Contextual Existence: Questions, Answers and Ontology

[SW VandeCarr]

I suggest that asking what exists as a general question is meaningless. It's only meaningful within a context where the ontology is well defined and an unambiguous answer is, in principle, possible. I think this was the philosophy of the young Wittgenstein.

Recently I posted in a thread (since locked) where the OP asked if anything could exist without space and time. If the context was physical space and time, then the question is a meaningless tautology. So I assumed a more general context and answered that things like the natural numbers exist outside the context of space and time. A member responded critically and suggested that the natural numbers were imaginary and were akin to "vampires and werewolves."

There is a clear context where one can ask sensible questions such as:

1) How many primes exist between two (arbitrarily large) primes x and y.?
2) Does a derivative exist everywhere for G(x)?

One can ask if a language contains a particular word, or if a particular short excerpt came from a particular Beethoven symphony.

I don't know what the ontological context of a werewolve is. For vampires, it's "bats".

 

[JoeDawg]

A member responded critically and suggested that the natural numbers were imaginary and were akin to "vampires and werewolves."

In a sense they are, as they are concepts, not physical objects.

Werewolf = human+wolf

You can further reduce by defining what a human is, and what a wolf is. Both a werewolf and numbers exist as definitions. So they don't exist the same way an actual wolf exists.

 

[SW VandeCarr]

In a sense they are, as they are concepts, not physical objects.

Werewolf = human+wolf

Both a werewolf and numbers exist as definitions.

Tell me about werewolves. Do they have tails? Where can I find one? What do they eat? Is their genome closer to humans or to wolves?

A definition is a constraint. You can make up a definition of a werewolf. So can I. My definition might be different than yours. There's no common constraint that forces me to make my definition the same as yours or yours to mine.

I say the number 11 is a prime number. What do you say?

 

[JoeDawg]

You can make up a definition of a werewolf.

Sure, but then you're not really talking about the concept 'werewolf'.
The concept of 'werewolf' has a history. Its not just random or made up by a single person.

I can make up a defintion of prime numbers too.

Prime numbers are trees.
Werewolves are ice cream.

The mathematical concept of prime numbers has its roots in a history too.
When it comes to definitions, it all depends on where you start... what are your axioms?

The axioms on which 'werewolf' are based... are obviously different from those on which prime numbers are based.

 

[SW VandeCarr]

I can make up a defintion of prime numbers too.

Prime numbers are trees.
Werewolves are ice cream.

This is nonsense. You're derailing what could be a reasonable philosophical discussion.

 

[JoeDawg]

This is nonsense. You're derailing what could be a reasonable philosophical discussion.

I think you're missing my point... about axioms...but derailing can be fun too.

You are the one who said you could make up a definition of werewolf.
That is what I did.

And yes, those definitions were nonsense... because they were random.
The actual definition of werewolf is not, just like the actual definition of 'prime number' is not.

 

[apeiron]

Tell me about werewolves. Do they have tails? Where can I find one? What do they eat? Is their genome closer to humans or to wolves?

A definition is a constraint. You can make up a definition of a werewolf. So can I. My definition might be different than yours. There's no common constraint that forces me to make my definition the same as yours or yours to mine.

I say the number 11 is a prime number. What do you say?

If you are talking philosophically, there is a useful distinction between the possible and the actual. So there could be both possible contexts (worlds we can imagine in which werewolves might exist) and actual contexts (like our world).

Then the big question you seem to be focusing on is where does maths fit? What is the context of maths? And is it either just purely a realm of the possible (so all mathematical facts or patterns are just concepts - imaginary somehow), or is the realm of maths actual (and so numbers/patterns really exist)?

The conflict is that it seems easy to view the material world (that which is constructed of substance) as being about both the possible and the actual. But then the realm of maths seems different. It is either all just about the possible, or all in fact just real.

I differ in that I would view maths as the science of form - the discovery of nature's patterns. And so it is on the same philosophical footing as physics, which generally sees itself as the science of substance, the fundamental materials out of which realities are constructed. The possible~actual (or rather, as I prefer Peirce's developmental ontology, the vague~crisp) would thus be a dichotomy that applies to both.

So there might be the mathematical equivalent of werewolves - you could glue various component ideas together and suggest a possible instance of something. But the real world is more constrained (the transformational powers of werewolves, for instance, would be a bit of a biological stretch no matter how many times evolution were re-run). And so the space of what is actual - either in terms of substance or form - would be much smaller.

