What number set are you talking about? The natural numbers?
I believe you meant the natural numbers, {0,1,2,3, ...}. For the sake of argument, lets assume that the natural numbers don't go on forever. Then there must be some largest number, n. But then n + 1 is a larger number, and n therefore can't be the largest number. This contradicts the assumption that the natural numbers don't go on forever, and no number can thus be the largest Q.E.D.
Side note, there exists finite number sets with a unique largest number.
You are the one who made me leave CD.
Your posts have been so sickenly arrogant and hateful as of late that I am actually in a worse mood logging off here than before logging in. Stop your conquest of proving idiocy of your fellow human beings, it serves absolutely no purpose, and will only leave you exhausted in a sour, painful mood and destroy whatever respect people have left for you on here. Do not fool yourself into believing that you are actually debating here. It's just a disguise you wrap around your petty power games.
I am not angry at you, I see no reason to. Goodbye.
Definitions aren't propositions. Therefore definitions don't have truth values and hence can't be valid or invalid. It's a misconception that a definition can be valid. A definition is not a proposition, it's not a statement about the nature of reality. That doesn't mean that it doesn't matter how we define things. It just means that definitions don't have to make sense.
Do I have to accept the supposed truths of a definition? No, if I define horses as circular squares I do not suppose that a square can be circular (which would be it's intrinsic supposed truth). In fact, if I go along with the definition then it's possible to show that no horses can exist because the existence of a horse would be a logical contradiction.
So this definition is useless because we can show that there exists nothing that has the quality of being a horse (a circular square). But that doesn't stop me from defining horses in this way; I am not proposing that a horse exists. I am in fact not proposing anything. I am not saying that what we usually mean by horse lines up with what I am defining as a horse here.
Therefore, if I have proved that no horses (circular squares) exists I have not magically proved that no actual horse (four legged mammal) exists. I have simply showed that a horse with the qualities I have defined do not exists. So if I were to make a debate about religion, and if I define religion in a specific way and then make some proposition about religion defined in this particular way, then I am not necessarily proposing anything about religion-as-commonly-understood. I have simply proposed something about phenomenons with the particular qualities I have designated. In order to say anything about religion as commonly understood, then I have to make sure my definition lines up with what we understand as religion. That's how we judge whether a definition is useful, we judge it by the extent with which it lines up with what we mean.
If wrong means impractical, and if peace of mind is desirable, then yes, there's something truly wrong with being closed minded. Keeping your mind closed means fighting off anything that challenges you, which undermines peace of mind. Since we are always encountering things that challenge what we think and believe, we will be in constant struggle. Therefore if our goal is to have peace of mind, then being closed minded is impractical, thus wrong.
The best argument against Winston Churchills legitimacy is similarly an ad hominem attack. This man was responsible for appaling crimes against humanity such as concentration camps in South Africa, and the Bengal Famine where a a number of people died roughly equal to the number of people who died in the Holocaust. But no one knows how to express his rascism better than Churchill himself.
""I do not admit… that a great wrong has been done to the Red Indians of America, or the black people of Australia… by the fact that a stronger race, a higher grade race… has come in and taken its place. " - Winston Churchill, 1937
Second argument
"The if-then presmise you present is not "religious science" but science applied to religion"
The strategy of my argument was to show that science is compatible with religion by showing that scientific principles can be applied to religion (i.e. religious content). If you don't believe the compatibility of scientific principles with religious content shows that science and religion are compatible, we have a disagreement we will have to settle.
Buddhism is a religion
"A not inconsiderable number of persons would contend that Buddhism does not represent a religion as the term is commonly defined."
There indeed is doubt about whether Buddhism is a religion or not. This doubt, however, has no rational ground, and is caused by the fact that people assume that religion is inherently like Christianity. Since Buddhism isn't like Christianity, people conclude that it can't be a religion. I will now solidly reason why Buddhism is a religion.
I will list the common characteristics of religion. I will not go into any detail in proving that Buddhism indeed has these characteristics as it will be immediately verifiable. Buddhism has: rituals, contemplative practices, a belief system, a monastic order with strict rules about living, a less strict set of rules of life for lay people (the 5 and 8 precepts), ethics (right talk, etc), Gods (many of the Gods known from Hinduism), holy places, a cosmology (karma, samsara, nirvana), a central spiritual figure, a thesis about the fundamental nature of human beings (to avoid Dukkha), and an ultimate goal of spiritual transcendence (the attainment of nirvana).
Delegitimation of core principles
"it must be demonstrated that [...] the process of science would not be distorted (intentionally or unintentionally) by the assumption of the conclusion"
I will paraphrase what the Buddha states in AN 3.65, the Kalama Sutta. The Buddha demands an experiential emphasis, he demands the neglect of bias caused by tradition, axiom, specious reasoning, authority and so on. It is demonstrated that the process of science would not be distorted by the assumption of the conclusion, because Buddhism has a doctrine that assumption should be systematically neglected. Practitioners are invited to 'see for themselves'.
