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Logic is Metaphysics (2011) [pdf]

philpapers.org

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Re: Logic is Metaphysics (2011) [pdf]

#41

Post by bodi »

trhway wrote: post #40
jc763 wrote: post #2

>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 ou…

>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 dif…

> 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-...

Re: Logic is Metaphysics (2011) [pdf]

#42

Post by dragonwriter »

trhway wrote: post #40
jc763 wrote: post #2

>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 ou…

>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 dif…

> 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.

Re: Logic is Metaphysics (2011) [pdf]

#43

Post by raincom »

Logic is metaphysics, only when one smuggles in one's intuitions as definitionally true; otherwise, it is not so: "If we look more closely how it comes about that these existential statements are logical truths in these logical systems we see that it is only so because, by definition, a model for (standard) first order logic has to have a non-empty domain. It is possible to allow for models with an empty domain as well (where nothing exists), but models with an empty domain are excluded, again, by definition from the (standard) semantics in first order logic. Thus (standard) first order logic is sometimes called the logic of first order models with a non-empty domain. If we allow an empty domain as well we will need different axioms or rules of inference to have a sound proof system, but this can be done." (From Hofweber, Thomas, "Logic and Ontology" https://plato.stanford.edu/archives/sum2018/entries/logic-on...)

Re: Logic is Metaphysics (2011) [pdf]

#44

Post by trhway »

bodi wrote: post #41
trhway wrote: post #40

Earlier quoted context omitted.

>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 dif…

> 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 ele…

>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.

Re: Logic is Metaphysics (2011) [pdf]

#45

Post by hiker »

arto wrote: post #7
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...

Source, pretty please?

It's from https://hott.github.io/book/nightly/hott-online-1174-g29279f...

Re: Logic is Metaphysics (2011) [pdf]

#46

Post by hiker »

mbid wrote: post #28
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.

> So you think the key for understanding constructive logic is to understand some peculiar syntax.

It's not only a syntax, it's a functional programming language which turns out to be a computational model for logic.

Re: Logic is Metaphysics (2011) [pdf]

#47

Post by hiker »

Sangermaine wrote: post #10
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...

>goes through type theory, not philosophy. You’re going to be very surprised when you look up the origins of type theory.

https://en.wikipedia.org/wiki/History_of_type_theory

Not that much surprised. History of type theory is a history of trying to define precisely computation. That is, try to allow recursion but enforce that all programs terminate.

The solution to this problem these days is to use a purely functional programming language with dependent types (e.g. Homotopy Type Theory, Lean).

Haskell, for example, being a practical functional programming language, is logically inconsistent. Using the fix function:

  fix :: (a -> a) -> a
  fix f = let x = f x in x
one can produce proof of everything

  Prelude Data.Function> :t fix id
  fix id :: a
that is just an infinite loop.

In a logically consistent functional language such as Lean https://leanprover.github.io, this definition is not allowed.

Re: Logic is Metaphysics (2011) [pdf]

#48

Post by yedawg »

Isn't logic simply the understanding of cause and effect and choosing to deny or approve of a cause depending on the level of accuracy of the effect on the context. eg. Santa doesn't exist inside conventional norms. Santa could have existed, however we don't know. We have no cause to say he does exist.

Re: Logic is Metaphysics (2011) [pdf]

#49

Post by placebo »

dragonwriter wrote: post #42
trhway wrote: post #40

Earlier quoted context omitted.

>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 dif…

> 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.

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.

Re: Logic is Metaphysics (2011) [pdf]

#50

Post by Twisol »

Twisol wrote: post #21
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…

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 th…

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.
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