Prime numbers, for instance, are impressive precisely because they survive as regularities in any base number system. You can generalise the context and you do not eliminate their "actuality".

Of course, the history of human thought has tended to put mathematics off in its own little corner. Ever since Pythagoras, maths has been de-naturalised and so made mystical. But that is just a prejudice which has developed.

It is the same as the desire to drive an ontic wedge between deduction and induction. :zzz:

The "scientific" attitude is really about the naturalising of knowledge - finding a way through all the mystery and posturing to a holistic, systems view, of reality. A view that does justice to the fact we are observers, as well as capturing the truth of what we can observe.

Mathematicians, like priests, philosophers and computer scientists, often don't appreciate being knocked off their pedestal of personal revelation though.

 

[SW VandeCarr]

If you are talking philosophically, there is a useful distinction between the possible and the actual. So there could be both possible contexts (worlds we can imagine in which werewolves might exist) and actual contexts (like our world).

I'm talking about meaningful statements. All possible worlds is not ontologically defined to the extent where a werewolf is defined. Your idea of a werewolf may be different than my idea of a werewolf. There is no existent that we can point to and say "That's a werewolf". That doesn't mean something could not exist somewhere that might fit our (vague) idea of werewolf. But until such a creature is discovered and described, statements about werewolves are descriptions of fantasies.

 

[Ferris_bg]

Try to imagine you posted this thread before 3k years so you can look from JoeDawg's point.

 

[SW VandeCarr]

Try to imagine you posted this thread before 3k years so you can look from JoeDawg's point.

If you're talking about belief systems based on faith, not evidence, I agree that well defined belief systems can have an ontology of their own. We can make meaningful statements about such systems. The same can be said about legal systems. They may be based partly on evidence of effectiveness, but also on what people believe is "right" or accept on faith. Clearly we can say that the speed limit on a particular road is 40 km/hr (25 mi/hr) even if we think it's ridiculously low. People study mythology and make meaningful statements about the subject matter even though they don't believe the myths.

If you want to argue that werewolves exist in the context of some mythology, I might agree if the concept was very well defined. The renditions of werewolves I've seen vary quite a bit, and they are not part of any well organized belief system that I'm aware of.

I think the test is, can you categorically say such and such a description of a werewolf is correct or incorrect within some generally accepted ontological context? For example, can we categorically say werewolves have tails?

EDIT: The problem with belief based contexts is that they are not subject to testing. Any description of their entities is limited to what the belief system allows. We cannot study the genome of a werewolf no matter how well defined it might be in some mythology. We can however study the arithmetic characteristics of the natural numbers because they are not fully understood even though they do not exist in a purely physical context.

 

[JoeDawg]

We can however study the arithmetic characteristics of the natural numbers because they are not fully understood even though they do not exist in a purely physical context.

We can study what werewolves look like within the context of the twilight movies.
We can study what natural numbers are within the context of modern mathematics.

Its true, one could argue that numbers are better defined within the context of mathematics, but numbers are also quite a lot simpler. A werewolf is a much more complex entity than a prime number. It has more dependencies.
Still, if one ignores the differences in complexity...

Human + wolf + magic= werewolf
a+b+c=d
1+2+3=6

All are abstract, all work within a set of rules, definitions or axioms.
One could even argue that all are derived from experience... the latter being simply more abstract... and less complex.

 

[SW VandeCarr]

We can study what werewolves look like within the context of the twilight movies.
We can study what natural numbers are within the context of modern mathematics.

Its true, one could argue that numbers are better defined within the context of mathematics, but numbers are also quite a lot simpler. A werewolf is a much more complex entity than a prime number. It has more dependencies.
Still, if one ignores the differences in complexity...

Human + wolf + magic= werewolf
a+b+c=d
1+2+3=6

All are abstract, all work within a set of rules, definitions or axioms.
One could even argue that all are derived from experience... the latter being simply more abstract... and less complex.

I started to edit the quote, but decided to not to. It's priceless. "Human + wolf + magic= werewolf". Observing werewolves in "twilight movies". What I can say? The philosophical musings of JoeDawg!

Just one question: Do werewolves have tails?

I learn so much in the PF philosophy forum!

 

[JoeDawg]

Just one question: Do werewolves have tails?

No idea... watch the movies and find out.

 

[SW VandeCarr]

No idea... watch the movies and find out.

Don't they wear pants in the movies?

