The philosophy thread general discussion

I disagree; truth has no relation to how useful it is. Truth is just there on its own. Usefulness is relative to the user. I would say knowledge is more crafted for usefulness.

That itself is an opinion. One that I disagree with.

It looks like you're saying that differing opinions imply that the subject matter is subjective. To an objectivist it means something else. An opinion is a person's idea of what that truth would be.

Generally, when one uses an argument favoring God, one would say that such a God would have an omni-objective point of view. So God's point of view is consistent with the absolute truth.

I suppose I can formulate it like this. People that do not think morality is objective would probably say morality is invented. By contrast, moral objectivists like me would say morality is discovered.

That's my way of dodging the post-modernist issue of "Well, our perceptions are our only way of comprehending the universe, thus, how can we trust anything?" (To grossly simplify it.) Also, I don't necessarily believe the human mind/any mind is capable of comprehending the "truth" of the universe. When you get down to it, we have to grossly simplify things, put them into mathematical language, bastardize and warp concepts that we have no reference point to, create crude analogies for concepts that simply "are." It's one of those things hard to talk about, because all I have in language, and language does a poor job expressing things we barely have a reference point for.

So I define truth as "what's useful" because, to simplify things, and to get around the issue of our senses/innate limitations giving us a terribly limited understanding of the underlying concepts of the universe we take for granted, and the horribly nuanced interactions of things (atoms, molecules energy) which are almost abstractions, even to people who have spent decades studying them, it's easier to accept truth as merely the gross simplifications of higher concepts, that we accept because without, we have no constituency, no references in our life.

And the problem is this sort of truth is functionally irrelevant to the average person, because unless it's your field of study, you aren't so much affected by it as naturally accept it, because you never question what the hell anything would be like if that "truth" didn't exist. You don't know why certain atoms bond, or how quarks interact, and it doesn't matter, because they're always going to interact like that.

Jesus. This is hard to explain. And I sound a little like a pretentious asshole. It's just most of what is literally "true" is so very alien to us. (and I mean alien in the Lovecraftian, Eldritch Abomination "you cannot grasp it's true nature" sense)

edited 6th Feb '13 8:02:47 PM by DrTentacles

Ok, I think I get what you're saying: that we describe what we believe to be true in a language that we can understand.

The impression I get from those who subscribe to moral relativism is that they place ridiculously high standards on the reasoning to begin with. It seems that the reasoning is often rejected precisely because it derives ought from is, even though that was the point. Moral objectivists are asked to defend their views with a successful is-ought argument, and then in the same breath, all possible is-ought arguments are categorically dismissed on the basis that 'you just can't'.

On the contrary, just because we aren't omniscient doesn't mean we can't or don't know some things as they are in the real world. And things can exist on different levels. A mathematician can get two apples and another two apples and put them together (getting four apples, of course) and say 'see, 2+2 is 4', and he'd be right. The fact that the apples are made of tiny wave/particles that behave in weird, counterintuitive ways we don't understand doesn't invalidate the fact that 2+2 actually does equal 4 and that the apples actually do represent that arithmetic truth. When you do the thing with the apples, the 2+2 = 4 logic actually happens; the component in your brain that handles 2+2 and the component of the Universe that handles how many apples there are do the same thing. They do it regardless of what other bizarre stuff might be going on.

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Some would say that people created abstract mathematical systems in which 2+2=4 because they can be used to model how certain physical objects, like apples, behave with respect to certain actions (like "putting apples together"). Imagine some intelligent being existing in a virtual reality and subject to the whims of some especially perverted AI that, whenever the being thinks of two pairs of objects, instantaneously destroys one of these pairs. Then I would guess that whatever mathematical system that entity would develop to try to make sense of his constantly shifting environment would not contain such a rule as 2+2=4.

Even assuming that some elementary arithmetics is instinctive and innate (after all, many animals are capable of counting, to a degree), the point stands that in the sensible universe there is no such thing as numbers or addition operations: these are either ideal objects in some abstract space of ideas (if one is a mathematical "platonist"), or mental constructions (if one is a constructivist), or purely arbitrary sets of "game rules" (if one is a formalist).

Philosophy of mathematics is quite entertaining, I think. Lately, I've been thinking that maybe the three classical "factions" of philosophy of mathematics (realism, constructivism and formalism) are not actually that incompatible. One could well agree with the formalists that a mathematical system is a purely arbitrary set of rules, and then agree with the constructivists that these rules and their consequences unfold as mental objects, and then agree with the platonists that the potential existence of these patterns and their consequences is entirely independent from the human mind — or from the existence of the physical world, for that matter.

edited 7th Feb '13 8:48:55 AM by Carciofus

But they seem to know where they are going, the ones who walk away from Omelas.

That's something that I've been trying to say a while.

Also, adding to my view on the "truth" there aren't truths. However, there is a truth. Everything is interrelated. Everything is intertwined. There is nothing exempt from cause and effect. Currently, scientists have been playing the role of the blind men to the elephant, uncovering little bits of a greater whole (which is the universe, and possibly beyond).

I've still yet to hear anything that makes me believe morality is anything but a human construct, however.

Given that the apples actually do consistently work that way, I would be inclined to say that we 'discovered' rather than 'created' the system. What we created was the model inside our minds, but the same logic was already out there in the Universe. For that matter, the whole point of the model was to implement that logic.

