Saturday, April 17, 2021

Regular Hyperreal and Qualitative Probabilities Invariant Under Symmetries

I just noticed that my talk "Regular Hyperreal and Qualitative Probabilities Invariant Under Symmetries" is up on YouTube. And the paper that this is based on (preprint here) has  just been accepted by Synthese.


Manuel said...

Please,How do we reconcile the PSR and the concept of brute facts?

Alexander R Pruss said...

You don't, at least not for contingent facts. The PSR says every contingent fact has an explanation. A brute fact is defined as one that has no explanation.

Alexander R Pruss said...

Basically, the PSR just says there are no brute facts.

Unknown said...

Unrelated but why would anyone reject methodological naturalism? I do not understand why I should accept unfalsifiable explanations based on theological virtue. Got any works on this?

Alexander R Pruss said...

Strictly speaking, pretty much all scientific explanations are unfalsifiable. All we can do is find evidence against them, but that evidence never pushes the proposed explanation to probability zero. What about theological hypotheses? Well, unless the hypothesis is accepted with credence one (say, on faith or due to a completely conclusive argument), there will be potential evidence that can raise or lower its probability, and there will be potential evidence that can lower its probability close to zero. So there is no falsifiability difference between scientific and theological explanations, unless one makes the further step of accepting the theological ones with credence one.

Manuel said...
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Manuel said...
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Manuel said...

[Please don't think I'm spamming you,I just corrected a few mistakes]

First and foremost,I have to say that I'm highly appreciative of your reply,
And I still have some more questions,I hope I'm not causing you inconvenience:

1]So okay, judgin by your reply,it seems to mean that the truth of PSR entails that there are no brute facts,it's a mutually exclusive state of affairs–either the PSR is true or brute facts exist,please inform me if I'm misinterpretin you.

But,I seem to be a little bit confused about this, doesn't it mean we'd go into radical positions–we'll have to deny that there are no such things as axioms,axioms by definition have their truths and factuality unexplained [cannot be proven], they're just self evidently true.

2] And I use to hear this thing about randomness being self explanatory,or even a brute fact,I'd like to confirm if it's true?

3) Can't the open question argument by Moore be also applicable to theological groundings of morality in God?
I thought of a way that one could circumvent that and make theism immune to it–Naturalism means that the "good" is REDUCIBLE to natural properties, whereas Theists simply assert that good is GROUNDED in God,or to put it in another way,God=Good.
But I'm stuck with a couple of issues here:
✓The Naturalist could also take my route and say that the Good is grounded in Natural properties
✓I can't seem to get a proper distinction between "grounded in" and "reducible to" that is relevant to this case.
✓I think that even if I succeed,the open question argument may still be assailable when used to attack theistic ideas.

Or is there another way?

(To be continued....)

Manuel said...

.....Finally, and kinda I feel,most importantly 4)
I came across this video on The “Capturing Christianity” YouTube Channel:
[I would've put the link here,but it's not working,in getting “Your HTML cannot be accepted” as feedback]

Where the guest speaker,Dr James N. Anderson,was effectin some lucubrations on an argument for God's existence–the Argument from Logic,I'm sure you're familiar with this argument.
Some take this form:
P1. Logic is an idea.
P2. Logic exists Necessarily
P3. Ideas can only exist in minds
Conclusion: Logic can only exist in a Necessary mind–God exists[ his arguments were a bit different]

However,A certain commenter gave this comment:

“"The laws of logic are necessary truths"

And already I disagree. That was fast.

Logical truths are in a category BEYOND necessary and contingent truths, because while necessary and contingent truths are true in, or of, a possible world, logical truths are presupposed in the very utterance of the phrase "possible world".

Let's illustrate this with a pretty non-contentious mathematical truth which necessarily holds and then show how the law of non contradiction for example is in a wholly different category.

Pick any possible world.

(To be continued....)

Manuel said...

....In that possible world, it's true that if you were in a possible world in which space was flat, the pythagorean theorem holds.

