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What I took away: If you want to say 'Santa Claus doesn't exist', you can't write a formula ~E x. x=Santa Claus. Because then you are conceding in your logic t

What I took away: If you want to say 'Santa Claus doesn't exist', you can't write a formula ~E x. x=Santa Claus. Because then you are conceding in your logic that some object Santa Claus exists. So there is some connection between the structure of sentences we can construct in our logic and metaphysical claims. We should then try to understand differences in metaphysical claims by finding differences in logics. The author then tries to show this for the metaphysical claim, 'Statements are true or false independent of whether they can be verified.' Instead of arguing about what is truth, what does it mean for a proposition to be verified. We can instead as about the differences in the logic. Because to even talk about truth and existence we need a logic first. So don't think there is a claim that choice of logic forces claims about real world existence. I think is the more subtle connection, that choice of logic forces a choice about rules of inference. Real world claims would need to be based on introducing propositions (which are independent of the logic?) and then using rules of inference (which are dependent on the logic).

ethn 8y ago
The platonic "Santa Claus" does exist, so it's completely valid. The statement "Santa Claus doesn't exist" is stating there is no judgement from experience which adheres to the concept of Santa Claus.
- danbruc 8y ago
  The platonic "Santa Claus" does exist, so it's completely valid. Most if not all people would would certainly agree that the idea or concept of »Santa Claus« exists in some way. But when you qualify it with »Platonic« you are implying - intentionally or not - a quite specific view about the nature of abstract objects and that will decrease the number of people agreeing with this statement substantially.
  - omon 8y ago
    Not really it's a common noun, which just means non-physical objects which exist in some way, even if Nominalist. You're confusing platonic with Platonic realism which are different things. But perhaps he should edit it to be more clear if the mistake is quite common, albeit perhaps meaning espoused by capitalization has been forgotten.
    - danbruc 8y ago
      In German we do not have that distinction between the different capitalizations, at least not that I am aware of, and the usage of platonic is probably essentially limited to platonic love and relationships. Something learned about the subtleties of the English language.
      - mcbits 8y ago
        We don't have that distinction in English, either. Words derived from names just tend to lose their capitalization over time and may gradually be diluted in meaning as people use them without understanding their origin.
        ethn 8y ago
        Bold, passive, and mistaken accusation: https://en.wikipedia.org/wiki/Proper_noun https://en.wikipedia.org/wiki/Proper_noun But I do see how it could be confused with platonic love, albeit I'm comfortable using it without clarification in the appropriate contexts. You're right, in German all nouns are capitalized.
        mcbits 8y ago
        A more appropriate Wikipedia article: https://en.wikipedia.org/wiki/Theory_of_forms https://en.wikipedia.org/wiki/Theory_of_forms If you simply meant to say that the idea of Santa Claus obviously "exists" in some sense, thus it's valid to compare our experiences with that idea, then I agree with the comment saying a lot of people would agree with you, but "platonic" is ambiguous at best. If you really did mean to imply that an ideal Santa Claus literally exists in a literal universe of perfect ideal forms, out of which everything in our universe emerges as an imperfect projection, then I agree with the other part of the comment saying you'll find much less agreement with that claim. My comment was that the loss of capitalization and the loss of the word's original meaning are independent phenomena. I.e. the adjective "Platonic" is often being used in the diluted sense of "conceptual" or "mental image of", and that has nothing to do with capitalization.
danbruc 8y ago
I think we mostly understand the paper the same way. Still this seems utterly unremarkable to me, but maybe I am still just missing the important point. If you want to come up with a language to talk about the world, a logical system in this case, you make choices. You decide if you want to be first order or higher order, whether you want temporal facts, what you allow your variables to range over, which inference rules to use, and what predicates you allow. Or whatever else. If you only want to talk about physical things, you may be able to get away with existential qualification. If you also want to deal with concepts like Santa Claus you probably have to be more sophisticated because now »exists« is an overloaded term in your domain and throwing the same existential qualifiers in front of everything won't yield results that can be meaningfully translated to statements about the world. In the end you have the world, you have a model of the world in your logic, and you have some kind of mapping between the world and your model, most likely even on a meta level. Not only do objects in your logic have to be related to objects in the world, but the very structure of your logic, its inference rules, the allowed constructs, and so on, have to map to some of the structure of how the world works. So as I said, it should come at no surprise that differences in logic have to be equated with differences in the world you are modelling, but the real significance of that, if any, is still beyond me.
- empath75 8y ago
  It seems to me that it’s possible to use logic while having no belief at all as to whether that logic has any connection to reality — it could simply be an exercise in symbol manipulation with no meaning at all, which is the formalist position. A formalist would have no problem using a logical system that implies a particular belief about existence while not holding that belief at all.
  - danbruc 8y ago
    Sure, but if you are only doing string manipulation with your logic, then you are doing mathematics and not philosophy. There is absolutely nothing wrong with that but it also says nothing about the relation between logic and metaphysics.
Twisol 8y ago
So this is a bit of a tangent, but your Santa Claus example really clarified something I've been reading about recently. I'm reading Lloyd's "Foundations of Logic Programming", which essentially explains the fundamentals behind logic languages like Prolog. We write programs using uninterpreted functions[0] to represent our data, and define predicates to drive the program. The idea of using the Herbrand universe is that it gives a convenient universal starting point: if the program has a model in some universe, it will have a model in the Herbrand universe, and if the program does not have a model, it cannot have a model in the Herbrand universe. Your Santa Claus example helped me understand why the Herbrand universe is only useful if you restrict yourself to clauses (disjunctions under universal quantification). The Herbrand universe consists of all objects one has named (and objects one can form with function symbols, but we have none of those here), so it must necessarily falsify "~E x. x = Santa Claus". It's easy to find a model where this statement is true (take the empty universe, or the universe which contains only the Tooth Fairy), but there is no model of this statement in the Herbrand universe. [0] https://en.wikipedia.org/wiki/Uninterpreted_function https://en.wikipedia.org/wiki/Uninterpreted_function
- Twisol 8y ago
  I guess I can't really edit this comment anymore, but it looks like I was wrong. That example is actually a perfectly valid clause, since it's equivalent to "forall x. ~(x = Santa Claus)". The only reason no model satisfies this clause is because we conventionally require equality to be reflexive, but for an arbitrary predicate the empty model would be a perfectly good model in the Herbrand universe.
deleted 8y ago
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nurettin 8y ago
I have been trying to articulate this important distinction to people. The notion that properties and conditions for existence need to be thoroughly defined and unified in order to discuss whether a meta has those properties.

