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.

I don't know why I'm participating in this. — Srap Tasmaner

Me neither. Banno's baiting into this thread is itself something I wished to avoid long before he resurrected this thread. If you had created a real thread on logical pragmatism we wouldn't be here. Blame's on you. :razz:

But it does match it, as I've already noted. Your mere assertions are getting old. — Leontiskos

@fdrake if you like: a circle is the two-dimensional subset of a sphere. A sphere is the set of points equidistant from a point in 3-space and a flat cross-section of a sphere is necessarily a circle, namely a set of points equidistant from a point in 2-space. As I've already said, a cross-section of a sphere conforms to the definition of a circle that I originally gave.

Either you consider the sphere as embedded in 3-space, and the cross section plane isn't "flat" in some sense - it's at an incline. Or you consider the surface as a 2-dimensional object, in which case there's not even a plane to think about. Pick your poison. The latter is the original counter example and is much stronger, the former is easier to remedy. — fdrake

I still think you're just plain wrong. Namely, a 2-dimensional object lies on a plane. Pretending that there is no plane is a curious move. How do we query whether a plane is present or not? A plane is an abstract object, much like a circle. It makes no more sense to say that the cross-section of a sphere does not lie on a plane than it does to say that one can delete the point in the middle of a circle, at which point it magically becomes a non-circle.

But clearly that's not true, as the definition you provided doesn't match something you clearly recognised as a circle! — fdrake

But it does match it, as I've already noted. Your mere assertions are getting old.

How will you parry my counterexample? — fdrake

I'm waiting for you to present one.

If it makes you uncomfortable, stop tromping on my bridge. — Banno

You artificially inserted an extraneous conversation into your own thread and then invited me here, remember?

And you are ignoring the fact that I used it twice. — Srap Tasmaner

So? The cross-section of a hollow sphere will be a circle regardless of whether I imagine a point at the center or not.

- Ever the troll.

He doesn't need to. The sphere is a 2-manifold, and his great circle is a set of points on that manifold. There are no planes here, nothing else, only the points on the surface of the ball.

You are imagining the sphere embedded in the usual 3d Euclidean space. Now, imagine it isn't. There is no point the points on this great circle are equidistant from. — Srap Tasmaner

Planes and points cannot be stipulated to exist or not exist. Your word "imagine" is on point given my earlier claim that "This idea of 'deleting' points mixes up reality with imagination." The points in question are coplanar, and therefore the figure they enfold is a plane figure.

What do you think a plane figure is? — fdrake

We took our definition from Euclid, and the term there means a figure that lies entirely on a flat plane.

that circle instead would be a closed curve inside a subset of R3 — fdrake

Do you think the "great circle" (which you have yet to define) lies in three dimensional space rather than two dimensional space? That ambiguity is why I asked you to be more clear about what you were depicting in the first place.

Cutting to the case a bit, it seems that you want to talk about "circles" instead of circles and "plane figures" instead of plane figures, etc. Now if we define "distance" in an idiosyncratic way, then of course there are taxicab circles. If we define "distance" in the commonly accepted way, then there aren't. Are we disagreeing on something more profound than that?

but it does not satisfy Euclid's definition of one verbatim — fdrake

I think it does. You've only asserted otherwise, you haven't shown it.

You could also have ardently insisted that indeed, the great circle was not a great circle because it was not a plane figure. — fdrake

It is a plane figure. What do you think a plane figure is? Did you delete the interior of the circle from the plane in the same way you deleted the point from the center of the circle? Deleting points or sections of planes is not possible.

To be clear, the cross-section of a sphere fulfills Euclid's definition of a circle. We could also define a circle as the cross-section of a sphere, but I was only saying that every (planar) cross-section of a sphere will in fact fulfill the definition I already set out.

Well who said anything about cross sections? — fdrake

You depicted one. I even asked what you were depicting and you weren't very forthcoming.

You'll now need to tell me in what circumstances can you take a cross section of a volume and have it work to produce a circle. Let's assume that you can take any volume and any cross section and that will produce a circle... — fdrake

Just read what I already wrote:

The cross-section of a sphere is a circle. — Leontiskos

Again, you seem to be resorting to sophistry, and I don't see this as a coincidence in the least. In order to try to draw an absurd conclusion you are helping yourself to false premises, such as assuming that planes are bounded, or points can be deleted, or that rectangular prisms are spheres. Why are you doing this sort of thing?