EDIT: Will you vouch for me that this link meets PF standards?

http://horror.about.com/od/horrortoppicklists/tp/bestwerewolfmovies.htm

 

[Ferris_bg]

SW VandeCarr, no matter if its knowledge (math) or belief (werewolfs), both has dependencies. Even if you reduce knowledge to simple logic (1 + 1 = 2) it still depends on information. And again information cannot exist without dependence.

 

[SW VandeCarr]

SW VandeCarr, no matter if its knowledge (math) or belief (werewolfs), both has dependencies. Even if you reduce knowledge to simple logic (1 + 1 = 2) it still depends on information. And again information cannot exist without dependence.

I'll say this Ferris_bg; you open deep subjects with short simple statements. (that's a complement).

First, we are not necessarily talking about knowledge or information when it comes to beliefs. In general, believes are beliefs, nothing more. (The epistemological definition of knowledge is a "justified true belief" according to the Stanford Encyclopedia of Philosophy. I admit I don't know why you have to justify something if its already known to be true.) However, we can reference well defined belief systems with clear unambiguous statements. That's the simple criterion that I suggest for contextual existence. The dependence is therefore an ontological one.

What's the ontological context for the natural numbers? Axioms? Well yes. There are the Peano axioms; but we've been using arithmetic long before these axioms were developed. The subject is too deep and unsettled to get into here. However we did not invent arithmetic. We discovered it by slow degrees. IMO any intelligence would have discovered arithmetic, the same basic arithmetic, if it were to progress to a technological level. I base this opinion on the accepted belief, supported by evidence, that the structure and laws of nature are universal, at least in our known universe; and that there is some connection between these laws and the structure of arithmetic (and a lot of other math.) It's not the arbitrary invention of some neolithic genius.

Now I linked to a site where someone's opinion of the 25 best werewolf movies are discussed. It looks to me like there may be as many as 25 different, though similar, ideas of what a werewolf is. What great system of thought do werewolves belong to? What are the common constraints in referencing werewolves with crisp unambiguous statements? What is the standard? I say werewolves have tails. Am I right or wrong? No maybe.

By the way, I'm not interested in trivial private belief systems. Belief systems that meet the contextual standard must be public and accessible to anyone who might be interested in studying and referencing it.

 

[GeorgCantor]

What's the ontological context for the natural numbers?

The ontological context for information is mind and numbers are properties of whatever is described. Numbers exist both in the mind and presumably in objects(manifested as physical 'properties').

 

[GeorgCantor]

So I assumed a more general context and answered that things like the natural numbers exist outside the context of space and time.

What discrete quantities would you designate with numbers, if space and time disappeared tomorrow?

 

[SW VandeCarr]

What discrete quantities would you designate with numbers, if space and time disappeared tomorrow?

There wouldn't be anything to count presumably. My point was simply that the ontological context of numbers doesn't require that they be located in space-time. They are abstract. I can unambiguously reference numbers without any reference to any set of physical objects.

I'm not about to get into a discussion of where mathematics comes from. I read George Lakoff ('Where Does Mathematics Come From?") a few years ago and cited him in a book I wrote. He's since come in for a lot criticism. I'm not going to say more about the subject then what I've already said. The point is that we don't just imagine the number of primes between two arbitrary primes. There's exactly just so many; no more, no less, It doesn't matter what we think. It doesn't matter what we know. It doesn't matter what we think we know.

Thanks for your interest though.

 

[JoeDawg]

Don't they wear pants in the movies?

EDIT: Will you vouch for me that this link meets PF standards?

http://horror.about.com/od/horrortoppicklists/tp/bestwerewolfmovies.htm

Not sure why you're obsessing about the werewolf example.
A system is a system, as long as it has defined parameters and internal logic.

 

[SW VandeCarr]

Not sure why you're obsessing about the werewolf example.
A system is a system, as long as it has defined parameters and internal logic.

I don't know what else to say. Werewolves are fantasies. They don't exist. They are just a vague collection of ideas with no hard reality behind them for reference. You can only talk about what this person's or that person's concept of a werewolf is. What parameters or "internal logic" are you talking about?

 

[JoeDawg]

I don't know what else to say. Werewolves are fantasies.

So are numbers.

They don't exist.

Both exist as concepts, abstractions. I've never met a werewolf or a number.

They are just a vague collection of ideas with no hard reality behind them for reference.

Werewolf is a fusion of concepts, but both human and wolf have arguably more reality than the number 1. So they are quite well defined. Mathematics is very precise, but its a system that has been systematically refined for thousands of years. Your objections to their difference seem irrational.

You can only talk about what this person's or that person's concept of a werewolf is.