This is what makes the pythagorean theorem "necessary" is the fact that even in a world in which there was no flat space, possibly there could be (in a different world). Then given that fact, the pythagorean theorem is correspondingly true.

That's an example of a necessary truth and why truths are necessary. But what of the law of non contradiction? Is the law of non contradiction of the form: "Given a world in which P: P"? Nope! It's deeper even then that.

Suppose you're in a possible world, W, in which F1 holds. Now my very utterance of that sentence pre-supposes several things:

1. I'm discussing ONE possible world and not others (uniqueness)
2. This possible world is defined in part by F1, and I would be talking about a different world if F1 didn't hold.

1 and 2 combined depend on the law of non contradiction. For if F1 and not F1 were true at the same time, then by 2 I would be in W and also fail to be in W.

But my failing to be in W and being in W means we are no longer talking about a unique possible world, violating 1.

Point being then that you can't even utter the phrase "suppose you're in a possible world where..." without assuming the truth of the law of non contradiction. Notice too that I don't have to know anything else about a possible world other than that we're in "one" and a definition of possible world that defines them in terms of "facts about" those worlds. That's it. The second I have that structure, I can't talk about modal logic AT ALL unless I have the law of non contradiction.

So trying to say that LNC is true "in all possible worlds" misses the point that you can't even utter the phrase "in all possible worlds" without presupposing the LNC. The LNC isn't "a necessary" truth, it's so baked into our language syntax, that uttering the word "necessary" makes no sense without its being under the hood.

I also disagree that "a truth" is "a true proposition". I think ineffable truths are fine - just privately held. Now if you want to say that all public truths are true propositions, I have no disagreement with that.

I disagree that propositions are real entities. Rasmussen and Malpass had a good discussion about this. Lots of paradoxes derail this kind of thinking. I think that propositions are linguistic markers "about" patterns that possibly exist, and it's the broad possibilities that necessarily exist (as possibilities) by S5.

I definitely disagree that propositions are mental entities. I think that there are thoughts "about" propositions which are mental activities, but that has no bearing on the propositions themselves.

Propositions are just carriers of modal information about possible circumstances, codified in language and processed by minds.

(To be continued....)

Manuel said...

(Last one)

..... The fact that propositions are independent of their linguistic expression just means that the underlying pattern they represent is independent of linguistic expression (indeed the patterns may hold in possible worlds in which there is no language!). But notably the same patterns articulable as propositions could hold even in worlds with no minds.

There would just be no minds in that world to think "about" the patterns and express them as propositions.

Now looking at the structure of the whole argument, there's a massive problem here. The laws of logic are supposed to be “necessary thoughts”, Problem is,you can't even talk about “a” thought without pressuposing the laws of logic.Again, without the LNC,you loose uniqueness,
You have to talk about all thoughts at once,or one thought contains everything.
So the LNC isn't a thought,rather,it's a built-in assumption for there to BE “thoughts”.This is putting billions of carts before the horse got there.”

Then he continues with explanations:

“The category error is strong with you. I'll break it down for you.

The law of non-contradiction is built into the structure of possible worlds.

It isn't a proposition that has any truth value within (or between) any possible worlds.
It's not like the contingently true statement "My name is Tommy", the possibly true statement "2+2=4" or the necessarily true statement "in a flat Euclidean space, the pythagorean theorem holds."
In order to even say any of these things, you have to assume the LNC.
Any and all discourse about any possible worlds comes with the LNC attached.
Once you remove the LNC, you aren't describing possible worlds, you're describing nonsense”

I think this objection to that video is very lethal that it just reverses the original argument–instead of logic being grounded in God,God is then grounded in logic,it just undermines everything about theology

That'd be also tantamount to saying that God “needs”logic inorder to exist in all possible worlds,[which would contradictory, because God by his essence should be self sufficient and not need anything].
With so many other implications that every theologian and Christian Philosopher would wish to avoid.

I'd like to hear your thoughts on this

Manuel said...

P S:
The video is titled: “Logic Therefore God”