@Corvidae and how to choose your axioms: So we have to be very careful here to define our terms and proceed in small steps, because "axioms" when applied to cultural outcomes like ethics is tends to generate strong opinions and is heavily beset with historical baggage.

First off, why do we consider science to be "unable to choose it's own axioms?" The axioms that science uses are things like the reality of space and time, the meaningfulness of zero and infinity, and the presumption that the stronger the consensus by independent observers, the closer to an objective truth. Science itself, however, cant test any of these as hypotheses, and cant even define most of them without making tautological assumptions (math itself is tautological). As someone mentioned, Godel's theorem applies, in the sense that no computational system can comprehensively model itself.

But when we say that philosophy, religion or art can systematically examine and select their own axioms, we obviously aren't talking about testing them as hypotheses (that would be science again). So, by definition, no system of thought can test it's own axioms in a scientifically rigorous manner. They do so in their own manner.

Within philosophy, the source of basic axioms is introspective self-reflection. "I think, therefore I am". The "I" and the "think" in that statement are drawn from the philosopher's own internal experience. They can be thought of as consistent patterns across multiple qualia. As Kant pointed out, experiences such as space and time are inherent in all conscious human beings- no one has to be taught these things, nor could they be taught these things if one lacked them. We possess them prior to all cognitive analysis.

With respect to ethics, basic axioms are things like "personal survival is desirable" and "individuals owe obligations to their communities". We appear to have a number of these axioms, and although they are taught at a very young age, they are near universal (even though the details vary) and rarely questioned outside of academia.

"Self-Interest" is practically undefinable, except as a perceived pattern across various qualia (observable only via internal self-reflection). These "quale-patterns" can be defined as perceptions which are the things themselves. When you see a chair, you are only experiencing an internal simulation of an objective chair, the reality of which is outside any one observer. But the experience of time is time, the thing itself. If an object didn't experience the passage of time, it would cease to change and become timeless, even if everything around it continued as before (this is in accordance with physics, and is supposed to be the case with photons). Likewise, the subective experience of "self-interest" is self-interest, the thing itself, and there is no objectively real "self-interest" outside the person experiencing it. In other posts I've termed this kind of thing "subjectively real" and made the claim that all ethics and morality are of this nature.

In any case, the answer to your question is "You derive your axioms from consistent patterns you perceive across your qualia". The metaphysical implications of this are that since everyone's internal perceptions are at least somewhat unique, subjective reality is different for every person. No two people experience time in the same way, nor social obligations.

Nevertheless, despite the fact that we cant test these things in any objective way, we can still share them, using the indirect medium of language. When we do, we discover that very large numbers of people apparently share very similar subjective perceptions. We can then use these apparently shared perceptions as the basis of the axioms of a philosophical approach.

I'm sure you can see the implications of this for something like a religion.

I think there’s a global conspiracy to see who can get the most clicks on the worst lies

Math is not of course entirely tautological. First, axioms are not tautological. They are assumptions. As they might be false (from one perspective), they cannot be tautologies. (from another perspective, some axioms can't be false, because they select their theories.)

Second, tautologies are useless statements. As they are trivially true, they provide no useful information. So they are usually avoided in serious mathematical work.

Except for deduction rules. I think these technically count as tautologies. Deduction makes up the vast bulk of the work of mathematics. In fact, I think I heard that any system of deduction is a math.

The first half of that seems self-evident. But I don't think the second half is true. A person who knows not time I suspect can't be taught anything, so I suspect that is true on a technicality. But space is not a necessary concept for life, and also a very easy concept to explain.

I recognise neither of those axioms. As they are not part of my ethical theory, I don't think they are basic axioms.

Here are some examples of basic axioms: "Something is desirable," "Choice is possible."

What do you mean? Concern for oneself seems one of the simplest concepts to nail down. That is when one person decides to do something for themselves.

edited 23rd Dec '16 10:10:43 PM by war877

What is or what would be that 'something'?

