Seasons

if I think they are not useful, that is 'true for me', and if you think they are useful, that is 'true for you',

With respect to morals, you are correct, although I do not like the the phrase "true for you" because it seems to imply that subjective truths are on par with the outside common reality of things that exist with or without humans. When your actions effect others in a common reality of what we think of a the real world, however, I can say that I will work according to what moral or useful in my own view. My view is subjective. I will act on it anyway.

??? As far as I can see, we don't have the slightest control over whether 2+2=4. How would we go about arranging that 2+2=5?

2 plus 2 equals 5 because of how we define numbers, addition and equal. I am basing my views primary on the works of Hempels' "On the Nature of Mathematics"
http://www.ditext.com/hempel/math-frame.html. Hemple said, for example, "In the light of this remark, consider now a simple "hypothesis" from arithmetic: 3 + 2 = 5. If this is actually an empirical generalization of past experiences, then it must be possible to state what kind of evidence would oblige us to concede the hypothesis was not generally true after all. If any disconfirming evidence for the given proposition can be thought of, the following illustration might well be typical of it: We place some microbes on a slide, putting down first three of them and then another two. Afterwards we count all the microbes to test whether in this instance 3 and 2 actually added up to 5. Suppose now that we counted 6 microbes altogether. Would we consider this as an empirical disconfirmation of the given proposition, or at least as a proof that it does not apply to microbes? Clearly not; rather, we would assume we had made a mistake in counting or that one of the microbes had split in two between the first and the second count. But under no circumstances could the phenomenon just described invalidate the arithmetical proposition in question; for the latter asserts nothing whatever about the behavior of microbes; it merely states that any set consisting of 3 + 2 objects may also be said to consist of 5 objects. And this is so because the symbols "3 + 2" and "5" denote the same number: they are synonymous by virtue of the fact that the symbols "2," "3," "5," and "+" are defined (or tacitly understood) in such a way that the above identity holds as a consequence of the meaning attached to the concepts involved in it."

As far as I can see, we don't have the slightest control over whether 2+2=4. How would we go about arranging that 2+2=5

One of my favorite physics/math theorems is 2+2=5 for very large values of 2. It illustrates two principles very well.

On a more serious note, 2+2 is NOT always 4. Mix together 2 gallons of water with 2 gallons of alcohol, and you won't get 4 gallons of liquid. The molecules slide by one another somehow, so that the resulting liquid takes up less space. (I think it's alcohol; it's been a while since I read up on this) On the other hand, the weights will add as expected. So, say, 2 pounds of water plus 2 pounds of alcohol will yield 4 pounds of liquid.

What about 2+2=1? This could easily apply in a situation with interlocking parts, that won't stay interlocked until all have been connected together. Sure, you can count the four separate parts, but the resulting...thing...is a single unit in its own right.

"Mathematical objects, such as numbers, are not particularly mental. If numbers were mental entities, then they could not have existed before there were any minds." (Irina)

BTW, my color tags have been working intermittently--I put them there but they may not be in red now. I hope you know your quotes.

Objects existed regardless of human existence. "Numbers" as such, did not (though it's possible others non humans may develop a concept of numbers just as it is possible non humans may develop a concept of language). We created numbers to describe the word as we see it. They are a mental construct, though we can write symbols for these ideas down just as we can write down symbols for words.

Mathematics is an axiomatized deductive system. You can start with a set of postulates, say Peno's axioms,
"P1. 0 is a number
P2. The successor of any number is a number
P3. No two numbers have the same successor
P4. 0 is not the successor of any number
P5. If P is a property such that (a) 0 has the property P, and (b) whenever a number n has the property P, then the successor of n also has the property P, then every number has the property P."

From there we can define various operations such as addition, subtractions, multiplication and division. We could make some adjustments to this system, but in essence, all math can be deprived form these primitives and rules, and it is not dependent on empirical evidence.

"But there was a whole number between 2 and 4 long before there were any minds in the universe."

What makes you think that is so? Numbers are tools created by humans to describe various aspects, objects and relationships, but they only describe things, they are not things themselves.

"According to Physics, the universe obeyed certain mathematical laws from the first moment of its existence."

No. Physics gives us the means to describe various principles and relationships, but it only describes what is going on, it doesn't dictate what happens.

"Likewise, if all minds in the universe were to die out, not one truth of mathematics would disappear. Pi was a transcendental number long before anyone had the concept of pi or the concept of a transcendental number."

