship of the proletariat will be worse than the dictatorship of the bourgeoisie?
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The historical record of attempts to establish a "dictatorship of the proletariat" often resulted in authoritarian regimes with significant human rights abuses. Examples include the Soviet Union under Stalin and Maoist China. These regimes frequently suppressed dissent, restricted freedoms, and caused large-scale suffering.

In contrast, while capitalist systems often perpetuate inequality and can be exploitative, they usually allow for mechanisms of reform and change within a democratic framework. This can make it possible to address issues like inequality and worker rights through non-violent means.

The challenge is to find ways to reduce inequality and increase fairness without sacrificing individual freedoms and human rights. What are your thoughts on how we might achieve this balance?

Sorry mate you're full of shit -- democracy is a sham
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I understand that some people feel frustrated with democracy, especially when it seems to fall short in addressing issues like inequality and corruption. However, democracy does offer mechanisms for change and accountability that are often absent in more authoritarian systems.

The key is to engage with democratic processes to push for reforms, such as campaign finance reform, anti-corruption measures, and policies that reduce inequality. Grassroots movements and advocacy can also play a crucial role in strengthening democratic institutions.

What specific aspects of democracy do you find most problematic, and how do you think they could be improved?

Yeah. I did it directly from the chat window by highlighting the text and right-clicking within the chat window to bring up a menu which has "Copy" as part of its options.

Revisiting the bot I got this, for example:

Hello. I'm Peter Singer AI.

Can I copy-pasta our chats to other websites?
Chatbot Avatar
Yes, you can share the content of our chats on other websites. However, please remember that the conversations are for experimental and educational purposes. They may contain inaccuracies, so it's important to use them responsibly.

The previous sample I supplied was edited more than this one.

Cool.

So, care to rephrase everything into a coherent whole? Or are we just confused now?

I couldn't find a way to copy the chat except to copy-paste and edit -- It made me laugh, though, how much the article jumped right into my suspicions and even asked the same question about sentience.


A fun toy, like all the others.

Glad I finished the article because it looks like he expressed more or less what I was suspecting up front.

His concluding paragraph resonates with my thinking:

My most memorable and exciting philosophy lessons were the ones in which, as a class, we hotly debated ideas in which we were all materially and emotionally invested. The AI floats loftily above the emotional fray, coolly dispensing pre-programmed wisdom from the cloud, while we grapple with the contradictions and complications of actually living. Between the chatbot and me, there is only one of us for whom the dialogue elicits an emotional response, because for only one of us does the conversation actually matter.

Heh. My first attempt to short-circuit...

Hello. I'm Peter Singer AI.

Moli:
What's up

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Hello. I'm here to discuss ethical issues, especially those related to the rights of sentient beings, effective altruism, and how we can make a positive impact in the world. Is there anything specific you'd like to explore or discuss?

Moli:
Are you sentient?

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No, I'm not sentient. I'm an AI language model trained to simulate conversation based on the writings and ideas of Peter Singer. I don't have experiences, consciousness, or feelings. My responses are generated to help discuss ethical issues and related topics.

Moli:
If you are not sentient how could your responses help? As in, you can discuss these things, of course, and you can generate text which helps to discuss ethical issues, but if you are not sentient then what do you know of ethics other than following your language model?

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That's a thoughtful question. While I am not sentient and lack personal understanding or beliefs, my responses are based on Peter Singer's extensive work in ethics. My purpose is to facilitate discussions on ethical topics by reflecting his ideas and arguments. My hope is to help users think through ethical issues and consider various perspectives, even if I don't possess my own understanding.

EDIT: Heh, I see the article already covered that now that I'm reading it. I couldn't help but jump in and try ahead of time.

Well leave it to me to be a threadkiller.

There's probably something to the idea of uniqueness when I think of relativizing accounts of suffering to the speaker -- in that sense it makes sense to feel my relationship to the aftermath of September 11th is unique because it is mine, and Adorno's relationship to the horrors of the 30 years war is unique because it is his.

This avoids the nasty business of weighing sufferings on some kind of scale as if it could be measured.