The axiom here is that there is at least one thing that is desirable. Possibly an outcome. If nothing is desirable, I can think of no reason to claim morality exists. What purpose would morality serve in that case?

edited 24th Dec '16 9:54:07 AM by war877

I've watched a documentary on a native Brazilian tribe that doesn't know the concept of time, I think? Google gave me an article talking about such a tribe, except it wasn't the one I was thinking about. This is the one I was thinking about. Google actually found me a BBC article about another tribe. Well, I suppose you could find it yourselves @_@

@war877: but what's your optimization problem specifically? What are you maximizing/minimizing?

What if your desire is to desire nothing?

I suppose a tautology could be useful in proving equalities or the validity of a proposition. "A = B is true if and only if (a series of propositions that result in) 0 = 0." Although depending on how you build it, it might not be constructive.

edited 24th Dec '16 10:40:03 AM by Victin

Through my own explorations, I was able to establish only that morality is a problem of optimisation. I was not able to narrow it down completely.

Yes. I have considered that. It is sufficient to say morality exists. Buddhists I believe quest for this mental state in some schools.

This is an example of a deduction rule. I think it is also a tautology:

x=e^{ln x}

EDIT: I'm an idiot. My brain immediately ran through exceptions to the above rule.

edited 24th Dec '16 11:55:36 AM by war877

I don't think that it is possible to define moral axioms in objective terms, because morality is inherently a "should/ought" statement projected onto a universe of "is".

Are we having a debate over what constitutes an irreducible moral axiom? I'm afraid that all this abstract logical terminology is obscuring the discussion rather than moving it forward.

edited 24th Dec '16 5:16:11 PM by Fighteer

"It's Occam's Shuriken! If the answer is elusive, never rule out ninjas!"

@War: No, of course axioms are not themselves tautologies, but basic math is. 2 + 2 = 4 is a tautology, "2 + 2" and "4" being just two different ways of saying the same thing. The reason this isnt useless is because you can make quite complex tautologies with many interacting parts. Interestingly, only the tautological equations in math are considered correct! (if the two side of the equation dont equal each other, it's wrong).

If you didn't possess a sense of spacial perception in the first place, no one could teach you to sense it. That would be like restoring hearing to the deaf by explaining to them what sound waves are.

"Something is desirable," "Choice is possible." I believe that desiring something, or perceiving a choice, insofar as experiencing them internally is concerned, are qualia, and not patterns across several qualia, and therefore are not axioms as I defined them. Of course, you may feel free to disagree with my definition.

"Self-Interest" is not just concern for oneself, it's defining some specific state of being as being desirable for oneself. The question is how do you logically justify that? What logical basis is there for preferring, say, existence to nonexistence, or happiness over sadness? Of course no one chooses preferences of that kind via any kind of analysis, you feel the desirability internally as a sensation. That's effectively an axiom providing the basis for a philosophical statement that could assess the implications of desiring one thing over another. The point is you can't justify the avoidance of pain as a preference, you just accept it as a condition of being.

@Victin: I'm not familiar with the Brazilian tribe in question, but while they may not have a concept for time in their language, I am certain that they experience change over time, since otherwise they would be frozen in place.

"I suppose a tautology could be useful in proving equalities or the validity of a proposition. "A = B is true if and only if (a series of propositions that result in) 0 = 0." Although depending on how you build it, it might not be constructive."

You seem unaware that statements like the one you just made are the basis of all mathematical equations. Proving equalities is exactly what math does.

edited 25th Dec '16 5:03:41 PM by DeMarquis

I think there’s a global conspiracy to see who can get the most clicks on the worst lies

@De Marquis: In my post I was regarding methods of proof that are generally used, like proof by contrapositive, proof by contradiction, proof by finite/transfinite induction, etc. I'm thinking in terms of what tools you could use in general when tackling an unspecific problem. That most of the time you're showing certain statements are tautological would be, well, useless and redundant (EDIT: because it'd be as if "How do I prove proposition A?" "Well, you just need to show that A is true.").

