The curious thing to me about the cogito, which is somewhat inferred in my answer, is the observation that our senses can be deceived. Firstly, doesn't that presuppose that we know something, that reality can differ from our perception? But more importantly, I question why this deception disproves all but the mind's existence. In the case of a mirage, for instance, even if there is no oasis, there's still something producing the illusion of the oasis. So it seems to me that, while we can't know if what our senses are producing are the reality or an illusion, we can at least be sure that there is something eluding us (I think that's the wrong word but oh well).

But consider the idea that our experience might be illusory, that is, everything we know about the world we live in isn't reality proper (for example a hologram or mischievous devil or whatnot). Does that mean we don't know anything, what we experience is false or that nothing truly does exist besides our minds? I don't think so. Even if that's all true, I think that the very fact that we experience the illusion makes the illusion as real as any other reality. I'll suffice to say that it's because existence isn't isolated to one notion of ultimate reality, but baked into the relationships between things. So the very fact that there is an illusion I experience makes us "real".

That's kind of a mouthful, so I'll stop before my reasoning becomes (more?) convoluted.

I'm a little confused by the question because to me, the only truths we can know most absolutely are those immediate to our human experience. For example, the most fundamental truth I can tell is that "I exist", and not in a cogito way, but because of my sense experience. Whether or not the stimulus I perceive is what it really is, the very fact that I feel something is what brings me into existence. Not only that, but I can know that the stimulus I perceive also exists, again, even if it's not the "true nature" of the stimulus, like a mirage. The last observation I'll add to this line of thought is that there is a relationship between me and the stimulus, and that "things are related" is another fundamental truth that I build my philosophy off of.

This is different from what you seem to be proposing, that our scientific knowledge of things external to our experience should form our most basic beliefs, but it's strange to me because there's so much to presuppose before admitting scientific facts. However, I do also agree that, if we take for granted our general experience and knowledge and such, we can construct truths that seem fundamental to the universe, beyond ourselves. Here are mine:

1. There is a reality (as shown by the reasoning above).
2. Reality is composed of relationships. That is to say, things exist in relation to other things, but the "things" are not fundamental necessarily, only the relations.
3. As such, there cannot be one thing.
4. I exist in a reality, hence other things exist too. I know this because the experiences I feel are the relationship that unite me with other things.
5. And more pragmatically, I feel emotion, most fundamentally the axis of good vs bad, things I desire vs things I avoid.

I am unsure of anything else I feel I know as absolutely. But there are many things I believe that, in conjunction with these truths, build the basis for a lot of my philosophy.

Actually, the Hindus about 628 introduced negative numbers to represent debts. Positive numbers represented assets. Euler, in the latter half of the 18th century still believed negative numbers were greater than infinity.

(I can't wait to see all the action when you guys move on to FRACTIONS :scream: ) — jgill

That Euler and other great mathematicians thought such things was the whole point of this thread in the first place. Is there no insight to be gained by understanding why the idea of a negative eluded such minds for so long? Also, although the rationals contain the integers, fractions are simpler as a concept, just given that they've a far longer history in mathematics. So this fraction meme you guys are doing is backwards.

Can I ask you where you got this from? I know Euler played fast and loose with infinite series, but I can only find this bit about negative numbers mentioned on an obscure Wikipedia comments page. Since Euler is one of the greatest minds mathematics has ever seen, this seems like an odd mistake. — Real Gone Cat

I forget whether or not it was Euler who made that claim, but mathematicians also argued against them in terms of ratios. It seemed ridiculous to them that the ratio of a greater to a lesser (1 : -1) could be the same as a lesser to a greater (-1 : 1). I can't precisely pinpoint the mistake being made there, though there obviously is one.

As someone mentioned elsewhere, negative numbers are typically built within set theory as equivalence classes of pairs of natural numbers, so they are very much one level up.

So -2 := { (2,4), (3,5), (4,6),...}.

