The misuse of science by William Lane Craig and othe Christian apologists.

[Sea of red]

Well this undermines your own argument that scientific modelling does not represent real phenomena in the real world.



Yep, right up there with meerkats.

As I understand him, he's saying that some mathematical concepts and branches have no connection to reality; I take it he believes mathematical infinities are one example.

[element771]

As I understand him, he's saying that some mathematical concepts and branches have no connection to reality; I take it he believes mathematical infinities are one example.

Right...I think.

There is a difference between saying that "infinity" is a valid mathematical tool for understanding real phenomenon and saying that an infinite amount of apples could exist in the real world.

[hansgeorg]

As I understand him, he's saying that some mathematical concepts and branches have no connection to reality; I take it he believes mathematical infinities are one example.

Right...I think.

There is a difference between saying that "infinity" is a valid mathematical tool for understanding real phenomenon and saying that an infinite amount of apples could exist in the real world.

Correct in both cases.

I am also doubting infinity, believed to be actual rather than potential could be valid other than as a reductio ad absurdum for any understanding.

Mathematical tools do not as such need to distinguish between "actual" and "potential" to be useful.

Also, some "mathematical tools" are indeed validated as real by real, physical observations. This is not the case with "actual infinity".

[hansgeorg]

Math is not subject to physical proof. Math is subject to philosophical logic subject the proof theory, set theory (Cantor) and computability of math.

The concepts of "two" or of "plane" can be proven physically by examplification. I do NOT agree correct mathematics has to be subject to Cantor's set theory.

Beyond basic concepts, some things are subject to philosophical logic - but that includes physical proof, as I have seen with Pythagoras' theorem.

[Boxing Pythagoras]

False. For two reasons, of which the banale one is that French schoolbook mathematics actually teaches "number line" only as "relative numbers", after teaching natural numbers as "natural" or "absolute" numbers.

You do realize that books intended for schoolchildren do not encompass the sum totality of the philosophy of mathematics, right? Such textbooks almost never even provide a rigorous treatment of the subject matter which they do teach, let alone of mathematics in general. The fact that your schoolbook utilizes a particular pedagogical method tells us nothing at all about how numbers are defined.

4 is 3 more than 1, 2 more than 2, 1 more than 3 (this is also the definition of 4), plus minus zero other than 4, 1 less than 5, 2 less than 6, 3 less than 7 and so on.

Is it possible to define 4 without reference to any other numbers? If not, then why are you making an arbitrary distinction between the Natural numbers and other numbers which are defined by reference to other numbers?

But in this example, we have a "number" we are talking about = 4.
We also have a lot of "numbers" (even so as yet not "relative numbers") we are comparing it to = 1, 2, 3, 4, 5, 6, 7 ad infinitum.
AND we have "relative numbers" which express the comparison between the two numbers which are compared.

You said that 4 is defined as "1 more than 3." So, 4 by definition is a comparison between two numbers. Since it is necessary to define a number before that number can have any meaning, it seems that even upon your definition, 4 is a relative number.

An obvious fact does not need an elaborate reasoning.

That'd be all well and good if we were discussing an obvious fact. We are not.

No, since Tycho Brahe and since spacecraft, I'll not settle for spheres of quartz. I do settle for:

a) an aether in which God moves the heavens around each day;
b) angels who move their respective planets in relation to the aether, as he thought they moved themwithin the spheres or turned the spheres of, as we would say, quartz.

Ahh, so then you do agree that there are places in which Aristotle, and Aquinas after him, were incorrect in their reasoning?

If you assumed that there was an actual infinite, you would be assuming an infinite and therefore always equal sum of apples.

Infinity minus anything would be infinity, and in this case infinity minus infinity would still be infinity.

Infinity is not a number. Mathematical operations are only defined for numbers. "Infinity minus [any number]" does not equal infinity, because the statement is not even cogent. It is just as nonsensical as the statement "blue minus any number" or "deliciousness minus any number" or "hansgeorg minus any number."

