Logic is Metaphysics (2011) [pdf] • Hacker News Board

Re: Logic is Metaphysics (2011) [pdf]

#21

Post by Twisol » Wed, Jun 06, 2018, 10:13 PM UTC

jjaredsimpson wrote: post #15

danbruc wrote: post #12

I am not sure whether I really understand what the author argues for, probably because I read the paper in a rush. Does he argue that [the choice of] a logic is in some sense equivalent to [a choice of] what kind of entities exist? If that is indeed the case, I would tend to disagree. While we often think of logic as a provider of undisputable truth, I am not sure that this is justified. There is more than one type o…

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 a…

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

Re: Logic is Metaphysics (2011) [pdf]

#22

Post by omon » Wed, Jun 06, 2018, 10:13 PM UTC

danharaj wrote: post #13

A philosophical discussion of logic in this decade should at least be aware of the Curry-Howard isomorphism and Linear Logic. This paper makes a passing mention of this by treating the law of excluded middle. I would say that denying that law has led to the most fruitful developments of logic in the last century. Philosophy without technical input is sophistry, technical developments without philosophy end up answeri…

Wholly irrelevant, the paper is specifically concerned with recovering a dialectic between W. O. Quine and M. Dummett. Even if the question was the more general, "Is Logic Metaphysics?", knowledge of formal logics isn't even of concern. It's trivial that we can construct a plethora of axioms with their own definitions, the problem remains: to even adhere to those definitions one is exercising another intuitive logic—even in the case of computation which is an engineered construction to proxy this very intuition, otherwise we would have never been concerned with the linear properties necessary for computation to begin with.

Re: Logic is Metaphysics (2011) [pdf]

#23

Post by danbruc » Wed, Jun 06, 2018, 10:19 PM UTC

ethn wrote: post #17

jjaredsimpson wrote: post #15

Earlier quoted context omitted.

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 a…

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.

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.

Re: Logic is Metaphysics (2011) [pdf]

#24

Post by omon » Wed, Jun 06, 2018, 10:28 PM UTC

danbruc wrote: post #23

ethn wrote: post #17

Earlier quoted context omitted.

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.

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.

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.

Re: Logic is Metaphysics (2011) [pdf]

#25

Post by empath75 » Wed, Jun 06, 2018, 10:43 PM UTC

danbruc wrote: post #19

jjaredsimpson wrote: post #15

Earlier quoted context omitted.

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 a…

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 ru…

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.

Re: Logic is Metaphysics (2011) [pdf]

#26

Post by danbruc » Wed, Jun 06, 2018, 10:46 PM UTC

omon wrote: post #24

danbruc wrote: post #23

Earlier quoted context omitted.

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.

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.

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.

Re: Logic is Metaphysics (2011) [pdf]

#27

Post by danbruc » Wed, Jun 06, 2018, 10:52 PM UTC

empath75 wrote: post #25

danbruc wrote: post #19

Earlier quoted context omitted.

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 ru…

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.

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.

Re: Logic is Metaphysics (2011) [pdf]

#28

Post by mbid » Wed, Jun 06, 2018, 10:59 PM UTC

hiker wrote: post #4

The key to understanding logic constructively goes through type theory, not philosophy. I'll just leave this here https://78.media.tumblr.com/bfc158b432199a3e4f5de2ddc1bd7381...

So you think the key for understanding constructive logic is to understand some peculiar syntax for a fragment of it. Ridiculous, but sadly quite typical among type theory cultists.

Re: Logic is Metaphysics (2011) [pdf]

#29

Post by mcbits » Wed, Jun 06, 2018, 11:12 PM UTC

danbruc wrote: post #26

omon wrote: post #24

Earlier quoted context omitted.

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.

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.

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.

Re: Logic is Metaphysics (2011) [pdf]

#30

Post by woodandsteel » Wed, Jun 06, 2018, 11:38 PM UTC

Logic, to be of any use in the real world, must in some important ways match the reality of the world. So any system of logic assumes a metaphysics. And going the other way, reality must be such as to be able to have creatures who can think logically.

This is one instance of a larger principle, namely the inherent mutual interconnectedness of the various areas of philosophy. So for instance, epistemology depends on reality being such that it can be known, and we can know about that reality only the sorts of things that a valid epistemology can determine. Similar mutual relations exist between every two main areas of philosophy.

This mutual interconnectedness is a key reason for Neurath's insight that in philosophy you can't tear it all down and change it radically, but only modify it.