[jc763]

>Does the number seven exist? Does the red color exist? What evidence do we have to answer these questions? What are the truth conditions for ∃x P(x) when P(x) stands for a number or a property? To respond to these questions is to set an ontology, and setting an ontology is to do metaphysics. This is exactly what Quine does when he states some reasons to include numbers and to exclude properties from the domain of our variables.

Good paper.

[westoncb]

Seems like from that it's just framework construction. It may have the same internal structure as an ontology, but to say the statements have any external correspondence (to the metaphysical; I'm using 'external' loosely) would require an extra step.

I can set an ontology where `thingamajiggers` are the only entity (so I guess the only truth condition for '∃x P(x)' is that P(x) is a thingamajigger), and I guess if you want to you can say I'm doing metaphysics at that point, though it does seem a little pointless to do so.

[trhway]

>Does the number seven exist? Does the red color exist?

those ones seem to be easy. There is no number seven. I mean there seven trees, seven stones, yet there is no number seven. It is only our mental construct (note: the construct itself, ie. neuron circuits and firing sequences do exist. It is like a map of non-existent land - the map exists while the land doesn't). The same is red color. There are EM waves of different frequencies. Color is mental construct triggered by perception of EM frequencies in specific range. Slightly different for different people. Completely missing for cats if i remember correctly. Like the number seven which is probably missing for cats too, and is known to be missing by various indigenous tribes separated from our civilization - people in this tribes know seven arrows, seven boats, ... yet completely don't understand just seven.

[dragonwriter]

> There is no number seven. I mean there seven trees, seven stones, yet there is no number seven.

There aren't trees or stones any more than there is the number seven: objects (other than elementary particles, maybe) are as much mental constructs as numbers.

[placebo]

Why stop at elementary particles? All objects are mental constructs of consistencies our brains detect in data that our senses pick up.

Humans have a great advantage in picking up on what I'd call meta-consistencies (which is basically what abstraction is) - creating a new mental construct by detecting consistencies not only in what the senses pick up, but detecting consistencies in those consistencies, or "thoughts about thoughts" if you will. This gives you numbers and other abstract concepts that enable far more powerful manipulation.

[madmax96]

>those ones seem to be easy. There is no number seven.

That's a very definitive answer for a complex question. It is not immediately clear at all that there is no number 7.

There are a few accounts for how numbers could exist. Let's break down each account:

* formalism - Mathematics is a formalized activity undertaken by humans, but is ultimately a language game. This approach is problematic because no formal system is capable of enumerating all truths about Mathematics. Hence, Mathematics is not a formal activity undertaken by humans, because otherwise the methods of its formalism would allow us to enumerate each true statement.

* intuitionism - Mathematics is a psychological artifact of minds, but is not a "natural" phenomenon. This approach has problems because it fails to account for (1) the remarkable consistency and success of Mathematics, and (2) leads us to Godel's disjunction. Godel's disjunction states that either there is no algorithm capable of enumerating all true statements that a human mind enumerates, or there are some Mathematical truths that can not be decided. If there is no algorithm capable of enumerating all true statements that a mind enumerates, then the mind is not a computational system -- meaning it can not be reduced to a mathematical model of neurons communicating -- and so the meaning of a psychological artifact needs reappraised. Specifically, numbers being a psychological artifact does not imply that they do not exist naturally. However, if a human mind is a computational entity, then intutionism doesn't work for the same reasons why formalism doesn't work.

* Realism - Mathematical objects exist. Given the problems of formalism and intuitionism, this actually is among the most probable of hypotheses.

Many Mathematicians fall into the Realist category, and there are good reasons why.

[coolgeek]

> there is no number seven

There is cardinality. There is ordinality. The "number seven" is a label for specific points in the cardinality and ordinality spaces.

> Color is mental construct triggered by perception of EM frequencies in specific range

You're conflating stimulus and sensation here

[bodi]

> There is no number seven. I mean there seven trees, seven stones, yet there is no number seven. It is our mental construct.

Crows, horses, and dolphins all have well documented[1] abilities to count numbers therefore as inconvenient and suggestive as it may be, the "number seven" most definitely exists somewhere outside human mental constructs and likely originates inside the abstract fuzzy designs that produce elementary consciousness.

1 - https://www.scientificamerican.com/article/how-animals-have-...

[trhway]

>likely originates inside the abstract fuzzy designs that produce elementary consciousness.

that sounds pretty close to what i'm saying - similar brains (and i do think that many animals' brains are much closer to us than we casually think they are) given similar experience (seeing seven stones, seven birds) produce similar constructs (incl. an aggregation/averaging of some aspects of that experience). That doesn't necessarily mean though the real existence of that aggregation/averaging (ie. what we call "number seven"), only the neuron config/sequence what actually encodes it is real.

[woodandsteel]

Whether or not you should say they exist depends on the particular meaning of the term "exist" you are using. And that in turn depends on what are your motives and purposes for asking the question.

Of course, if you are a Platonist then you will believe that there is a single, perfect meaning for the term that everyone should use.