I rarely ask this, but could you provide a quote for your statement that “empirical science is founded unpon the ** knowledge ** that 2+2 = 4 hold true in ** all possible universes **” ?
May I point out that empirical science is…well…empirical, hence based on the observed reality, hence cannot make statements concerning other alternate realities/universes?
Sure, you could use different symbols. You could replace “π” with “5.5”–it wouldn’t change a thing. The ratio of a circle’s circumference to its diameter would remain exactly the same.
It wouldn’t be grounded in our universe or any universe. You are trying to provide a counter example to my statement, but you are simply denying it, in effect. I’ll ask this again: could you keep everything in our universe the same and have pi = 5.5? If you say “no,” then you are as as much as admitting that pi could not be 5.5 in any possible universe. Why? Because you are thereby admitting that the rules of pattern and number are not arbitrary creations.
Yes, that’s true. We are required to perceive directly that they are true. In fact, geometry itself is based on undefined terms: point, line, plane. There are not even definitions for these things! You simply have to “get” what they are.
No, they are NOT based on perceptions of physical reality–there is no such thing as a perfect circle in nature. Nowhere.
Wait wait! You said, “the same mathematical logic.” Yes, it’s those basic principles that must always be true.
I’ll say it again: the facts of mathematics are NOT based upon a particular physics. Matter gravitates matter at a particular rate: so much acceleration per gram at the square of the distance between bodies. This number is, practically speaking, arbitrary. If it were twice as much, our mathematics would be exactly the same.
This is like saying, “Modus ponens is wrong, and I’ll prove it to you.” Either you get it or not.
You want a “quote”? From whom would you like a quote? I argued the proposition myself; I am not making an appeals to authority.
Empiricism is science based upon measurement and observation. Such science treats mathematics as basic fact–it does NOT question it at all. For example, there are no scientific experiments to test the “hypothesis” that 2 + 2 = 4. Hence, if we were to encounter a “different” universe, science would have to examine this universe with the mathematics that we have now. And it would be correct to do so.
Quite right. Whether our mathematics applies in an alternate universe is a purely philosophical question.
I’m surprised that people have such trouble with this. Did you see my argument about the room above?
Why should I not consider the opposite side of the room an “alternate universe”? How can I be sure that, once I cross the middle, 2 + 2 will not equal 5?
To put it differently, suppose there is an alternate universe that is exactly the same as this one except that 2 + 2 = 5. I go to grocery store and say to the clerk, give me 4 packs of cigs. He says, “OK. That’s 4 bucks a pack for 4 dollars.” I take two packs in each hand and inadvertently bring them togather. Now I have 5 packs, since 2 + 2 = 5. The clerk looks at me and says, angrily, “Are you trying to rip me off? That’s 5 packs but you only gave me 4 dollars.”
This is what is known as a “contradiction.” I’ve created a pack of cigs out of thin air, too, which violates laws of physics. Hence, the term “2 + 2 = 5” is incompatible with the term “everything else is the same.”
Now, you may argue that this is a straw man. Maybe 2 + 2 could equal 5 in another universe–but other things would have to be different as well.
To which I would reply, Then you agree that there are at least some principles of pattern and number that would hold true in all possible universes? Which would pretty much be a Q.E.D.
I can only suggest the OP be careful at zebra crossings.
Actually, that is what you’re saying. In a non-Euclidean space, the ratio of circumference to diameter is not necessarily 3.1415… (http://mathforum.org/library/drmath/view/55021.html, for example). It has been unclear for quite some time what the shape of our universe is, whether closed or open or flat (Euclidean). It’s not too hard to imagine differently-shaped spaces with different values of pi.
Yes, this is correct. From your site:
Well, you’re both right in different cases. Whenever you’re talking
about perfect circles on flat (Euclidean) surfaces, then pi, which
represents the ratio of the circumference of the circle to its
diameter, is a constant… However, if you go into NON-Euclidean geometry, where you deal with curved surfaces, then the ratio of a circle’s circumference to its
diameter does not remain constant. For example, say you stretched a
piece of rubber over a circular hoop. When the rubber lies flat,
you’ve got a flat (Euclidean) circle, and the ratio of the
circumference to the diameter is pi = 3.14159265358… But say you
poked your finger through the center of the circle and stretched the
rubber a bit. Then the diameter of the circle would grow, but the
circumference would be the same.
This is by no means a problem for my argument. In the above example, we are conceiving of a different kind of space in which this different kind of circle has a different kind of ratio between its circumference and its diameter. Presumably in a universe different from ours they could conceive of two-dimensional space (as we do) and see that, in such a case, pi is equal to 3.14…
The very fact that we can conceive of different possible realities and see that the the same principles apply strengthens my argument.
Sorry, didn’t get this one.
First, you may like to look at the similar thread Did God choose the value of Pi
Secondly, I am not sure why God being everything is not monotheistic. I believe that for a God to be omniscient and omnipresent it requires that everything is part of God (or it could be said ‘made from God’). This leads me to believe their is only one God.
I think the difference is not between monotheism and polytheism, but between the notion that the deity has a personality seperate from creation - or not. I am inclined strongly towards the latter belief (I see no evidence for an outside force at work), but I strongly doubt that any mathematic or other proof will ever resolve this controversy.
What if God wanted to bake pi in a square pan?
Thanks Malthus I had mistakenly assumed pantheism was the worship of a pantheon of Gods.
Depends does he add Pythagoras rum to the dough?
Not to the dough. To the filling.
What if he removed the universe or altered it so there were no entities? Then 2+2 could equal anything or nothing.
Not so. God himself would be an entity cognizant of those same truths.
In a non-Euclidean space the circumfenrence of a circle divided by it’s diameter isn’t necessarily pi, but this ratio will always to tend to pi as the diameter tends to zero.
Obviously…
According to most definitions of pantheism that I read by googling define: pantheism it now seems clear to me that pantheism is redundant.
It is a synonym for ‘everything’ or for ‘universe’, with the addition of the adjective ‘divine’.
But if everything is divine, then what is not divine? Nothing is not divine. Divine becomes devoid of any meaning if it encompasses everything and has no opposite or absence of.
Therefore, we’re left with pantheism=everything or pantheism=universe, which makes the word pantheism redundant.
At least in Aeschines’s case (correct me if I’m wrong, Aeschines), pantheism is a philosophy that states that the universe is divine (which, admittedly, means nothing if everything is divine) and has a purpose. That’s what sets it apart from a simple belief in the universe.
I don’t agree with Aeschines, but I don’t think he’s just saying “the universe exists.”
I believe in one God (the Christian God, His Son Jesus Christ, and the Holy Spirit – Three in One). I believe that God created this universe, and put into effect the basic scientific laws that govern this universe (gravity, laws of thermodynamics, etc.)
I also believe that God is omnipotent, and can circumvent these laws that He put into effect. To those observers that are finite and do not share this omnipotence, these displays are referred to as miracles.
For example, a dead person cannot come back to life without divine influence. The sun cannot remain still for about a day without divine influence. A few loaves and fishes cannot feed several thousand without divine influence.
Obviously, these miracles are at odds with the very laws that God put into effect. However, being supernatural and omnipotent, He can circumvent these laws at will.
In summary, God made the rules. He can break the rules.
These are my beliefs.