Ancient Greek philosophy was divided into logic, physics and ethics. Metaphysics was categorized as logic.
Logic is Metaphysics (2011) [pdf]
11–20 of 64 posts
Re: Logic is Metaphysics (2011) [pdf]
#12I 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 of logic and they lead to different conclusions or contradict each other in the general case. Therefore it seems to me that the obvious thing to say is that logic is a human construct we use to reason about the world, it does not reflect universal truths but was invented and constructed in a way to be useful to deal with our world.
In consequence it is obviously very likely that logic and metaphysics are strongly correlated, but that would hardly be any deep insight but just a consequence of the way we constructed or choose the logic we use. If the logic I use to deal with the world makes a prediction about the world, for example the existence of a certain entity, then that entity might actually exist if may logic is a good match for the world, but I see no reason why the entity would have to exists, my logic could just be a bad choice.
Re: Logic is Metaphysics (2011) [pdf]
#13A 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 answering questions of no interest. Girard is an entertaining source of both philosophical and technical insight: On the meaning of logical rules I : syntax vs. semantics http://girard.perso.math.cnrs.fr/meaning1.pdf
Per-Martin Lof's ideas are also important: ON THE MEANINGS OF THE LOGICAL CONSTANTS AND THE JUSTIFICATIONS OF THE LOGICAL LAWS https://uberty.org/wp-content/uploads/2017/06/Martin-Lof83.p...
This only scratches the surface.
Re: Logic is Metaphysics (2011) [pdf]
#14The first step in any logic is to make a distinction. This act is within the mind. The world itself is unknown except as sensory experience. Leaving aside the so-called "Hard Problem of Consciousness" for the sake of discussion, the fact that distinction happens in our heads means that all of our logic is contingent (as opposed to inherent) if our thinking is wholly internal to our brains.
However... none other than Kurt Gödel believed that thinking about e.g. infinities involved a kind of perception of a "higher" world.
"Science does not remove the Terror of the Gods."
Re: Logic is Metaphysics (2011) [pdf]
#15I 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 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).
Re: Logic is Metaphysics (2011) [pdf]
#16>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…
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.
Re: Logic is Metaphysics (2011) [pdf]
#17I 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…
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.
Re: Logic is Metaphysics (2011) [pdf]
#18A 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…
> Philosophy without technical input is sophistry, technical developments without philosophy end up answering questions of no interest.
This is such a great formulation.
Re: Logic is Metaphysics (2011) [pdf]
#19I 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…
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.
Re: Logic is Metaphysics (2011) [pdf]
#20A 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…
> Philosophy without technical input is sophistry, technical developments without philosophy end up answering questions of no interest. This is such a great formulation.
I should say, definitely not mine. I don't know where I got it, or where they got it.