(There's a direction-of-fit thing here: in one case, the center determines the circle; in the other, the circle determines the center.) — Srap Tasmaner

There are different ways to rationally conceive or define (and draw) a circle. Equidistance from a point is one. Aristotle prefers another, "The locus of points formed by taking lines in a given ratio (not 1 : 1) from two given points (KM1 : GM1 = KM2 : GM2 = ...) constitute a circle":



But what a circle is and how a circle is drawn are two different things. Similarly, two different ways of conceiving a circle are immaterial to the question at hand when they are formally equivalent, as is the case here. When I gave some arguments against square circles, I suggested that one could quibble with the arguments, but not oppose them in any way that goes beyond a quibble. I think that has turned out to be right. Aristotle's circle and Euclid's circle are formally equivalent. The definition of a circle is not specifying the manner in which a circle is created; it is specifying what a circle is.

- :up:

-

The two arguments (mine and the OP) are logically equivalent under deductive logic. — Hanover

Except they're not, because your "So..." is entirely different than the OP's "So..." I explained this <here>. — Leontiskos

Teasing this out a bit more, the OP contains an implicit move, "Supposing God does not exist..., I should not pray." The formal translation does not take this route, but the connotation is part of the parlor trick.

The parallel in your own example is, "Supposing I am not a billionaire..., I should not scream."

They are completely different. The implicit connotation in the OP makes perfect sense. Your parallel is perfect nonsense. Not all parlor tricks are created equal. The parlor trick of the OP is a great deal better than your attempt regarding billionaires. Your argument possesses no plausibility because it is so obviously unsound. You are trying to make yourself a billionaire with specious reasoning. The OP is not praying on the supposition that God does not exist.

- :up:

Earlier logicians had drawn up a number of rules of inference, rules for passing from one proposition to another. One of the best known was called modus ponens: ‘From ‘‘p’’ and ‘‘If p then q’’ infer ‘‘q’’ ’. In his system Frege claims to prove all the laws of logic using this as a single rule of inference. The other rules are either axioms of his system or theorems proved from them. — A New History of Western Philosophy, by Anthony Kenney, 155

Contemporary logicians like Enderton and Gensler begin the exact same way. Other starting points are possible, but they are not all on a par if one wants to do actual logic. Of course for metamathematics the starting point is arbitrary. Banno, under the spell of metamathematics, will be at a complete loss before your question about how true reasoning and logic interrelate. As Apokrisis has pointed out numerous times, Banno begins and ends with nothing more than a bit of posturing.

- I am very familiar with Buddhism on its own terms, and I was once a practitioner. It is surely not exactly the same, but the point here is that for the Western mind two-truth theories are either unnecessary or problematic. If the two domains in question do not interact, then it is unnecessary. If the two domains in question do interact, then a two-truth theory is a simplistic bandage on a rather difficult problem. I consider that route a temptation, not a promise. And the concept of methodological naturalism is always flirting with two-truth theories, so this is very relevant.

As to Buddhism, it is strongly influenced by a significantly dualistic ontology in a way that the West is not. I think the Buddhist theory is also wrong, but it is more complicated given the way that it fits more nicely into that organic dualistic ontology. Beyond that, Buddhism grows out of praxis and Western science grows out of theoria, and therefore these are very different animals (even though the West is now becoming preoccupied with a different praxis, namely a Baconian praxis).

- Sure, but Popper's criterion is very strict and seldom followed, given the way that it excludes the soft sciences. Physicalism is metaphysical, and it is also one possible paradigm for scientific inquiry. It is falsifiable in the way that any paradigm is falsifiable, but as you say, not as a theory of the hard sciences. Again, "Metaphysical theories are just a bit harder to falsify insofar as they draw nearer to first principles and presuppositions."

The point here is that the metaphysics involved in physicalism and the metaphysics that I would argue is present in methodological naturalism are adjudicable and non-arbitrary, and therefore they do not succumb to the critiques of metaphysics that many have leveraged. We don't need to be afraid of metaphysics, or believe that it represents some kind of unadjudicable free for all.

- The West rejected the two-truth theory in the Medieval period, and I think it did so for good reason. Simplifying, some theologians at that time posited the idea that there are scientific truths and theological truths, and never the twain shall meet. The two kinds of truth were said to be unable to contradict each other by definition, because they are hermetically separated. I take it that such schizophrenic approaches are very bad, and that it is similar to ask the non-naturalistic scientist to "turn on" a belief in naturalism when he walks into the office and "turn it off" when he leaves. I don't think that sort of bifurcation makes any sense, metaphysically or psychologically.