It's also possible to declare that every number in a given system has an additive inverse. — Pie

For me, these kind of constructions raise a lot of questions about the sort of ontology of mathematical objects. That certain entities are "prior" to others in these formalisms, does it have any meaning to how we view physical reality? Like how magnitudes (positive numbers) are natural, but signed values seem synthetic. Also:

It's not that Euler was stupid, but maybe the reverse. — Pie

:up: Had Euler really never heard of debt before? And would our examples of holes and sea level and temperature convince him otherwise?

I want to focus on one particular aspect of this discussion, which is the matter of "context" required when manifesting negatives in nature. At first, I found it odd that positive numbers seem natural and automatic in our thinking, but when we consider negatives we have to construct these contexts (like debt) which allow negatives to exist.

However, as noted, it could also be the case that positive numbers also do operate within a context, just a more invisible one. What I want to consider is that there are actually two different mathematical concepts that are being conflated when we look at the nature of positive numbers. And it is that of magnitude and signedness.

My claim is that when we do ordinary math like counting, we aren't actually operating on "positive" numbers per se, but rather unsigned numbers, or magnitudes. And that is the context we operate in normally, that of magnitude. However, when we want to consider negative values, we introduce a new context, that of signedness, and this is the "weird" context that makes negative numbers seem one step removed from unsigned numbers.

Of course, when we do math, we don't really make such distinctions between unsigned or signed numbers: numbers are always signed, and so, distinct from their oppositely signed counterparts. That is to say -1 isn't 1 with - sign, -1 is a completely distinct entity from +1. What I wonder then, is if there's any merit to make such distinctions, perhaps from a philosophical perspective. Clearly, the math works out and doesn't care about our intuitions. But if we can get a finer grasp on the nature of such entities, it could inform our philosophical considerations.

As for multiplying by a negative, it's not hard to find examples. — Banno

My point isn't quite that there aren't applications of multiplying by a negative, physics has it all over the place, and computer programs can also make use of them heavily. My point is more so about how some of the intuitions of the rules don't match the applications. Yes, we can interpret (-5) * (-1) as a "$5 debt" being "lost", hence $5 credit, and that rule gives us the correct value, but it doesn't match the usual "flipping" interpretation of multiplying by a negative. Furthermore, that "flipping" interpretation of a negative doesn't occur in the other usual examples of temperature, sea level, height of dirt as describes.

The point is that we are using sloppy intuition to justify the rules of negatives, intuition that clearly didn't convince mathematicians of the past, and perhaps there's some value in recognizing that.

Think of 2 representing the height of a mound of dirt and -2 representing the depth of a hole beside it. — Pie

This is an example of introducing context to make sense of negatives, which I described here:

The main difference I perceive is that negative numbers require a context within which to function, unlike positive amounts which I seem to be able to measure or count in any situation. . .I think that this required context does make negative numbers at least seem one step removed from the naturalness of the positives. — Jerry

Now it could be the case that regular counting has its own context, which I feel is eluded to indirectly by , although I don't yet understand the meaning of the quotes they provided. To quickly reiterate, it's not that I think negative numbers can't refer to things in nature, it just seems like extra steps are needed to make them make sense, which makes them somewhat different from positive numbers.

Disappointing we seem to have a stalemate so soon. I feel like I've sufficiently expressed the "exceptionalism" of humanity, not just in relation to other animals, but with regards to our place and size in the universe.

Notice, I'm not saying we're "cool" or "important" or even that what we do "matters" to anything but ourselves. Rather I'm saying that we're exceptional, meaning we're unusual, bizarre, and so far removed from all else around us. The former assign value to our actions, while the latter is an observation (removing the connotations that come from a word like "bizarre").

Let me try to clarify the discussion thus far in an argumentative form:
1. I claim there is a "strange discrepancy", an exceptionalism to humans, and this (may) imply some creator (I didn't really explain why that's the case though)
2. You say the discrepancy isn't that great (we've barely left solar system and such), and that it only seems significant because we're impressed with ourselves. So my claim is not true, and therefore the argument doesn't hold.
3. I counter that our "significance" (but more accurately, our exceptionalism) is justified by describing how our influence is greater than you think. Namely:

We may not have literally left the galaxy, say, but we've spanned the entire breadth of the universe of what we can observe; once again, we have pictured the universe and can film atoms. We're able to model the very fabric of reality itself, large and small. — Jerry

4. You respond with a few more thoughts, saying that what we do "isn't that big a deal", of all the organisms in the world, "humanity is just one more", and that "we're important because we think we're important". However, I don't think you've really addressed the claims I had made in the previous point, which are precisely the reasons I do think these last claims aren't entirely accurate.