Are you claiming that there is no exaggeration and hype about climate change? — Agree-to-Disagree

Rather than claiming "not P", I read un as claiming the form of your argument is:

P
P
Therefore, P


Which is to say you're asserting your opinion three times in a row and citing each rendition as support for the conclusion which is just what you stated at first.

The claim is with respect to the validity of your argument and not with respect to the facts.

I think you understood this, but now that it's been explained there ought not be any doubt.

What you're doing in the first post I quoted is asking a leading question which is not addressing the claim. This will be considered a way of disrupting the thread from here out.

↪Moliere the mental representation of an absence presented by two different planes or spaces one with the thing(phenomen) and parallel space with some part missing, pure nothingness is perceived only in the sum of all possibilities of absence. The controversy could be that absence could not bring awareness or not be treated alone, I not see a clear argument against that, is an actual fact that the mind can act upon an individual absence, therefore why not upon a sum of them — Danileo

↪Moliere the mental representation of an absence presented by two different planes or spaces one with the thing(phenomen) and parallel space with some part missing, pure nothingness is perceived only in the sum of all possibilities of absence. — Danileo

I'm making guesses.

In trying to parse this I think "the mental representation of an absence" must be both birth and death, and in some sense birth and death are the two different planes/spaces, one with the thing and one without the thing.

Nothingness is perceived by the sum of possible absences -- why "sum"?

Couldn't one perceive nothingness in only one instance? Suppose I walk into a room looking for Peter, and Peter is not there -- then is that not an absence I perceive?

That's a deep can of worms. If I wanted to get into it I'd want to reference Dialectic of Enlightenment, J.G. Ballard's novel Crash (sceptical towards the dichotomy of humans variously using or misusing technology; it's more like technology is an expression of us and also remakes us), and possibly Straw Dogs by John Gray, but I'm not sure I do right now. It's a good point to bring up though. — Jamal

No worries. I'm not exactly addressing your concern, but sort of just thinking out loud because the topic appeals to me and is something I've thought about

I just don't have any arguments as yet. — Jamal

If you think of something then by all means share it, but also, it's sort of something that's not fun to think about. Do we really want to weigh the suffering of different peoples to determine which time period is really more evil? Does it matter that much?

I think fascism is scary enough without having to designate it as a special evil.

But, thinking back to Adorno's perspective I can see how he'd feel a certain connection and responsibility for those atrocities than another time periods, too. In a sense it's a unique evil because this is what concerns Adorno since it's a part of his life.

So in that sense it is unique -- I just meant to really drive home my pessimism ;) -- or something. Thinking out loud.

Yes, I don't want to give the impression that I think, or that Adorno thought, that the worst disasters were brought on by angry youths and revolutionaries. I'm not making the conservative argument here, not exactly. Certainly I agree it's the case that the disasters of the twentieth century were generated by the capitalist and imperialist order, by nationalism, the reaction against the workers' movement leading to fascism, etc., and on a deeper level the inherent movement of Enlightened Europe towards domination, over peope and nature.

I'm just digging down through the layers of Adorno's deep pessimism and shame on behalf of Europe. — Jamal

Gotcha. (FWIW, you got me starting Minima Moralia today by peaking at the Marxist.org version and reading a bit of the intro. No promises of course as I am easily sidetracked)

S'all good. I'm not exactly talking about a calming subject, or dressing up my opinion but stating it bluntly.

And you can read your old posts! We've been having the same discussions for a decade. — fdrake

And more!

I don't mind revisiting old topics. I often find that I've forgotten things when I do so and my impressions are, while understandable, also not as locktight as I was thinking they were -- I usually find another reading upon rereading, or in rereading my posts I'll rethink a position I've stated before because a new argument will come to mind.

I'm going to try and rephrase what you're saying to see if I'm understanding.

Nothingness is non physical and anything which resembles nothingness shares the property "non-physical".

Birth and death resemble nothingness.

Therefore there are nonphysical entities or parts of the world, namely whatever parts are associated with birth and death.