It appears to me that you miss the point. Physicalism is a metaphysical theory, not a scientific theory. All coherent metaphysical theories are unfalsifiable. It's certainly reasonable to remain agnostic to metaphysical theories, but it's not UNreasonable to treat some metaphysical theory as a working hypothesis to see if it can account for everything we know about the world. Personally, I treat physicalism is the most reasonable default position- my working hypothesis, so I label myself a physicalist. I haven't encountered anything that isn't explainable from this framework... — Relativist

I think you make fair points here, and you are giving my theoretical physicalist rejoinder flesh and blood, which is helpful. But it doesn't sound like you treat physicalism as unfalsifiable. In fact it seems like you believe physicalism would be falsified insofar as you encounter things which are not explainable within the physicalist framework. I think that's as it should be, and what it means is that metaphysical theories are not unfalsifiable. Metaphysical theories are just a bit harder to falsify insofar as they draw nearer to first principles and presuppositions.

- I only meant the foundation of the logical system. Frege's foundation is explicitly modus ponens, and many propositional systems similarly ground themselves in modus ponens. In fact we can think of modus ponens as the basis for the material conditional in propositional logic, where the modus ponens inference is more intentionally foundational to the system than the idiosyncratic behavior of the material conditional (which we are considering elsewhere). I tried to speak a bit to the odd foundationalness of modus ponens <here>.

If you want something more universally foundational, I would point to the principle of non-contradiction, and ultimately its unique character of being simultaneously subjective and objective, which Kimhi alludes to. A lot of the silliness in this thread is either a direct or indirect attack on the PNC.

- I was interpreting you, not Carroll.

yet — Banno

Yet. (!)

I'd vote yes. I think there are plenty of scientists who are to all intents physicalist as far as their work is concerned but agnostic or open-minded with respect to matters that can't be adjuticated by science. — Wayfarer

Well again, the definition of science comes into it.

If methodological naturalism means (temporarily) behaving as if naturalism is true, and if science is bound up with methodological naturalism, then to instruct someone to, "Behave as if you're doing science," amounts to the same thing. Yet the instruction, "Behave as if you're doing science," is useful in showing up the circularity of the argument in question.

And as far as your set of interests are concerned, I would say that methodological naturalism is little more than a stand-in for mechanistic natural philosophy. It asks us to behave as if mechanistic natural philosophy is true. But if mechanistic natural philosophy is false, then why would we behave as if it is true? This is one example of what I meant earlier when I said that for the non-naturalist methodological naturalism is irrational. Then the rejoinder says that science itself presupposes the scientist's behaving as if mechanistic natural philosophy is true. The obvious question is, "Why?" Why accept such a definition of science?

- The closer you get to the foundation, the surer it becomes. For example, modus ponens is arguably the most basic inference or law of propositional logic, and I don't see that it fails.

Circles are straight lines. Squares are circles. Logic is just the manipulation of symbols. And there are no laws of logic. Really a brilliant thread, all around. Everyone here deserves a pat on the back. :wink:

I can't wait until tomorrow, when we show that 2+2=5.

It would appear obtuse to the layman, and maybe it just is. — Leontiskos

- I agree. :up:

"Just the place for a Snark!" the Bellman cried,
As he landed his crew with care;
Supporting each man on the top of the tide
By a finger entwined in his hair. — Banno

And @Hanover, here we see Banno abandoning his Godless ways:

Snark = Jonah
Bellman = God
Crew = Jonah's shipmates

The Biblical allusion is too obvious to ignore. Banno made light of belief in his OP, and now a strange twist of fate has brought it about that his OP led to his belief, not unlike the subject of the OP. :grin:

My question still stands, what’s the use of symbolic logic if the analysts comes before the logic? — schopenhauer1

Well, at the very least it is a useful aid for error-checking, even if it is not infallible. It represents a form of calcified analysis that is useful but limited. And it is useful for conceptualizing extended arguments that are difficult to capture succinctly. There are probably other uses as well. I have fought lots of battles against the folks in these parts who have a tendency to make formal logic an unimpeachable god, so I agree with the sort of objection you are considering.