To offer a different perspective, that there's only one intelligent species (humans) suggests an antonymous, dark(er), reality - is intelligence becoming extinct? Are brains,, ergo, intelligence/sentience/consciousness going out of fashion? — TheMadFool

Tossing aside the creator talk for a second, I would offer that one reason there may only be one overtly intelligent species is because once there is one, it becomes so intelligent so quick that there's almost no room/time for another. Rather than intelligence becoming extinct, it's in its infancy, where no other intelligence has had the time to reach an equivalent. But similarly to your concern, it may also be the case that once intelligence reaches a certain level, it becomes destructive, similar to how we're destroying our own environment and putting ourselves at constant danger of nuclear weaponry and such things. That would mean intelligence does become extinct rather quickly, and is never able to flourish. Pessimism wins again.

Thanks for the compliment.

The things humanity has done may have had more of an impact on the planet than most other organisms, but what we have accomplished only seems significant to our own self-fascinated eyes. — T Clark

You know, I think I have to disagree here. I think that there is, in some either cosmic or objective sense, something significant about what we're able to do. We may not have literally left the galaxy, say, but we've spanned the entire breadth of the universe of what we can observe; once again, we have pictured the universe and can film atoms. We're able to model the very fabric of reality itself, large and small. And these are the results of a random ape-ish species of life on a medium-to-small-sized planet designed for semi-intelligent organisms to eat, sleep, and die.

Ultimately, we have no reference other than ourselves to claim what's significant and what isn't, but I think we can at least say that humans are beyond exceptional, specifically given how our prowess extends to the very edges of all there is. Hm, seems like I'm just reiterating at this point, but what I would like to hear is a little more on how either we aren't exceptional (some more argumentation against the claims I've made or support for your own) or, even if we are exceptional, some argumentation against why that would entail a creator.

@TheMadFool
Interesting that you would say a burden of proof falls on an agnostic. I don't think by the standard understanding of the burden of proof you would have to account for a position of agnosticism, as you would not be making any claim either way about a proposition. However, I do sympathize and agree with you that you should be able to explain your position regardless.

@Bitter Crank

I don't find a difference in these two formulations....

Well, to make the difference a little more clear, I'll point out that "I lack belief that some god exists" is the same as saying "I do not believe that some god exists". Oh, also "some god exists" is the same as "god(s) exist". So the two statements become:

"I do not believe that some god exists"
"I believe that no god exists"
Notice that "no god exists" is the negation of "some god exists".

These are actually not the same. I'm gonna use "the gumball example". Excuse me if you know of this example and reject it, or that you think it doesn't apply. Anyway, it goes:

You have a jar of gumballs. You know the number of gumballs is either even or odd. The question is, "do you believe there are an even number of gumballs"? You would say:

"I do not believe that there are an even number of gumballs" (because there is an equally likely chance that there are an odd number)

Is this the same as saying "I believe that there are an odd number of gumballs"? No, because you also wouldn't believe that there are an odd number of gumballs, for the same reason you didn't believe the number was even.

What you are saying then is "I do not believe that there are an even number of gumballs" and "I do not believe that there are an odd number of gumballs". You don't believe either because, in this case, the possibility is equal, and you can't have a good degree of certainty either way.

That's also my position on the existence of gods, which I use agnosticism to mean, which is also a common use case of agnosticism.

Oh, and you are right, I don't know whether a god exists or not, although most atheists don't claim to know either.

Oh, I just realized I didn't describe what I mean when I say I'm agnostic.

Simply, I do not believe that no gods exist and I do not believe that some god exists.

Numbers can carry information that is both passive (like a newsreport) and active (like a software program). — TheMadFool

I would really like to hear more on what you mean by numbers being passive and active. I'm currently struggling to get my thoughts together on this, but I think we might have very similar views.