ethn 8y ago

The platonic "Santa Claus" does exist, so it's completely valid. The statement "Santa Claus doesn't exist" is stating there is no judgement from experience which adheres to the concept of Santa Claus.

danbruc 8y ago
The platonic "Santa Claus" does exist, so it's completely valid. Most if not all people would would certainly agree that the idea or concept of »Santa Claus« exists in some way. But when you qualify it with »Platonic« you are implying - intentionally or not - a quite specific view about the nature of abstract objects and that will decrease the number of people agreeing with this statement substantially.
- omon 8y ago
  Not really it's a common noun, which just means non-physical objects which exist in some way, even if Nominalist. You're confusing platonic with Platonic realism which are different things. But perhaps he should edit it to be more clear if the mistake is quite common, albeit perhaps meaning espoused by capitalization has been forgotten.
  - danbruc 8y ago
    In German we do not have that distinction between the different capitalizations, at least not that I am aware of, and the usage of platonic is probably essentially limited to platonic love and relationships. Something learned about the subtleties of the English language.
    - mcbits 8y ago
      We don't have that distinction in English, either. Words derived from names just tend to lose their capitalization over time and may gradually be diluted in meaning as people use them without understanding their origin.
      - ethn 8y ago
        Bold, passive, and mistaken accusation: https://en.wikipedia.org/wiki/Proper_noun https://en.wikipedia.org/wiki/Proper_noun But I do see how it could be confused with platonic love, albeit I'm comfortable using it without clarification in the appropriate contexts. You're right, in German all nouns are capitalized.
        mcbits 8y ago
        A more appropriate Wikipedia article: https://en.wikipedia.org/wiki/Theory_of_forms https://en.wikipedia.org/wiki/Theory_of_forms If you simply meant to say that the idea of Santa Claus obviously "exists" in some sense, thus it's valid to compare our experiences with that idea, then I agree with the comment saying a lot of people would agree with you, but "platonic" is ambiguous at best. If you really did mean to imply that an ideal Santa Claus literally exists in a literal universe of perfect ideal forms, out of which everything in our universe emerges as an imperfect projection, then I agree with the other part of the comment saying you'll find much less agreement with that claim. My comment was that the loss of capitalization and the loss of the word's original meaning are independent phenomena. I.e. the adjective "Platonic" is often being used in the diluted sense of "conceptual" or "mental image of", and that has nothing to do with capitalization.