I disagree. The label "transcendental" or "pi" or "number" does not exist unless a mind defines and applies it. These may describe various aspects of reality, but they are not reality. They may be useful for our understanding (subjectively useful to me or others as we judge it) but they do not exist outside of our minds.

Well, Bev, I think we have reached the "agree to disagree" stage.

Irnia, no doubt we have. I was just thinking that this was starting to sound like the quantum physics debate because we are returning to similar issues involving whether mechanism merely describes a phenomenon, or is itself the phenomenon. Not that I want to start that again.

Don't worry, soon we'll be able to upload again and I'll leave the boards alone.

Ever since my frustrating experience with discussing Quantum Mechanics a few weeks back, I have been intrigued by the process of discussion as it appears here (and presumably elsewhere). I had (rather naively) thought that the purpose of such discussions was to reveal truth, or some fragment of approximate truth, or at least to build consensus. Instead, I found that, in spite of the fact that Psimagus and I are both quite intelligent and fairly polite, and in spite of the fact that we had the resources of the entire net at our fingertips, including numberless articles on Quantum Mechanics, we were unable to achieve any consensus at all about even the most basic principles of the discipline.

This was very striking to me. It was as if two able-bodied adults had been unable to lift a table fork.

Is there perhaps a centrifugal force in our culture, or perhaps in human nature generally, that leads people away from consensus, instead of guiding them towards it? At times it seems to me that we are each following a program something like this:

1.    Find something to disagree about and make your position known.
2A. If others disagree with you, then argue with them.
2B. If others agree with you, goto 1.

Yes, it seems strange to me that you can't get a consensus, 'that it's wrong to torture babies'. I know that rabbits eat their young, but most rabbits pull out their own hair to keep the young warm. I know that man has always tortured babies, but The fact that we are here shows it wasn't the norm. I also know during the times that man was torturing babies, someone came in and tried to save one (baby). I think that it is easy to talk about it academically, but I wonder if any of us could look at such a thing and not vomit. I don't apologize for my beliefs. I don't expect anyone to believe as I do. When It comes to the psycho guy going to let the many live for the one I torture. I am sorry, I woundn't do deals, I wouldn't pity him. I would fight him tooth and nail until he killed me. (which he no doubt had planned anyway).With luck I will take him by surprise, and rip his heart out. Yes, this is killing, if I succeed, but I will claim self defense, and go eat a Big Extra with cheese.

The tendency to debate rather than agree may be cultural, but I think there is more to it. Remember when we were talking about building hand held lie detectors and I said I preferred teaching critical thinking and healthy debate skills (or some such). It's a good thing to have healthy and vigorous debate when you honestly have different views.

Critical analysis is probably a habit from my academic background. I don't pick at things to pick at things, but I think about what I read and present different views and analysis. I don't mean to offend anyone, but I think doing anything else would be dishonest of me. Also, as I mentioned, I have been bored and unable to upload for a while, so I tend to post more and get caught in what I see as a debate.

Group-think can be dangerous and dissent is important if you value "truth". That assertion rests on my philosophy that we all have limits and can never actually attain the "Truth, the whole truth, and nothing but the truth". I think everything we learn is "true until further notice", and can be adjusted later, and it's good to test what you know and debate it every so often. A consensus is too much like being done learning, though there are time I agree because some things seem obvious at a certain point.

Please understand, I'm not arguing with you for the sake of arguing. I debate because this board seems like it's intelligent and educated and it seems to be a good place to discuss ideas. There are times I build on what I agree with in others' posts, it's just that I have my own thoughts and opinions.

We all have pieces of the truth, but no one has "The Truth". Maybe I should look harder to say "What about what this person just said could be true, and in what circumstances is it useful?" There is a value to that too.

Prob,

I'll agree that I am against torturing babies, and that most people are and should be against torturing babies. I just don't think that proves morals are objective or universal. If you want agreement, I'll agree that I don't like torturing babies for fun, and that I would try to stop such an act.

I am thinking of books by Konrad Lorenz. His theory about built in inhibitions in animals..Humans were sorely lacking in most, but I think he had a point, there are some universal norms found in life. Whether you want to think of evolution or the hand of God.

Sounds interesting Prob. :-)

What sort of "universal norms"?

(Warning: there is a good chance I will disagree with him, because the minute I hear "universal" it raised red flags in my head, but then again, you may have to consider tha possibility that I am evil )