I'm studying Applied Mathematics in college although I have yet to take any logic courses. I was remembering one or two times a colleague came to me "I was trying to prove a certain proposition A, but instead I just found '0 = 0'." "Well, if you just proved A is equivalent to '0 = 0', then you just proved A is true." "... Ooooo OOOOOHHH." Probably in Algebra I @_@

edited 25th Dec '16 6:26:07 PM by Victin

I did some research between the last time we had this conversation and this time. A tautology is a statement that is true for all possible values of its variables. 2+2=4 is a statement with no variables. Technically this makes it a degenerate tautology (assuming it is true). But this is never what people are talking about when they say tautology.

You are correct that only true equations are considered correct. However, do not forget the inequalities either. For example 2+2>3. There are more than equations in math. Sets, and mappings for example.

If you were talking about how colour is perceived, I'd concede the point. But what does space feel like?

You believe that choice and desire are only experienced internally. This is fine in terms of these basic axioms, namely that choice and desire both exists. They hold so long as they exist. The nature of their experience is not important.

The definition of an axiom is simple. An axiom is an assumption that we assume is true. If we try to defend it, it becomes a derived principle. The defence we used will contain our actual axioms. (the existence of empirical evidence throws a wrench in here. It is neither an axiom or a derived principle, but may be part of our defence.)

The self interest you define is different than mine. Which I define purely in the behavioural sense. As far as ethics is concerned, I think that whether a person experienced desiring one state over another is relevant, but I call it purely desire. Self interest is a funny name for it in my opinion.

But yes. Desires are illogical. Or, to put it the other way, there is no outside reason for desire. However. No desire, no morality, as far as I can tell.

You have to be careful with that. If you substitute an equation into itself, you often arrive at 0=0, but end up demonstrating only that you didn't divide by zero. (as if you do that, you can get 0=1).

Which is I worded it as "I suppose a tautology could be..." It's not like a single tool can solve everything, and it can't even solve a problem it's good for if you don't know how to use it I don't think I've used it since that one time, I was just reminded of it by the discussion.

I do have to agree that the axiom "something is desirable" is necessary, and that there's no outside (logical) reason for it. I mean, without desire, there is no such thing as better or worse, and thus one wouldn't even be able to argue in favor of a logical reason for desire over an illogical reason, because there'd be no preference.

Axioms can mean different things in different cases. If the axiom is tied to a concrete thing then it could of course be wrong. The logic that follows if it is true remains the same however. The logic isn't a fundamental part of the universe in some cases it can be relevant to us or some other intelligent live as it allows us to think abstracting.

Another thing is humans are born already in motion. We don't start as empty ghost deciding what to do with our lives. A empty ghost wouldn't do anything. Our brains are wired to do things and see things in a certain way and any decision we make on what to do is base on that and any logic will matter to us only base on that.

The logic of how we decide to what to do with out lives, and how to push it father is what ends up mattering to do us. We will never become paper clip maximizers unless it helps us progress what we are born doing.

When life gives you lemons, burn life's house down with the lemons.

This post was thumped by the Shillelagh of Whackingness

Nvm. I don't understand why it was thumped.

Ah, ok.

edited 8th Jan '17 6:14:08 PM by Quag15

That's a self-thump, just to be clear.

Quod gratis asseritur, gratis negatur.

To make sure what I said above is understood.

Concrete logic, saying that if Apple A is blue then B must be red. you can that seeing that isn't the case just by looking.

Abstract logic, using axioms to define a notion, follow the reasoning and seen what works like the abstraction. The axioms for number aren't assumptions about something that exist but rather define something that may have an instance in reality.

if we have three apples and the axioms of number apply to them then when we remove on we will have two, we can then test that and the result. Do this enough times and you can safely say that apples work like numbers and you can think about numbers without having to talk about anything in particular

When life gives you lemons, burn life's house down with the lemons.