The concept of Dukkha is complicated
"Dukkha is a bit more indistinct and complicated than you represent it to be"
I present Dukkha as a very specialized, well-defined concept. This does not mean that it is not complicated, for Dukkha is indeed a complicated concept. Dukkha is defined as the five clinging-aggregates. The five clinging-aggregates are clinging to form, clinging to feeling, clinging to perception, clinging to mental formations, clinging to consciousness. The five aggregates have further explanations and definitions. Clinging too is well-defined in Buddhism. Therefore Dukkha is well-defined.
I do not believe, that everyone, or anyone, will understand the five clinging-aggregates upon first reading them. This, however, does not mean that they are not well defined. Religious language is often imprecise, but is not necessarily so.
Scientific principles can be applied to Buddhism
"Effectively, your argument is that because a religious belief is falsifiable that makes it compatible with science."
No, this is not what I propose. My proposition is that since the theory that the Path leads to the cessation of Dukkha is 1) falsifiable, and 2) experimentally testable, it is compatible with science.
"The Eightfold Path (the pursuit) is a subjective process of emotional development rather than an objective scientific one"
Your rejection of my argument is akin to saying that the claim that a drug cures depression isn't objective and scientific because the drug initiates a subjective process. The pursuit involves a process of emotional development, that is true. But the claim that the pursuit develops the mind emotionally in a specific way (towards less Dukkha) is objective and scientific.
How to measure Dukkha
"You openly acknowledge that Dukkha is observable as a first person experience, and yet again make not even the slightest allusion to any scientific means of observation."
Scientific means of observation can be based upon subjective data. I can sensibly answer whether it hurts to cut myself with a knife without relying on third-person neuroscientific methods. It is sufficient to observe what first person, subjective data shows. Equally, Dukkha is a mental phenomenon so I can sensibly answer questions about it by relying on first person experience.
You would probably counter that subjective measurements of this type are inherently unreliable and thus unscientific. You would be right in expressing this doubt, as indeed Buddhism admits that there is a problem here. The solution to the problem is meditation and concentration. Buddhism borrowed and further developed methods from Hinduism that allows one to still the mind so that it's easier to investigate the nature of the mind. This exactly is what makes these first person measurements reliable; the measurements are made accurate by first cultivating certain mind states that allow for greater (converging on perfect) clarity of perception.
Ending remarks
I think your critique of the vagueness and impreciseness of religious language is your strongest point. If you don't think I have answered your doubts I will gladly elaborate.
I am sometimes too thick to accept a disapproving argument. I can simply ignore it by assuming what is being said is stupid, or engage in sophistry which helps no one, certainly not myself. A downvote though, that's not so easy to reject. If I know someone disapproves of me, but I don't know why, I start to wonder. It makes me self-analytical, making me more likely to discover why I am wrong.
Specifically the claim that you can't prove a negative is outrageous because it implies that you can't prove anything about the material world.
Let's say that you want to prove the non-existence of a bananas in your apartment. In order to prove it you would have to check each and every part of your apartment. Let's say you haven't found a banana after looking everywhere. Have you proved that there are no bananas in your apartment? Now let's say I don't believe it's possible to prove a negative existence claim, and I ask you a question that puts doubt into your conclusion. For instance I could ask "but what if someone placed a banana somewhere in your apartment after you checked that spot?"
Notice that I can always ask questions like this. Theists say but maybe you haven't found God because you haven't looked at the world the right way right yet". Now when people say that you can't prove a negative, this is the reason why. They think you can't prove a negative, just because you can ask skeptical questions, just because you can doubt the conclusion.
But let's say that you want to prove the existence of water in your apartment. In order to do that you take a glass and fill it up with tap water, and there you go. You have proved a positive existence claim. But notice that for the very same reason that you (alledgedly) can't prove a negative, you haven't proved your positive claim either. I could ask, "but what if it isn't water?", "how do you know it's not something that just looks like water". Clearly, if negative existence can be refuted just because you can ask skeptical questions, then so can positive for the very same reason.
But this extends to all synthetic claims. For instance, let's say that you are happy and you express this feeling. I could then ask "but how do you know that you aren't just deluding yourself?". To return to my initial post. The problem is that all synthetic claims rely on inductive reasoning and inductive reasoning isn't 100% certain. Therefore there's always* room for doubt. So when I tell you that "you can't know that a banana didn't magically appear somewhere you already looked", all I am really saying is that "I am going to ignore your overwhelming amount of evidence, and still believe what I want."
I guess this is why atheists get pissed off at theists. There's a overwhelmingly good reason to say that there's no reason to believe in the existence of God(s). Theists however want to maintain their position and so they retort: "but, but, but you can't know that God isn't a magical banana that appears everywhere you aren't looking."