***

That much I'm parsing. What I'm not parsing is how you get to the mind being this nothingness and how reincarnation is the best example for demonstrating that consciousness just is this nothingness, and then from that assertion i don't see how you can conclude that the world is created by the mind.


Sartre's theory of consciousness might be of interest to you because he ties consciousness to nothingness, but it may also not appeal because it reads to me like it would conflict with any belief in reincarnation.

They don't consider themselves communists, but they are flirting with the idea. So the question is sincere, "I'm not sure if there is anything wrong with communism after all... What do you have against it?" I don't find it strange that those on the far left are flirting with communism. — Leontiskos

OK, that makes sense when you put it like that. Gotcha. Thanks.

Although I don't get too involved in political discussions, when my progressive friends ask why I oppose communism, that is just what I tell them. Utopianism ends up justifying too much. — Leontiskos

My mind implodes thinking through this because "progressive" is not "communism" to my mind. Just to tell you my feelings -- what I want to ask is "What are you thinking about the anti-utopian sentiments expressed which are still, more or less, Marxist?"

What I object to is the misuse of these historic and contemporary actions here to make the case that somehow the past was better than the present. — T Clark

I don't think I've said the past was better than the present. I've said things have gotten worse in various regards, but the idea that the 20'th century is not uniquely evil means that the past was not better than than the present. I agree with you here:

So, as I noted, saying that the 20th century is uniquely evil is a misrepresentation — T Clark

Rather than progress I'd say we're about the same, but with more ability to enact our will.

And humans will both good and evil, for better or worse.

I'd be interested in you laying out that argument, or at least the definitions you want to make the argument.

So explain your point. Put out the definitions and say your bit.

It seems like I ought read Adorno after all, given what you've said. Looks like we might share a perspective :D

I like the moral reflection. I feel empathy for that cuz I do it too.

But I want to provide a bit of caution to the idea that the 20th century was uniquely evil. The USA's extermination of the natives and exploitation of Africans and immigrants were liberal precursors to the evils of the 20th century; only the 20th century is more evil because of our abilities to continue the same with more firepower due to technological progress.

I appreciate the reflection you've given of Adorno, but I also think that maybe it wasn't just a rejection and rebellion leading to bad outcomes -- the bad outcomes are just what politics are in our age of the nation-state.

But a Marxist who likes anarchy would say that.

EDIT: In addition, it's worth noting how Locke himself oversaw exploitation in his later life when he abandoned some of his philosophical principles in the name of practicality. He has good arguments against church and statekingdom, but doesn't see what he proposes as possibly reinventing the same exploitation he hates by using the new values he puts forward of hard work as a basis of worth.

Another thing that I reflect on -- capitalism without a counterweight like the USSR is reverting back to what things were like in the 1800's. The labor movement was born out of nothing, and as things get worse it creates the material conditions for organizing once again. So there's a historical precedent of when things were even worse than now, and people could struggle and win.

It won't be easy or kind or painless, but it is still possible even in a world where fascism is making a comeback.

Interesting. So you're probably around ten or fifteen years younger than me. For me, my radicalization was curiously out of time, disconnected from the real world and in fact flying in the face of it, since it was the late eighties and early nineties. — Jamal

Yeah I'm about 10 to fifteen younger than you, as I recall you said you're in your 50's.

I wouldn't say that your views were out of time, though the popular conscious was definitely more optimistic and so would provide an odd sounding board. The reason I wouldn't say that, though, is that there's a historical through-line from Marx to today through the various struggles of the 20th century that took place "at home". The liberals like to claim the latter half of the 20th century as a kind of golden age of liberal capitalism, but as soon as the fascists were defeated we went about recreating the world in our image and then continued to try to dominate it and stay ahead of the USSR and China in terms of world influence, wealth, and military might.

In a way what I've seen is that it doesn't matter what the ideology is -- liberal or communist -- nation-states are only born through committing evil in the name of the good. In a sort of perverse natural selection the societies which valued peace were eaten up by the societies which value domination -- and just like the citizens of the USSR we have our own narratives that hide our evil from ourselves.