<throws obvious spanner into the analogue> Red-green colour blindness. Even if one apple has been painted blue, for some people... the other is going to be a weird taupe other people call two different things. Let alone the people who have to take it on faith that the first apple is blue, because they've got blue-yellow issues. "Just looking" to anchor concepts isn't always available, even if guessing using other cues might be (a sticky, tacky apple is probably a painted apple: other people are uncomfortable around it or amused by it, ergo it's unlikely to be painted yellow... that's as sure as I'm going to get without asking — crossed fingers they aren't all gaslighting me).

No, I'm not just spiking your wheel for fun: the problem with axioms is... they are derived usually from the collected perspective of the middle of the population bellcurve. But, the other ends issue a warning: perception is not reality. Even if an axiom works most of the time because its yet to have something it won't work in applied to it... it doesn't mean it always will.

Murphy's Law breathes Outside Context.

edited 10th Jan '17 2:56:34 AM by Euodiachloris

I feel we aren't digging deep enough. An axiom is something held true without evidence. If we support the axiom, then the axiom becomes a conclusion for an argument. The premises of the argument are the support.

If the support includes observational evidence, then it is the observational evidence we are taking on faith, not the conclusion we draw from the observational evidence. That we take as a derivative.

In such a case, the axiom is the interpretation or reliability of the observation.

Wait, what? An axiom is where you start an argument, not end one. Axioms must be assumed and cannot be proven, because axioms (and logic) are what you use to prove conclusions.

As an example, let's say your argument takes the form

1. if A is true, then B is true
2. A is true
3. therefore, B is true.

"If A then B" and "A" are your axioms (they're assumed to be true without evidence for the purpose of the argument) and "B" is your conclusion.

Arguments like this can be valid, true, and/or sound. An argument is valid if its logic follows, it's true if its conclusion is correct, and it's sound if it's both valid and true.

eg

• all fruit is blue, apples are a fruit, therefore apples are blue is valid (but not true or sound)
• all fruit is red, apples are a fruit, therefore apples are red is true (but not valid or sound)
• all humans are mortal, I am human, therefore I am mortal is sound (both valid and true)

And that's formal logic vocab 101.

edited 10th Jan '17 12:55:28 PM by NativeJovian

Really from Jupiter, but not an alien.

An argument is true if and only if it is sound. It is sound only if the premises are true and it is valid.

You should indicate who your post is in reply to. Because I can't tell.

edited 10th Jan '17 2:49:00 PM by war877

I was replying to you because of your use of the word "axiom".

And I actually got true/valid/sound a little confused. True applies to axioms (they're assumed for the sake of argument, but they're only true if they accurately reflect reality), valid applies to logic (it's valid if it follows, invalid if it doesn't), and "sound" applies to arguments as a whole (arguments are sound when they have true axioms and valid logic).

Really from Jupiter, but not an alien.

basically what abstract reasoning is that you can use axioms about a concept like for say "numbers" and then at another point in time replace "numbers" with "apples" and see if the axioms of "numbers" apply to apples as well.

this means that if we remove an apple from a group and three and end up with 4 or some other answer other than three then it doesn't mean were wrong about numbers(most of the time) but rather that apples don't work like numbers

A lot a problem in philosophy are due to thinking too much about the abstract. An abstract concept only matters if there is a concrete thing that work like that concept. It is kind of like a trying to explain what red is to someone by saying it's a color rather then pointing at a fire trunk, pointing at a stop sign, and maybe pointing at blood and saying that these things are all red.

When life gives you lemons, burn life's house down with the lemons.

On the other hand, find an abstract concept that cannot be applied in real life and does not contain the word infinity.

Outside of religious belief, I don't think there are any.

There's something here that sounds too limiting, but I can't quite pinpoint why...

Ok, how to do you prove it is 'true'? Because the condition that supposedly makes it true seems to be a bit limiting, since it doesn't account for a priori judgements nor the distinction between analytic and synthetic (which remains an open question).

edited 11th Jan '17 1:42:12 AM by Quag15

tldr: science.

Really from Jupiter, but not an alien.