However, there are numbers which have the property of being infinite. If you subtract any finite number from an infinite number, you do find that the difference is also an infinite number. However, it is not necessarily the same infinite number. The fact that two numbers are infinite does not imply that they are equal any more than the fact that two numbers are even implies that they are equal.

Cantor explicitly cites the cardinality of all natural numbers as being equal to the cardinality of all even natural numbers as evidence that if they were actally existing infinite sets, they would be equally infinite, and equally great.

And I am happy to disagree with Cantor on this point. It is incredibly easy to define a Hyperreal number which is equal to the quantity of Natural numbers, and another Hyperreal which is equal to the quantity of only the even Natural numbers, and to compare these two numbers.

Next cardinality would be the one of so called "real numbers" which do not deal with numbers, but with geometry.

No, the Real numbers actually do deal with numbers. One of the most famous of all the Real numbers, Euler's number, is not defined in terms of geometry, at all. In fact, the only way to rigorously define the very concept of the Reals is with sets of numbers.

Sounds a bit surrealistic.

Naming conventions are fairly irrelevant to the applicability of mathematics to the real world. We could just as easily have named these "Totally-Applicable-to-the-Real-World numbers" instead of "Surreal numbers." Or "banana dog numbers." Or "letters of the alphanumbers." Or "mxyzptlk." Whether or not these numbers are applicable to the real world is not dependent upon their name.

Equivocation. Something is "more" (Latin "plus", Swedish "mer", German "mehr") than nothing, but it is not "more" (Latin "plures", Swedish "fler", German "mehrere") than nothing, because the second adverb deals with number, not with quantity in a more abstract sense, and cannot therefore be compared to zero, which the first can.

Now you are attempting to draw a distinction between quantity and number? So, you would say that zero represents an actual quantity, but not an actual number?

Supposing these had any other than imagined and therefore conventional existence.

Thus far in the discussion we have maintained that we are not taking a Platonist view of the ontology of numbers. As such, all numbers-- including the Natural numbers-- only have "imagined and therefore conventional existence." Are you trying to claim that the Natural numbers exist in the Platonist sense, but all other numbers exist only in the Nominalist sense?

[element771]

I agree that infinity is not a number. However, you are still using theory and not reality.

There is a scenario that is able to be actually realized where someone physically possesses 4 apples. There isn't a scenario where someone physically possesses -4 apples. That is the difference and the point that I am trying to make although it doesn't seem to be as clear as I would like.

[Boxing Pythagoras]

I agree that infinity is not a number. However, you are still using theory and not reality.

Again, though, we've already agreed that we're taking a Nominalist view of mathematical ontology, and not a Platonist view. As such, all ascription of number to concrete objects is theory and not reality. The Natural numbers are every bit as much a conceptual abstraction as are the Integers, the Rationals, the Reals, the Complex numbers, the Hyperreals, et cetera. Similarly, the Natural numbers are no more a reality than any of these other number systems.

There is a scenario that is able to be actually realized where someone physically possesses 4 apples. There isn't a scenario where someone physically possesses -4 apples. That is the difference and the point that I am trying to make although it doesn't seem to be as clear as I would like.

I understand what you're saying-- really, I do. I simply don't agree with it. Numbers are not concrete objects. Numbers are used to describe concrete objects. It is no less correct to say that a person who has promised the next four apples he would receive to a friend is in possession of -4 apples than to say that a person holding four apples in his arms is in possession of 4 apples.

Or, if we're talking about Rationals, if a person cuts an apple into two equal parts, then tossed one of those parts away, we would be perfectly correct in saying he has 1/2 an apple.

If one wants to argue that the Reals, Complex numbers, Hyperreals, and other number systems are not applicable to the real world, one needs to present a better argument than incredulity.

[shunyadragon]

Right...I think.

There is a difference between saying that "infinity" is a valid mathematical tool for understanding real phenomenon and saying that an infinite amount of apples could exist in the real world.

It is interesting that your endless vindictive diatribe does not consider the fact that my view very closely follows that of Boxing Pythagoras.

[MaxVel]

It is interesting that your endless vindictive diatribe does not consider the fact that my view very closely follows that of Boxing Pythagoras.