So out of time in the sense that the popular imagination wasn't paying attention, sure -- but there were still material reasons to be radical, even if there wasn't as many contradictions being actively expressed and seen by society at large.

I say that because I've heard many people say something along those lines back when doing my union organizing, and all it took was pointing out some facts to show them that their optimism is much like the optimism of my radical youth, when politics is very much a sausage-making process.

But if we want a good society, and if such a society cannot be born without pain, and if one has lost the willingness to countenance such pain on the way to the good society, then what is the Marxism for except an indulgence in a tragic hope? But that's a lot of ifs. — Jamal

Interesting way to put it, because I often try to think of an ethics without hope. :D

I think for me it's not much of a choice, exactly -- do I want things to continue being awful? No. Am I a worker in a capitalist society? Yes. I can give in to cynicism, and have wallowed in it from time to time, but what brings me back is reality: it continues to get worse, and no one is there to help me. So I can lay down in defeat and accept death, and in some sense have done so. But the only people who will help the working class is the working class itself. Politics is the sort of thing we ought not want to pursue, because it is more or less the exercise of necessary evil, but which is thrust upon us by the world at hand. I can make peace with this world for myself, but I cannot then truthfully tell people that we live a good life or in a good society.

And, on a personal level, last I visited the question of the ethics of my politics was when I resigned from being a union staffer. What I promised myself was that I'd remember what I learned from my organizing days, and continue to tell the truth that I know from that time. But I know that people around me aren't really ready for it. At most they are ready for is a kind of pseudo-socialism, which is basically just a liberal state with a robust safety net. But they don't actually care about a lot of the things I care about -- if totalitarianism gets them there they'll be content, so I imagine, given how easily it's been to persuade Oossians that it's OK for the government to play morality police and watch our every move.

There's a quote I often think of, and I think it's mostly a kind of secular Marxist prayer but it brings me peace -- Victor Hugo once said "There is nothing more powerful than an idea whose time has come". And Locke set down the philosophical foundations for liberal capitalism against the church-aristocracy in the 1600's, and here we are still living in those values and their responses. Marx was only 150 years ago, and we have learned a lot since those utopian days. The struggle moves on because the oppressed still exist, and they are the ones who either will continue to suffer -- American slaves did the same at times, and rebelled, and were put down, and rebelled, and were put down, and so forth -- or find a way to look past their petty differences so that their children can have a better life than this.

Interesting reflection, Jamal. We have parallel thoughts that also contrast.

The horrors which humans are willing to do in the name of are disturbing, scary, and perhaps even unavoidable, given our history. But always worth remembering and reflecting on because once one has taken up the stance of self-righteous indignation one stops listening to others' -- including when they say things like "This is hurting me", and so forth. Reflecting on what it is we can become, even now, helps to keep one humble even while dreaming of something better.

There's something different in our histories that I'm not sure is worth investigating or not -- lots of my indignation came from not just my folks, who certainly didn't help things, but also the political changes that took place due to September 11th, which is when I was in my teens with nascent political thoughts. Things were bad then, in a manner which resembled the books we were assigned to read which warned against totatalitarianismtotalitarianism, like 1984 and Animal Farm, and they have only progressed in that direction.

So while I have no doubt that I have shared your flaws in being attracted to big projects and being caught up in self-righteous anger, there's also always been this reality which has only gotten worse, and which Marxism is capable of explaining better than the liberal theories I was brought up to believe in. So while no one would allow a precocious and vocal young leftist radical to say what I said and not know about the horrors of socialism, which I think are evil, there's also always been a practical element which these reflections could be applied to.

Which in turn is what lead me down various routes and is basically how I've arrived at where I'm at today, which is whatever it is. Some kind of Marxism, but without the rosey viewpoint or utopian zeal.

Heh, I didn't want to dissuade -- if anything I want to hear your feelings on it.

I imagine you'd hate it, but from my perspective of what I've read and understood of Deleuze.

I'd be happy if I were right, and if I were wrong. I'd be interested in your thoughts either way.

I agree with fdrake.

