
Logic is Metaphysics (2011) [pdf] - lainon
https://philpapers.org/archive/ALVLIM-3.pdf
======
jc763
>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 our variables.

Good paper.

~~~
trhway
>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
different frequencies. Color is mental construct triggered by perception of EM
frequencies in specific range. Slightly different for different people.
Completely missing for cats if i remember correctly. Like the number seven
which is probably missing for cats too, and is known to be missing by various
indigenous tribes separated from our civilization - people in this tribes know
seven arrows, seven boats, ... yet completely don't understand just seven.

~~~
dragonwriter
> 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.

~~~
placebo
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.

------
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...](https://plato.stanford.edu/archives/sum2018/entries/logic-ontology/))

------
danbruc
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 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.

~~~
jjaredsimpson
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).

~~~
Twisol
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
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.

------
danharaj
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 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](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...](https://uberty.org/wp-
content/uploads/2017/06/Martin-Lof83.pdf)

This only scratches the surface.

~~~
omon
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.

~~~
TheOtherHobbes
"Intuitive" being another word for "subjective."

The experience of truth and logical consistency is entirely subjective. We can
build networks of concepts that trigger the experience in ourselves and in
others, but that doesn't make them objectively true - it makes them
subjectively persistent and shared.

We acquired a cat recently, and it's interesting that her experience of basic
spatial relationships is very different to ours.

She doesn't have the same experience of physics that we do. She sometimes gets
confused by inside vs outside, and her experience of moving objects seems to
be different to ours. She also gives the impression of experiencing hands and
feet as disconnected objects, and not part of a gestalt "human".

We have no guarantees that from an alien point of view, our own experience of
physics and of relationships doesn't have equivalent limitations. If the
limitations exist, we're not aware of them. But to the extent that our cat's
view of the world is probably recognisable by other cats, she's not aware of
her limitations either.

It's more of a stretch, but not impossible, that our experience of logical
abstraction and consistency may also have limitations. There may be non-human
viewpoints where the basic subjective qualia of truth and consistency are more
coherent, reliable, and inclusive than our own.

None of this can be proved, but it seems optimistic to me to believe that our
version of logic is as good as logic can possibly be.

~~~
omon
Yet we're able to discuss topics with each other, this is the basis of
Poincare's Inter-subjective reality. There must be some commonalities of
experience which allows us to map our whole experiences between each other. We
are definitively limited to our experience, it is impossible to discuss or
probe anything outside of it when the entire world and its phenomena is only
dictated through experience to us.

Experience is a language which makes meaning from the not-experience.

As Bohr put it, "We're all suspended in language."

------
woodandsteel
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.

------
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.

------
qntty
Ancient Greek philosophy was divided into logic, physics and ethics.
Metaphysics was categorized as logic.

------
carapace
The 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."

------
dmfdmf
Logic is based on the principle of non-contradiction (identified by
Aristotle). The principle, in all its various forms, is used to guide valid
thinking (i.e. truth) because contradictions cannot exist which is its tie to
metaphysics.

~~~
pmoriarty
_" Logic is based on the principle of non-contradiction"_

That's merely one type of logic. There are others which can deal with
contradictions. See the Wikipedia entries on _Paraconsistent logic_ [1] and
_Dialetheism_ [2].

Logicians enjoy coming up with new logics that have any desired or interesting
properties. They are not limited to staying within the bounds of classical
logic.

[1] -
[https://en.wikipedia.org/wiki/Paraconsistent_logic](https://en.wikipedia.org/wiki/Paraconsistent_logic)

[2] -
[https://en.wikipedia.org/wiki/Dialetheism](https://en.wikipedia.org/wiki/Dialetheism)

------
hiker
The key to understanding logic constructively goes through type theory, not
philosophy.

I'll just leave this here
[https://78.media.tumblr.com/bfc158b432199a3e4f5de2ddc1bd7381...](https://78.media.tumblr.com/bfc158b432199a3e4f5de2ddc1bd7381/tumblr_nuj7qbMUa71qc38e9o1_1280.png)

~~~
arto
Source, pretty please?

~~~
hiker
It's from [https://hott.github.io/book/nightly/hott-
online-1174-g29279f...](https://hott.github.io/book/nightly/hott-
online-1174-g29279f5.pdf#page=23)

~~~
arto
Thanks!