Maybe the difference is that Boxing Pythagoras treats his interlocutors with respect, by stating his views in his own words instead of endless cut-and-paste 'citations' from 'sources'; by refraining from insults when someone disagrees with him; by not maligning his interlocutors motives or integrity; by acting like an adult and trying to answer challenging questions instead of resorting to emojis and 'Bob, Duck and Weave'.

Maybe, just maybe, the problem is how YOU interact with others here.

[Tassman]

As I understand him, he's saying that some mathematical concepts and branches have no connection to reality; I take it he believes mathematical infinities are one example.

Yes, I too think that's what he's saying. But my point is that he's using an analogy which undercuts his argument, namely the image of a turtle. Turtles are very much connected to reality.

[Tassman]

Whoa whoa whoa....

Where did I say that?

That is a gross misrepresentation or misunderstanding of what I am claiming. I never said that nor meant to imply that. If you believe that is what I am trying to imply, then we aren't on the same page. Please let me know where you think I implied that so I can clear up any confusion.

I make my living off of using scientific modeling to represent the real world.

1. Turtles
2. Gorillas
3. Merrkats

We may be stumbling over each other here. I took you to be saying that a drawing of a non-existent unicorn was analogous to scientific modelling of 'infinities', which is not necessarily a real phenomenon in the real world. In short the unicorn drawing is real but the unicorn itself is not, just as the models of infinities are real even if actual infinities are not. This I understand. But when you introduce an existent

[shunyadragon]

Maybe the difference is that Boxing Pythagoras treats his interlocutors with respect, by stating his views in his own words instead of endless cut-and-paste 'citations' from 'sources'; by refraining from insults when someone disagrees with him; by not maligning his interlocutors motives or integrity; by acting like an adult and trying to answer challenging questions instead of resorting to emojis and 'Bob, Duck and Weave'.

Maybe, just maybe, the problem is how YOU interact with others here.

I believe the reverse is true concerning the likes of element771, and you. As usual condemning the sources, Ad hominem, and not addressing the information in the citations. In fact the sources I cite are indeed legitimate, and you have not been able to find justifiable fault in those I cited.

Nonetheless, my view is very much the same as Boxing Pythagoras, and my sources cited confirm this.

[element771]

We may be stumbling over each other here. I took you to be saying that a drawing of a non-existent unicorn was analogous to scientific modelling of 'infinities', which is not necessarily a real phenomenon in the real world. In short the unicorn drawing is real but the unicorn itself is not, just as the models of infinities are real even if actual infinities are not. This I understand. But when you introduce an existent

OK great and I agree. Sorry about my slander of turtles...

I don't understand how this relates the point that you made of me saying that mathematical modeling cannot model reality.

Maybe the analogy isn't the best. Let me think about it after some coffee.

[element771]

Again, though, we've already agreed that we're taking a Nominalist view of mathematical ontology, and not a Platonist view. As such, all ascription of number to concrete objects is theory and not reality. The Natural numbers are every bit as much a conceptual abstraction as are the Integers, the Rationals, the Reals, the Complex numbers, the Hyperreals, et cetera. Similarly, the Natural numbers are no more a reality than any of these other number systems.

I understand what you're saying-- really, I do. I simply don't agree with it. Numbers are not concrete objects. Numbers are used to describe concrete objects. It is no less correct to say that a person who has promised the next four apples he would receive to a friend is in possession of -4 apples than to say that a person holding four apples in his arms is in possession of 4 apples.

Or, if we're talking about Rationals, if a person cuts an apple into two equal parts, then tossed one of those parts away, we would be perfectly correct in saying he has 1/2 an apple.

OK, I think we are on the same page with the exception of the final point.

If one wants to argue that the Reals, Complex numbers, Hyperreals, and other number systems are not applicable to the real world, one needs to present a better argument than incredulity.

It isn't an argument that the number systems are not applicable to the real world, it is an argument that some aspects of these systems cannot be actualized in reality.

[element771]

It is interesting that your endless vindictive diatribe does not consider the fact that my view very closely follows that of Boxing Pythagoras.

Go away Shuny...the adults are having a conversation.