It's pretty easy to define negative and positive existence claims (e.g. there exists a chair is a positive existence claim, there exists no God is a negative existence claim), but given that we aren't talking about existence claims , I think the problem lies in the inherent ambigiousness of defining what a positive claim is.
Is the claim that "my middle name is not Nebeling" a positive claim? That statement appears to affirm 'positively' that my middle name has some property, and thus it must be a positive claim. I guess, given your response, that you agree. Equivalently, the statement that "it is not the case that my middle name is Nebeling" might be a candidate for a negative claim; I take it again that you agree? But if that indeed is a negative claim we are in deep trouble because then we have constructed two logically equivalent claims where one is positive and one is negative, hence making the distinction meaningless.
In order to make sense, any sentence logically equivalent to a positive statement must also be positive. This appears to not be the case and therefore I don't think the term is useful at all (at least when we aren't talking about existence claim in which case we may argue that they do make sense).
I think the statement comes from the fact that you can't prove the non-existence of something. That is, you can't prove a negative existence claim. (This again is a pretty outrageous claim, assuming which we end up saying that we can't prove any synthetic claims).
Opening argument
I will argue that this claim is wrong by showing that scientific principles can be applied to religion. I believe this shows that science and religion are not incompatible.
The structure of the argument is as follows: I will prove the existence of what we may naively call a 'religious science'. This religious science need to meet some criteria in order to show that science and religion are compatible. First of, this religious science must have something that is legimately religious as its goal. And secondly, the pursuit of this goal must be guided by scientific principles. If it can be showed that there exists a pursuit which satisfies both criteria, then the argument is over. I will now show that a particular pursuit within the Buddhist tradition is both religious and scientific.
A religious pursuit
For the sake of argument I will assume that Buddhism indeed is a religion. The Buddha is known to have said that he has "taught one thing and one thing only, dukkha and the cessation of dukkha". Since Buddhism is a religion, its most central pursuit should be considered religious, i.e. the pursuit of ending dukkha is religious. Therefore I will define the pursuit of the 'religious science' to be the cessation of dukkha. Since this pursuit is legimately religious, the first part of the argument is over.
The pursuit is scientific
I will now show that the scientific method can be applied to the cessation of Dukkha. In Buddhism, Dukkha has a very specialized meaning. The term is well defined, and therefore the concept of it's cessation too is well defined. Furthermore since Dukkha is a phenomenon of the mind, Dukkha is directly observable through first person experience. Therefore Dukkha can be measured. The Buddha gave a framework for ending Dukkha which is known as the Noble Eightfold Path. The theory goes that if you practice the Noble Eightfold Path to perfection you will be free from Dukkha. Therefore we have both a question, "how does the cessation of Dukkha come about" and a theory, "the Noble Eightfold Path leads to the cessation of Dukkha".
There's one last requirement that must be met before this pursuit can be considered scientific. The theory must be falsifiable. Falsifiability of a theory is the property that the theory can be proved wrong by experimentation. Therefore is must be possible (in principle) to prove that the Noble Eightfold Path doesn't lead the cessation of Dukkha. This is indeed possible. The 8 parts of the Noble Eightfold Path are testable. The Path asks us to live in a very specific way; talk a specific way, think a specific way, meditate a specific way, so forth and so on. Because the Path puts forth specific principles to live by, it is possible to put the Noble Eightfold Path into practice. Because it's possible to put into practice it is possible to test if being on the Path diminishes the amount of Dukkha one is experiencing. In other words, the question of ending Dukkha is a religious science.
Conclusion
Dukkha is observable through first person experience. Therefore, if the Path is a true theory one should experience a dimmishing amount of Dukkha while being on the Path. The theory is thus falsifiable for two reasons. We can 'measure' how much Dukkha we are experiencing, and we can see how Dukkha is affected by being on the Path. Therefore the legimately religious pursuit of ending Dukkha can be approached scientifically. Therefore a 'religious science' exists. Therefore science and religion are not incompatible.
Of course you can prove a negative. For example. I am sitting on a chair right now. Therefore I have proved that it is not the case that I am not sitting in a chair.
To say that you can't prove a negative is mainstream pseudo-logic. Actually, the statement you can't prove a negative, is in and of itself a negative, so if you could prove it you would automatically have proven yourself wrong.
The problem I think that's being hinted isn't that you can't prove a negative, but that inductive proofs aren't certain. For instance, all life we know of is carbon based, therefore if we were to discover a new life form, it will probably be carbon based. This is an inductive proof. It's the same with proving that God doesn't exist. An anti-theist would say that there's no evidence for the existence of God, therefore we are likely never to find evidence for the existence of God. (This is the induction part). If God existed, he would leave evidence of his existence. (This is a commonly used premise). Therefore God probably does not exist.
