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When we ask "do they exist", we invite a certain type of reasoning. "Well consider chairs. We can all agree they exist. In what ways are mathematical objects si

by im3w1l 5y ago

When we ask "do they exist", we invite a certain type of reasoning. "Well consider chairs. We can all agree they exist. In what ways are mathematical objects similar and different from chairs?" But I have an idea. What if we turn it upside down? "Do mathematical objects *not exist*?" Now we invite the opposite metaphor. "Well consider ghosts. We can all agree that ghosts don't exist. In what ways are mathematical objects similar and different from ghosts?" I think that fundamentally if you say that mathematical objects do exist, then you have to admit basically everything in - including ghosts. Fundamentally, definitions are a matter of taste and aesthetics, and I dislike a definition that is so broad as to contain everything. That makes it useless for reasoning and discussing.

Igelau 5y ago
> We can all agree that ghosts don't exist. I don't agree that the nonexistence of ghosts is definitively settled, and I doubt I'm alone in that here.
Koshkin 5y ago
Would you say that there exists something in common between the 21 sheep and the 21 dry peas in the shepherd's pocket which he uses every evening to see if any of the sheep have been lost? That common which exists, in a very clear and practical sense, is called a Number.
- tremon 5y ago
  No, I would not say that there exists something in common between those. Cardinality is an emergent property of a set, but that doesn't mean that cardinality exists on its own. Did Plato ever make the argument that because his Shapes have corners, edges and angles, that therefore corners, edges and angles exist in the same way as the Shapes? I don't recall if he ever described Shapes in those terms.
- kdtsh 5y ago
  What does it mean for something to exist then? Does an apple exist in the same sense that a number exists? There is something in common between two chairs; there is something in common between a red ball and a red book; there is something in common between 21 sheep and 21 dry peas. It is _emphatically_ unclear that each of these three statements of 'existence' have anything at all to do with each other except in the most intuitive sense - that they refer to things which are as opposed to are not. At some point the bar for existence becomes so low that Harry Potter exists - really exists - because we can conceive of the idea of him. The question of whether numbers 'exist' is more than that.
  - Koshkin 5y ago
    Language, having evolved over tens of thousands of years of the human practical use, is often smarter than us, and where we are forced to say that something exists, it usually does. It means that more often than not something that we describe in words is not merely an idea but has an objective meaning, i.e. has to do with reality and therefore exists, independently from from our minds. Thus not only “objects” exist, but also their properties as well as relations between them. A tip of the needle enjoys the same objective existence as does the needle itself, and this fact is easy to verify by sticking it in you finger. What other existence do you want?

by im3w1l 5y ago

Igelau 5y ago

> We can all agree that ghosts don't exist. I don't agree that the nonexistence of ghosts is definitively settled, and I doubt I'm alone in that here.

Koshkin 5y ago

Would you say that there exists something in common between the 21 sheep and the 21 dry peas in the shepherd's pocket which he uses every evening to see if any of the sheep have been lost? That common which exists, in a very clear and practical sense, is called a Number.

tremon 5y ago
No, I would not say that there exists something in common between those. Cardinality is an emergent property of a set, but that doesn't mean that cardinality exists on its own. Did Plato ever make the argument that because his Shapes have corners, edges and angles, that therefore corners, edges and angles exist in the same way as the Shapes? I don't recall if he ever described Shapes in those terms.
kdtsh 5y ago
What does it mean for something to exist then? Does an apple exist in the same sense that a number exists? There is something in common between two chairs; there is something in common between a red ball and a red book; there is something in common between 21 sheep and 21 dry peas. It is _emphatically_ unclear that each of these three statements of 'existence' have anything at all to do with each other except in the most intuitive sense - that they refer to things which are as opposed to are not. At some point the bar for existence becomes so low that Harry Potter exists - really exists - because we can conceive of the idea of him. The question of whether numbers 'exist' is more than that.
- Koshkin 5y ago
  Language, having evolved over tens of thousands of years of the human practical use, is often smarter than us, and where we are forced to say that something exists, it usually does. It means that more often than not something that we describe in words is not merely an idea but has an objective meaning, i.e. has to do with reality and therefore exists, independently from from our minds. Thus not only “objects” exist, but also their properties as well as relations between them. A tip of the needle enjoys the same objective existence as does the needle itself, and this fact is easy to verify by sticking it in you finger. What other existence do you want?