No, actually there is quite a bit of agreement, as well as disagreement about what a werewolf is. But again that has to do with the complexity of the term. Most english speakers, if questioned about 'what a werewolf is' could give a description that is similar and recognizable.

What parameters or "internal logic" are you talking about?

Stories and legends always have these things, to one degree or another, that is what distingishes them from random letters on a page.

You seem to be going out of your way to distinguish mathematics as some special way of thinking... when human beings have many different sorts of abstract thinking. I don't see your point.

 

[SW VandeCarr]

So are numbers. (fantasies)

I guess this is the crux of the matter. I strongly disagree. I gave an example which I will repeat:

Between any two arbitrary prime numbers, there exists a certain number of prime numbers (including zero prime numbers). There's no known pattern as to how primes occur on the number line. The number of primes between two arbitrary primes is a definite quantity, not subject to our will or whim. It exists independently of our culture or ideas. It is not a fantasy.

You didn't answer my specific question about the parameters and "internal logic" of the werewolf idea. You say stories and legends always have these things. What do you mean? What parameters? What logic? Give a specific example. I just did for my argument. You can always talk about the specifics of a particular book or movie. But that's only an instance. What's the concept? Is it vague or well defined?

 

[JoeDawg]

Between any two arbitrary prime numbers, there exists a certain number of prime numbers (including zero). There's no known pattern as to how primes occur on the number line. The number of primes between two arbitrary primes is a definite quantity, not subject to our will or whim. It exists independently of our culture or ideas. It is not a fantasy.

But prime numbers don't exist independently of mathematics, any more than werewolves exist independent of the stories about werewolves.

As an example... within mathematics you have fractions, ratios, decimals, exponents etc...

The number 1 within these different contexts is somewhat different in each( 1/1 compared to 1.00000... ) and within each, the number 1 can represent either a place value (or base) or the actual number digit.

Prime numbers may be a common relation across number systems, but so what? Nouns, verbs and pronouns are common across natural languages.

You didn't answer my question about the parameters and "internal logic" of the werewolf idea.

You may not agree, but I very much did.

As particular to werewolves, it usually involves a curse, a bite, changing during the full moon, etc...

Internal logic is essential to a good story, especially with regards to legends and 'fantasy' stories.

 

[SW VandeCarr]

Internal logic is essential to a good story, especially with regards to legends and 'fantasy' stories.

I edited my last post since you responded. You can always talk about the specifics of a book or movie about werewolves. These are just instances and of course they exist. But the concept is vague, not well defined across different representations. Books about mathematics are not mathematics. Books and stories about werewolves are not werewolves.

EDIT: Regarding your argument that prime numbers, specifically, are fantasies; I don't really think you understand the context. Books about mathematics may differ in their approach or even concepts regarding some of the subject matter. However, they will not differ on the fundamentals of arithmetic, and certainly not the prime numbers. And don't confuse the existence of numbers with the representation of numbers.

 

[JoeDawg]

Books about mathematics is not mathematics. Books and stories about werewolves are not werewolves.

And mathematics, and prime number relationships, are not prime numbers.

Stories about werewolves generally have a basic structure, stories in general tend to have a basic structure, language itself has a basic structure. That doesn't mean words or sentences can exist outside of language. Mathematics is a language.

When you are talking about abstract systems you are talking about meaning and syntax.

Prime numbers are a function of the way number systems are constructed. They don't exist outside the number system, any more than werewolves exist outside werewolf stories.

The fact mathematics is more precise in certain ways doesn't really change its abstract nature.

 

[SW VandeCarr]

Prime numbers may be a common relation across number systems, but so what? Nouns, verbs and pronouns are common across natural languages.

I want to comment on this too. I agree with this comparison because parts of speech do in fact exist independently of particular natural languages. I'm not sure how this fits in with your contention that prime numbers are fantasies.

 

[SW VandeCarr]

prime number relationships, are not prime numbers.

What does that mean?

Prime numbers are a function of the way number systems are constructed.

Wrong! Prime numbers are the fundamental elements from which the natural numbers are composed.

The fact mathematics is more precise in certain ways doesn't really change its abstract nature.

So? Abstract things exist insofar as their ontological context is well defined. Go back to my first post.

 

[JoeDawg]

What does that mean?

It means 'prime numbers' are a structure within the system, whereas one can also talk about individual prime numbers.

Wrong! Prime numbers are the fundamental elements from which the natural numbers are composed.

If you say so, but how does that make what I said wrong?

Go back to my first post.

Yeah... and?