(There is also a normative use in teaching reasoning skills, for we have some common sense intuitions which are fallacious, and which can be ironed out easily with formal logic. seems to overlook this latter point in his analysis of Aristotle.)

- This OP should not cause you to despair of logic, lol. As I've noted elsewhere, the material conditional is a disproportionately artificial logical construct. A false antecedent makes a material conditional true, and this is something like a bug or at least dross. Much like a bit of imperfect code, as long as you don't exploit the bug the logic is useful. The OP is a fun way of exploiting this bug, among other things. I don't think it is meant to be more than that.

I would give @Banno the credit of levity here, not snark. It is a philosophical joke, aptly placed in the lounge. The justifiable decision to not pray turns out to backfire and prove God's existence, given a logical translation that is initially plausible. Hanover is reading all sorts of strange things into the OP.

Do they need to be counterexamples to Aristotle? — Moliere

They are supposed to be objections to Aristotle, so yes, of course they do. You might as well have objected to Mr. Rogers by telling us that you prefer people who put on shoes. Mr. Rogers puts on shoes in every episode.

(1) is false. (1)

Read that as (1) being the name of the sentence so that the sentence references itself like we can do in plain English. — Moliere

As has been pointed out numerous times, this is just gibberish. What do you mean by (1)? What are the conditions of its truth or falsity? What does it mean to say that it is true or false? All you've done is said, "This is false," without telling us what "this" refers to. If you don't know what it refers to, then you obviously can't say that it is false. You've strung a few words together, but you haven't yet said anything that makes sense.

I guess the silence speaks for itself :meh: — schopenhauer1

Hanover's trying to tell us something?

The two arguments (mine and the OP) are logically equivalent under deductive logic. — Hanover

Except they're not, because your "So..." is entirely different than the OP's "So..." I explained this <here>.

Deductive logic says nothing at all about the world. — Hanover

Sure it does.

(1) All dogs are cats, all cats are rats, therefore all dogs are rats. That is true, except for the fact that dogs aren't cats and cats aren't rats. — Hanover

It is unsound, and that is why it fails to be informative. It is not uninformative because it is deductive.

(1) and (2) are represented the exact same way deductively and are therefore both true deductively. — Hanover

You're flubbing the difference between soundness and validity. A premise being true does not make it inductive.

The crux is that this claim of yours is entirely false:

the speaker has decided to do something to create God — Hanover

- Sure and Lionino's thread delved into this in some detail.

-

- No, I don't think so. The OP is nowhere near as "ridiculous" as your argument about billionaires. The English argument of the OP makes sense in a way that you haven't recognized. I don't see that any of this has to do with deduction vs. induction.

An odd bug.

I go to my post <here>.
I left-click on Lionino's name.
I am taken to the first post of the current thread.

I go to my post <here>.
I right-click on Lionino's name and then select, "Open link in new tab."
I am taken to Lionino's post, which is located in a different thread.

Maybe it has something to do with the hexadecimal symbol in the post reference number?

Same question — schopenhauer1

Same answer: ,

- Then check out 's response.

It seems that Lionino will not sign up ever again, sadly. :sad: — javi2541997

Maybe. He left in frustration but will perhaps change his mind in time. I hope he returns.

I don't see how the conclusion can be derived conditionally from the premises- it is tacked on. — schopenhauer1

Do you agree with this:

~P
∴(P→A) — Leontiskos

Why isn't the conclusion just a non-sequitur? — schopenhauer1

Because [page 1]. :razz:

I tried to summarize why <here>.

3. (¬G→¬(P→A)∧¬P)→G — Michael

There is an ambiguity in the order of operations here which echoes my point to . Which has precedence? The '→' or the '∧'? Depending on which, the nature of the falsum arguably changes.

Going back to this:

(As a proof this runs into some of the exact same difficulties that were discussed in this thread.) — Leontiskos

Suppose the '∧' has precedence: (¬G→(¬(P→A)∧¬P))
Then we have (¬G→falsum)

But what happens if the '→' has precedence? : ((¬G→¬(P→A))∧¬P)
Then the same paradox from the previous thread arises, where you have (¬G→¬(verum)), along with the quandary of whether ¬(verum) is the same as falsum (and also whether the consequent should be interpreted as ¬(verum), or as ¬(P→A) conjoined with the recognition that (P→A) happens to be true in this case).

