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28 votes

Why can't numbers be 'used up'?

Does a song get 'used up' when we sing it? Does a story get 'used up' when we read it? Does a path get 'used up' when we walk it? Forgive the computer science analogy here, but all of these things — ...
  • 14.3k
18 votes

Why can't numbers be 'used up'?

Actually, your young student friend may be contemplating an astoundingly subtle notion. Linear logic (invented (or is it discovered?) by Jean-Yves Girard) is a substructural logic that's resource-...
  • 382
8 votes

Why can't numbers be 'used up'?

Monkey Brain Although it seems trivial at first, there are a few interesting implications about his question, why do we talk about abstract ideas as if they are real objects? Because that is the ...
7 votes

Why can't numbers be 'used up'?

I suspect the problem is that the child is imagining a machine with preset number tiles. When it spits out the only tile with a "2", of course it's used up. If you clarify that it has a huge ...
5 votes

Why can't numbers be 'used up'?

... he could not understand how when you put '2' into the machine you it's not gone, you can get it back and put it into the machine again. One potential idea to think about here is to "design&...
  • 4,903
5 votes

Why can't numbers be 'used up'?

Short Answers [W]hy do we talk about abstract ideas as if they are real objects? And from this, is it a property of abstract 'objects' or ideas that there is no situation where they do not 'exist'? ...
  • 11.5k
5 votes
Accepted

Are analogies between ethics and mathematics philosophically coherent?

The ethico-mathematical analogy is ancient, but it did gain some recent prominence among analytic philosophers. Clarke-Doane's Moral Epistemology: The Mathematics Analogy, Franklin's On the Parallel ...
  • 41.2k
5 votes
Accepted

What are all attributes of God and what is the manner of knowing them according to Aquinas?

God's attributes known negatively Following St. Damascene (De Fide Orth. i, 4), St. Thomas Aquinas writes (Summa Theologica I q. 2 a. 2 arg. 2): we cannot know in what God's essence consists, but ...
  • 7,306
5 votes

Why can't numbers be 'used up'?

Free new instances of the same class Perhaps the proper analogy to use here is to note that each invocation of the number 2 is a 'separate instance' of the general concept of number 2 - you may obtain ...
  • 1,211
5 votes

Why can't numbers be 'used up'?

Numbers are names Numbers are names and functions are not machines. Your name, say "Roger", does not get used up when your friends refer to you. If you have two apples in a basket, you can ...
  • 151
4 votes
Accepted

Are analogies logical arguments?

Here is Wikipedia's description of an argument from analogy: Argument from analogy is a special type of inductive argument, whereby perceived similarities are used as a basis to infer some further ...
4 votes

Why can't numbers be 'used up'?

This discussion is missing the concept of units, which I think the child is intuiting (correctly). You give Alice 2 apples. She had 3 apples. Now she has 2+3=5. Do you have the original 2 any more? No....
  • 421
3 votes
Accepted

why analogies work?

You are simply noticing that generalization works; not everything is a special case. Electrons have a position (sort of). People have a position. Both can move. Both can be constrained while they ...
  • 15.7k
3 votes
Accepted

What are the similarities and differences in the ways Aristotle and Thomas Aquinas define the "Analogy of Being"?

Thomas Aquinas's short work De Principiis Naturæ concisely summarizes the three types of predication: […] "Being" [ens], however, is not a genus because it is not predicated univocally, but only ...
  • 7,306
3 votes

"Jim and the Indians" and killing someone to harvest organs, is it equivalent?

Yes, Williams "Jim and the Indians" and the drifter problem (the usual name for what you describe as the five transplant recipients vs. one drifter case) are philosophically distinct and generally ...
  • 24.1k
3 votes

Is this an inductive or a deductive argument?

Especially in introductory logic textbooks, deductive arguments are usually defined something like this: "the conclusion must be true given the premises" or "it's impossible for the premises to be ...
  • 2,407
3 votes

What are metaphorical sayings similar to “As Above So Below”? How can I find them?

This phrase is also found in discussions of Gnosticism. Gnosticism became extinct. The Nag Hammadi Library dates back to the 4th century (CE) and it is currently in print. A text you might be ...
3 votes

Why can't numbers be 'used up'?

I think that's a really interesting point that your student has a doubt in. I believe the issue is that when we do calculations, the numbers and related concepts are something we come up with our ...
3 votes

Why can't numbers be 'used up'?

As others have remarked: Because the mathematical "2" is not a physical object but a thought, an idea, a concept, a property. Existing purely within our minds, it has almost no physical ...
2 votes

Why can't numbers be 'used up'?

A function is a process, algorithm, or explicit mapping. Rather than talk about a machine churning up the input number to produce the output number, I would instead compare the act of applying a ...
  • 121
2 votes

What are metaphorical sayings similar to “As Above So Below”? How can I find them?

"As above, so below" is a phrase from Hermeticism, which is more of an occult tradition than a philosophical one (though it has certain similarities to Neoplatonism, perhaps because both emerged ...
  • 2,779
2 votes

I search an example of an ad hominem argument, which is not simultaneously an argument from analogy

It seems that most ad hominem arguments are analogies. Comparisons of people to Hitler and Stalin are among the most familiar. Often the comparison is inappropriate, but it is still an analogy. ...
  • 4,935
2 votes

Why can't numbers be 'used up'?

To your question, we treat abstract ideas as real objects because many people can comprehend a real object and not the abstract idea. Or rather, we try to present the idea in a form that the listener ...
2 votes
Accepted

Would a physical near-equivalent to continental nuclear war have roughly the same moral status as an actual such war?

By virtue of the quantity of explosive force unleashed, and the mutagenic residue left in its wake, here, does this [conventional bomb] consist in a physical near-equivalent to continental nuclear war ...
  • 4,935
1 vote

Do those who deny a univocal understanding of "God is good" conflate sense and connotation?

The example cited to argue against "univocalism" -- "Good Bull" being very different from "Good God", is instead a clear case of equivocation. "Goodness" as ...
  • 5,218
1 vote

What undergraduate-level books focus on analogical arguments?

Irving Copi's Introduction to Logic discusses analogies in depth and yet at an undergraduate level. Since this book presents logic in general it also has parts on other topics related to logic such as ...

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