Well, of course the Universe has no words like 'number' or 'addition' to refer to those things. Nevertheless, the relationship that actually exists in the Universe between sets of 2 apples and sets of 4 apples is such that the logic which we refer to as 'numbers' and 'addition' is implemented.

A person adding 2 and 2 in their head and the apples being physically brought together are not the same thing, because there's a whole lot of other stuff going on in each case (ions racing around the brain, the change in gravitational potential energy of the apples, etc). But to the extent that each performs the 2+2 operation, they are the same.

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I personally think numbers are "real". They're part of the abstract truth, dealing with quantities.

Ah. Well, there's a difference between us. I don't believe in abstractions. Whatsoever.

I don't see how you would say that, considering that you just noted "there is a truth".

Yes, but the truth is purely physical. It's the energy and matter in the universe, and the way they interact. Abstractions are our way of imperfectly comprehending the truth, but they don't exist, or only exist in the sense that they're useful neurochemical interactions that we perceive as reality. (Thoughts.)

...No. Truth is the description of what is there (physical or otherwise). It's not energy/matter itself, it's the abstract condition of being correct, including about that energy/matter.

On a note, 2 + 2 = 4 is true, even before you apply it to any real objects like apples.

edited 7th Feb '13 12:47:06 PM by Trivialis

2+2=4 is meaningless, and thus, not true, in a vacuum, without real-world concepts to apply it to.

Applications have no bearing in math. It's not dependent on the universe. We could have a different universe (classical Newtonian) and math would still be true.

The meaning behind 2 + 2 = 4 is that quantity of 2 added to quantity of 2 equals quantity of 4. It does not require that you specify what you're talking about; it's like a variable.

It is universe depending, because otherwise, you're talking in tautologies.

I'm not sure what you mean by that; mathematical true statements are supposed to be tautologies in the first place.

Anyway I'm saying that truth is not a tangible object but a condition about the object.

In order for 2+2=4 to exist, it must be recorded or thought.

Which requires a mind or something..

Which requires a brain..

Which is matter and energy..

I'm saying that 2 + 2 = 4 is independent of whether a human thinks about it or not, and has been true (and applicable to nature, for instance) before a human being thought of it.

A thought can be without being thought.

The 'way they interact' is where you find abstractions. Sets of apples (and most other fruits, for that matter) interact in a way that implements the same logic as adding 2 and 2 in our minds.

But it is. The system of mathematics we use is the way it is because that's what best matches the world we live in.

Like Dr Tentacles said, if we lived in a universe with different laws such that 2+2 didn't equal 4, we would have come up with a different system. Of course we have difficulty comprehending any sort of logic that could make 2+2 not be 4, but then, that's exactly what we would expect, having evolved in this universe. Beings living in a universe where 2+2 equals 5 would presumably find our mathematics just as incomprehensible as we would find theirs.

On the contrary, the apples would behave the same way even if there were no one watching them. Or at least, that's the convenient assumption we make about reality, given that it doesn't change every time we turn around.

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Apples don't add themselves.

"Adding" is not an action you have to execute. Addition is just a relation. You or themselves don't have to "do" it.

Again, I would say mathematical truths are discovered. 2 + 2 = 4 isn't something you can curb just by living in a different place. It deals with quantities of unspecified objects.

That depends what you mean by 'add'. What I'm saying is that apples behave (by themselves) in ways implementing the same logic as what we call 'adding'.

Not any of the places we know about, at least...

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Which numbers, though? A set of entities satisfying Peano's Axioms? But we do not even know if they are consistent (and, if they are, it is provably unprovable that they are so) — actually, a few years ago there was a bit of a scare when Edward Nelson (one of the current top mathematicians, and definitely not a crackpot) claimed that he had found a way to derive a contradiction from them. Later he found a mistake in his proof and retracted his claim, but still it is definitely possible that Peano's Axioms are inconsistent — they look very reasonable, sure, but so did Frege's axioms for set theory until Russell proved that they are inconsistent.

And we cannot rely on instinctive intuitions here: intuitions may well be wrong, and furthermore I at least am entirely unable to capture intuitively the meaning of such numbers as 10^10 and so (let alone of ones far bigger than that). In effect, there are mathematicians who argue that these numbers do not exist.

Personally, I think that numbers are real, but only in the same sense in which any other formal system is real. They have a compelling nature: once you accept their premises, you have to accept their conclusions, and this is a truth which is entirely independent from the existence of humans (or even from the existence of an universe). But the same can be said of any other set of axioms: the one corresponding to natural numbers has very useful practical applications and it describes a structure which is more complex and interesting than most, but still, there is in principle no ontological difference between the natural numbers and — say — the p-adic numbers, or the Gaussian integers, or even stranger systems.

Just my two cents, of course — it is said that there are no two mathematicians who entirely agree about the nature of mathematics

edited 9th Feb '13 1:12:30 AM by Carciofus

But they seem to know where they are going, the ones who walk away from Omelas.

Numbers aren't so much a thing as a property of things.

You might even call them the property by which all other properties are derived. Size, for example, is simply the macroscopic interpretation of being composed a particular number of particles with a certain distance between them, and distance itself can be considered a certain number of planck lengths.

edited 9th Feb '13 3:52:08 AM by Elfive