(The difficulty is apparently that falsum is context-independent whereas propositional negation is not. Does the modus tollens require propositional negation, or will falsum also suffice? And then what about ¬(verum), which is a combination of the two?)

(CC: @Lionino, @TonesInDeepFreeze)

The "So" in "So I do not pray" is a clever twist, as it suggests the speaker has decided to do something to create God... — Hanover

I want to say that this is off, and that the trick is the ambiguity of, "If God does not exist..." The valid argument looks like this:

1. Suppose God does not exist
2. Therefore, It is false that if I pray, then my prayers will be answered
3. Therefore, I do not pray

But the logical translation makes the "if" a logical condition, not a supposition (i.e. not a condition whose scope extends to (3)). "So I do not pray," is a hanger-on from the alternative English translation which the formal presentation opts out of. ...Of course the idiosyncrasy of the material conditional is also doing a lot of work here.

Chomsky's criticism — Baden

But can't the same be said about talk of "the natural"? Is naturalism any less shifty than physicalism? — Leontiskos

To give a pertinent example, can Chomsky's mysterianism really be said to conform with naturalism?

-

Edit: This is perhaps a pithy way to phrase my objection: If the physicalist pivots to methodological physicalism, has he then solved the problem? Or is there something suspicious about trying to solve the problem in this way?

This is where I wonder if a certain logic to the situation is obscured. Is there something practical to the suitcase I can't see? What is the minimum we should need to get on with science optimally? Methodological natualism seems to be the answer to me. But I am open to reasons why more might be needed. — Baden

Right, and I think this is a good way to capture methodological naturalism:

Methodological naturalism says behave as if it were and get on with it. — Baden

I want to ask whether this is coherent, and perhaps the physicalist would want to ask that too. How much mileage can we really get out of "behave as if it were," or, "pretend"?* My nephew recently told me that it was incumbent upon me to pretend that the dog is a tiger. If I had asked him why, he might have said, "Because it will be fun!"

I think methodological naturalism asks us to do more than behave as if reality were measurable. It seems that it asks us to behave as if naturalism were true, at least for the duration of our inquiry. If I asked methodological naturalism why, what would it say? Whatever its answer, I suspect that the answer will betray metaphysical commitments that it purports to not have.

On this account we might have an interaction like the following:

• Methodological Naturalist: "Stop doing metaphysics. We should be metaphysically neutral."
• Physicalist: "No one is metaphysically neutral. You are fooling yourself. Every thoroughgoing methodology comes with metaphysical commitments."
• Methodological Naturalist: "Even if that is so, it remains true that your metaphysics is too thick for science."

(I would say that the second and third statements are both true.)

More succinctly, you seem to be saying, "Methodological naturalism is sound and solid in itself; physicalism is problematic; therefore we should take the former and leave the latter." I think there is a strong argument to be made that methodological naturalism is not sound and solid in itself. The first premise here aligns with your (1), which in the OP is more of a presupposition than an argument.

* It is curious to me how much pretending we are told to do with it comes to religion, both from secularists and religious alike. Apparently this began when the phrase "etsi Deus non daretur" took on a certain meaning.

-

'At best, talk of “the physical” acts as a placeholder for whatever we discover, or could discover, to be true about nature.' — Baden

But can't the same be said about talk of "the natural"? Is naturalism any less shifty than physicalism? In each case it would seem that certain explanations are ruled out a priori for no articulated reason, and whenever phenomena which support those explanations are encountered, the conception of what is "natural" or "physical" is simply broadened to accommodate. My thesis here is that these critiques of physicalism also function as critiques of naturalism, just in a mitigated way.

The supernatural is just that which can't be reliably measured, replicated etc. in principle. — Baden

This is a crucial attempt to articulate a reason for ruling out supernatural explanations, and as always it is bound up with a specific conception of science. On this definition science has to do with what is repeatable, and therefore the supernatural is ruled out (along with, perhaps, the psychological, the sociological, the historical, etc.). For the Western mind supernatural encounters fall into the genus of interpersonal encounters, and it is the interpersonal nature of the phenomenon that is not repeatable.

The alternative is a view of science which opens the door to the soft sciences, including theology. If the repeatability requirement is softened then interpersonal realities can be the subject of scientific study, because repeated interpersonal interactions do yield true and reliable knowledge, even though the repeatability is not as strict as that of the lab scientist who deals with a passive and subordinate substance.