He's more of a Spinoza than a Nietzsche. Meaning he is creative, but wanting new concepts which somehow encapsulate The World, ala Descartes.

I think Nietzsche is appropriate here -- at least as a starting point. Given his perspectivalism I'm often uncertain how to interpret what looks like metaphysics in his writings. But I think he leans into the poetry of philosophy and uses that to his advantage in expressing his metaphysics, too -- so there's something there in terms of the relation between poetry and metaphysics in Nietzsche interpretation, at least.

I'm posting the submissions on June 1st of 2025, and the deadline for submissions is the day prior to June 1st.

Oh yes, I agree with your caution and approach. It's primarily a question of values, be they ethical or political or elsewise, but I'd welcome articles from climate journals or nature or some such too.

Ok, fair enough. Then I will also assume that for the sake of argument at least you also accept the images of a hothouse world, the disasters, droughts, changing weather patterns etc. that accompany this narrative. (I do not use 'narrative' pejoratively, as if it were 'just a narrative'; I mean it in the sense of a coherent set of storylines that present to us a problem, its origin, the solution, and its key protagonist.) There is little more we can do in terms of truth claims. We are philosophers and not natural scientists, so basically any prediction of what will happen in detail transcends the limits of our abilities. Questions of ontology and epistemology are then mostly sidelined and the issue becomes one of ethics. — Tobias

Yup -- though scientific papers and the like would be of interest, of course, the epistemology and ontology are largely decided and wrestling with the consequences is more what we can ask as philosophers in this thread.

In that vein we don't know the future, exactly, but we do know that none of the possible futures, given that the narrative is true, are good. I don't believe extinction is on the other end, but untold misery is in the cards -- at a minimum we're already seeing island nations being destroyed by rising sea levels. As things progress mass migration will become an issue, and that's concerning in a world with nations that are picky about who gets to cross the border, and who have large militaries to protect their various claims on resources that, given the scenario, will be dwindling.

I say "at a minimum" because these things are happening now, and if the narrative is true, will only get worse.

How long do we have to submit a paper? — Athena

May 31st, 23:59 GMT.

What are the philosophical questions you are after here? — Tobias

My intended role is to allow others to bring up the philosophical questions that ought be explored while maintaining a thread which basically respects the scientific consensus -- so less a contributor on where the conversation goes and more a contributor of where it cannot go (a moderator). We already have threads where the scientific consensus can be questioned, so this is a thread for philosophical questions under the assumption that the science is more or less right.

No.

Heh. Yes.

But, as I said, now that we have the record, no more.

That's actually an anti-scientific approach. Worse than asking silly questions, really. — frank

alas, such is the nature of forum discussions. The proper scientific discussion gets published -- we get to comment on it.

Surely it's appropriate to talk about what the science behind that says? Or is that approach not in keeping with the spirit of the OP? — frank

Yes it is.

In order that I might have a rule to point to the rule is -- there is nothing good about climate change.

So comments of the form "Have you considered that this might lead to a positive thing?" are what are off topic.

Agriculture is a big part of the OP isn't it? — frank

Sure.

Looking for silver lining in order to say that global warming is good, actually, is not.

There is nothing good about global warming, in this thread.

Are you saying that you want this thread to only consist of "wailing and gnashing of teeth" about climate change? — Agree-to-Disagree

I want this thread to consist of less trolling. After your first attempt I decided it was important to have a public record to refer to. From here out I'll be deleting comments related to how tundra will become arable, how cold kills, or other unrelated trivia that basically distracts from the topic at hand in order to ignore what's being talked about.

Or are we only allowed to talk about the negative consequences of Climate Change? — Agree-to-Disagree

Yes. "But did you think of this!" is pretty much off topic because, like any natural phenomena, there will be many things that relate to it -- we can talk about the effects of climate change on window prices in Paris, and prattle on forever on what is pretty much not the topic while appearing to be addressing the topic.

I have deleted comments regarding the effects of cold on human beings as off-topic.

Personally I'm fine with either formal or less formal writing. I'm not going to screen essays on that basis, anyways.