danbruc 8y ago

I think we mostly understand the paper the same way. Still this seems utterly unremarkable to me, but maybe I am still just missing the important point. If you want to come up with a language to talk about the world, a logical system in this case, you make choices. You decide if you want to be first order or higher order, whether you want temporal facts, what you allow your variables to range over, which inference rules to use, and what predicates you allow. Or whatever else. If you only want to talk about physical things, you may be able to get away with existential qualification. If you also want to deal with concepts like Santa Claus you probably have to be more sophisticated because now »exists« is an overloaded term in your domain and throwing the same existential qualifiers in front of everything won't yield results that can be meaningfully translated to statements about the world. In the end you have the world, you have a model of the world in your logic, and you have some kind of mapping between the world and your model, most likely even on a meta level. Not only do objects in your logic have to be related to objects in the world, but the very structure of your logic, its inference rules, the allowed constructs, and so on, have to map to some of the structure of how the world works. So as I said, it should come at no surprise that differences in logic have to be equated with differences in the world you are modelling, but the real significance of that, if any, is still beyond me.

empath75 8y ago
It seems to me that it’s possible to use logic while having no belief at all as to whether that logic has any connection to reality — it could simply be an exercise in symbol manipulation with no meaning at all, which is the formalist position. A formalist would have no problem using a logical system that implies a particular belief about existence while not holding that belief at all.
- danbruc 8y ago
  Sure, but if you are only doing string manipulation with your logic, then you are doing mathematics and not philosophy. There is absolutely nothing wrong with that but it also says nothing about the relation between logic and metaphysics.

Twisol 8y ago

So this is a bit of a tangent, but your Santa Claus example really clarified something I've been reading about recently. I'm reading Lloyd's "Foundations of Logic Programming", which essentially explains the fundamentals behind logic languages like Prolog. We write programs using uninterpreted functions[0] to represent our data, and define predicates to drive the program. The idea of using the Herbrand universe is that it gives a convenient universal starting point: if the program has a model in some universe, it will have a model in the Herbrand universe, and if the program does not have a model, it cannot have a model in the Herbrand universe. Your Santa Claus example helped me understand why the Herbrand universe is only useful if you restrict yourself to clauses (disjunctions under universal quantification). The Herbrand universe consists of all objects one has named (and objects one can form with function symbols, but we have none of those here), so it must necessarily falsify "~E x. x = Santa Claus". It's easy to find a model where this statement is true (take the empty universe, or the universe which contains only the Tooth Fairy), but there is no model of this statement in the Herbrand universe. [0] https://en.wikipedia.org/wiki/Uninterpreted_function https://en.wikipedia.org/wiki/Uninterpreted_function

Twisol 8y ago
I guess I can't really edit this comment anymore, but it looks like I was wrong. That example is actually a perfectly valid clause, since it's equivalent to "forall x. ~(x = Santa Claus)". The only reason no model satisfies this clause is because we conventionally require equality to be reflexive, but for an arbitrary predicate the empty model would be a perfectly good model in the Herbrand universe.

deleted 8y ago

[deleted]

nurettin 8y ago

I have been trying to articulate this important distinction to people. The notion that properties and conditions for existence need to be thoroughly defined and unified in order to discuss whether a meta has those properties.