If the government insists on flying in "inadmissible" immigrants, then they should be carefully chosen to
benefit the nation in some manner. Doctors and nurses, scientists, engineers, might well be encouraged to apply. That does not appear to be the case. — jgill

It seems like a compassion mindset where no one who wants to come can be denied entry. How does one go about opposing a compassion-motivated decision?

I honestly don't know that we will even begin to address this problem until the costly consequences of excessive compassion are felt. I think the voters in the next generation or two will make it worse.

E A Burtt, is relevant: — Wayfarer

Sure, but when I read that I see a great deal about metaphysical naturalism and nothing at all about methodological naturalism.

I am wondering if the empty suitcase is actually methodological naturalism. Who needs it? Not the naturalist. He has as much need of methodological naturalism as a Saudi Arabian Muslim needs methodological Sharia. Not the non-naturalist. For her methodological naturalism is irrational. If methodological naturalism is superfluous for the naturalist and irrational for the non-naturalist, then it looks like an empty suitcase or an outward badge of honor. Probably it is part of the pact of classical liberalism, a kind of compromise.

What about the Original Post? Perhaps "methodological naturalism" is doublespeak for soft metaphysical naturalism, and physicalism really does deviate insofar as it is a form of hard metaphysical naturalism. On that view the problem is not that physicalism is metaphysical, but rather that it is too confident, too far out over its skies. The underlying issue is the difficulty or impossibility of adopting a thoroughgoing epistemological methodology without also adopting some form of metaphysical commitment.

- It would be interesting to know when and where the idea of "methodological naturalism" was historically born.

I suppose it's then an odd question why whether the same set of points can be considered a circle or not depends upon whether you consider them as part of a larger space. — fdrake

As I understand it, the "plane" in the definition of a circle is not a space, at least in the sense that your term "larger space" indicates. The cross-section of a sphere conceived as two-dimensional is planar in one sense and non-planar in another.

So is there some impediment to taking the basic definition of a circle given and saying that the cross-section of a sphere conforms to this? I don't see any real impediment. Any three-dimensional translation that occurs will not be contentious. If we interpret the abstract space presupposed by the definition of a circle to be incommensurable with the abstract space presupposed by the cross-section of a sphere, then there is clearly an impediment, but this sort of exclusion is less plausible than the alternative. How exactly do the three-dimensional points of a sphere translate to the two-dimensional points of its cross-section? I don't know, but it doesn't strike me as a great problem.

In any case we are very far from demonstrating square circles, which was the original topic.

Are you not used to this sort of maths? — fdrake

It's been too long to do much more than mildly jog the memory.

I suppose that means the great circle isn't a circle, since there's no coplanar points on it... Since there's no way to form a plane out of the points on a circle's surface when you're only allowed to consider those. — fdrake

It seems that we mean different things with the words "point" and "plane." On my view you have reified abstract realities, making them, among other things, delete-able.

Regardless though, there's no word for "coplanar" in Euclid's definition of a circle either. So we've needed extra concepts from Euclid regardless. It would be odd if Euclid ever conceived of the word, considering his is the geometry of the plane. — fdrake

These objections are too subtle, such as supposing that I meant to confine myself to Euclid in an especially strict manner, or that the cross-section of an abstract sphere cannot be an an abstract circle.

- My contention would be that there is no such thing as coplanar points without a plane, and that the cross-section of a hollow sphere is a collection of coplanar points.

For me this quote is most indicative of the relativism I have opposed:

Take all the points Euclidean distance 1 from the point (0,0) in the Euclidean plane. Then delete the point (0,0) from the plane. Is that set still a circle? Looks like it, but they're no longer equidistant from a point in the space. Since the point they were equidistant from has been deleted. — fdrake

For fdrake it would seem that when we see a shape he has drawn on a piece of paper, which looks like a circle, we must ask him if he "deleted the point at the center" before drawing the conclusion that it is a circle. Apparently in order to identify a circle, formally or materially, we must worry about whether the center point has been "deleted." This is taking the subjectivism and relativism a bit far.

(Like points, apparently planes can also be "deleted.")

It would if you give yourself the liberty of hammering the cross section down onto a flat plane. — fdrake

I take it that a cross-section is flat (i.e. two-dimensional) by definition. But this all goes back to the ambiguity of your figure. If the cross-section you indicated is not two-dimensional then I would of course agree that it is not a circle.