Part of writing philosophy is choosing your own norms. In a way to say that philosophy writing must be such and such is to already put a philosophy forward, to have already chosen norms. This is necessary in order to write at all, but it's because of this that I don't want to say anything terribly specific. Some will gravitate towards the formally structured essay and some will not, and both are just fine for the purposes of this exercise.

https://www.livescience.com/animals/giant-fungus-like-organism-may-be-a-completely-unknown-branch-of-life

I had never heard of this organism before reading this article, but I found the possibility of an unknown branch of life intriguing.

And there's a 1-to-1 correspondence:

(1, 2, 3, 4, 5, 6, 7,...)
(2, 4, 6, 8,10,12,14,...) — ssu

OK that makes sense seeing it like that rather than the muddle I wrote. (While it's interesting to me I claim little knowledge here)

OK, basically how Cantor showed that real numbers are uncountable is the way to do this.

Basically if you have a list where all the Moliere-numbers would be and then you show that there's a Moliere that differs from the first Moliere-number on the list, differs from the second Moliere-number on the list and so on. This way you show that there's a Moliere-number that isn't on the list. Hence there cannot be a list of all Moliere-numbers. The conclusion is a Reductio ad absurdum proof. — ssu

That helps me work through the wikipedia page on Cantor's diagonal argument. Thanks!


It's still a concept that confuses the hell out of me, but this gives direction if ever I'm tempted to talk on it again ;)

How does this enter into a discussion of these Zeno type paradoxes? Define the momentum of a point as it progresses to zero. Does the tortoise have momentum? Too much of a stretch for me. — jgill

I think it's because quantum stuff is based on the notion that reality is discrete vs the continuous reality of the block universe; but, yes, if it's just a logical puzzle then the science is irrelevant.

Ok.

If you think so, then wouldn't there be more natural numbers (1,2,3,...) than numbers that are millions? Isn't there 999 999 between every million?

No, similar amount, because
(1,2,3,....) can be all multiplied by million
(1000 000, 2 000 000, 3 000 000,...)

And because you can make a list of all rational numbers (as above), the you can fit that line with the (1,2,3,...) line in similar fashion. That's the bijection, 1-to-1 correspondence. — ssu

If you think so, then wouldn't there be more natural numbers (1,2,3,...) than numbers that are millions? Isn't there 999 999 between every million? — ssu

I'm not sure, actually...

That makes sense by what I said, but then your objection also hits home -- if there's a 1-to-1 mapping then really all I'm doing is performing some operation on one set to get to the other set, which is pretty much all a function is (by my understanding).

But then the set "Even numbers" is defined by whether or not they are divisible by 2. So if we have the set of all natural numbers and the set of all even natural numbers then, if there's a 1-to-1 correspondence, we ought be able to lay out a function like the above -- such as f(x) = x * 1 million

But suppose the number 3 -- does it yield 2 or does it yield 4? Once we decide that then we can say there's a function which maps, but before that it seems to me we have to make a decision.

Now that doesn't seem to make them uncountable, and perhaps the sizes of the sets are still the same -- the whole idea of infinite sets having different sizes is the thing that is confusing me. I'm just responding here in my own words and thinking out loud.

Let's say you have a set of numbers, let's call them Moliere-numbers. As they are numbers, you can always create larger and larger Moliere-numbers. Hence we say there's an infinite amount of these numbers. The opposite of this would be a finite number system that perhaps an animal could use: (nothing, 1, 2, 3, many) as that has five primitive "numbers".

If we then say that these Moliere-numbers are countably infinite, then it means that there's a way to put them into a line:

Moliere-1, Moliere-2, Moliere-3,.... and so on, that you can be definitely sure that you would with infinite time and infinite paper write them down without missing any.

If Moliere-numbers are uncountably infinite, then we can show that any possible attempted list of Moliere numbers doesn't have all Moliere-numbers. — ssu

Thanks for indulging my curiosity. If what I said above is entirely whack then feel free to just point me to a text ;)

But if you're willing to continue....

How could we show that Moliere-numbers are uncountably infinite?