The great circle is the circle I've highlighted on the surface of the sphere. Since the circle is confined to the surface of the sphere, it is not a plane figure. — fdrake

The cross-section of a sphere is a circle. A circle is always "confined" by its circumference, but it does not follow that it is not a plane figure.

Euclid says: not a circle. The great circle is not a plane figure. — fdrake

Why do you think this? And what is "the great circle"?

Let's change track. You tell me exactly what you mean by a circle with an intensional definition, and we'll go with that. Then do the same for roundness and pointy! — fdrake

I hope I'm not the only one who recognizes that you are more interested in this conversation than me. :grin:

I am fine with taking Euclid's definition:

A circle is a plane figure bounded by one curved line, and such that all straight lines drawn from a certain point within it to the bounding line, are equal. The bounding line is called its circumference and the point, its centre. — Circle | Wikipedia

And we can say that a square is a plane figure with four equal sides and four right angles.

Something like "roundness" I take to be a simple concept, not especially reducible to further explication. We could say that it is something like the curvature of a line.

- I realize that someone prior to fdrake made it up.

If the presupposition is that all systems are equal, our preferences for them arbitrary, then of course logical impossibility is pretty much meaningless.

But we don't pick systems arbitrarily. — Count Timothy von Icarus

Yep. If everything were arbitrarily stipulated, then all of the strange ideas in this thread would be gold. ...Or at least as valuable as everything else.

Imagine you start at a point, and you go 1 step north and 1 step northeast
The taxicab metric says you've travelled 2 total units - you add the steps.
The euclidean metric says you've travelled sqrt(2) total units - you measure the line. — fdrake

But this isn't right. The Euclidean metric says you've traveled 2 total units. Yet the distance of a straight line between your starting point and your ending point is sqrt(2). Apparently taxicab geometry measures the distance between points differently.

A circle in taxicab geometry, a set of points defined as equidistant from a single point, looks a lot like a square in euclidean space. — fdrake

Not really. Only if the radius is a single unit. The larger the radius, the more circular it will be.

I could also insist that it is a circle, and how are we to decide between your preference and my preference? — fdrake

You're presuming that your made up "taxicab geometry" is on a par with Euclidean geometry. But it's not. What you've done is engaged in equivocation. You want to say, 'A circle is the set of points equally "distant" from a single point.' Scare quotes are required, because we both know that your artificial definition of "distance" is not the accepted definition. Similarly, 'This figure is a "circle" in taxicab geometry.' But I was talking about circles, not "circles."

The derivative of a curve... — fdrake

We could say that a circle is a figure whose roundness is perfectly consistent.* There is no part of it which is more or less round than any other. In calculus that cashes out as a derivative, but folks do not need calculus to understand circles. Calculus just provides one way of conceptualizing a circle.

A circle is, by definition, a set of points Euclidean equidistant from one central point.

And thus we've revealed what sneaky hidden presumption you had through lemma incorporation. — fdrake

Is it more "sneaky" to think that circles go hand in hand with Euclidean geometry, or to think that Euclidean geometry and taxicab geometry are on a par? Not only are they not on a par; taxicab geometry presupposes Euclidean geometry.

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

But they are. You have an odd assumption that points are stipulative, as if we could delete a point or as if a point could have spatial extension. The set of points is still equidistant from a point. This idea of "deleting" points mixes up reality with imagination.

If we go by Leontiskos intuition that round things cannot be pointy in any context, well the Earth is in trouble. — fdrake

I think you are falling into the exact sort of quibbling and sophistry that I warned against. The answer here is simple: the Earth is not perfectly spherical or perfectly round. A cross-section of the Earth is circular, but is not truly a circle.

I just wouldn't call them circles to my students learning shapes. — fdrake

And the reason why is very important.


* And of course also possesses roundness

That's the nub of the issue - methodological naturalism is taken to be a metaphysics, which it actually is not. — Wayfarer

Yes, but it is worth asking whether a methodology as culturally significant as methodological naturalism can ever be prevented from spawning its own metaphysics (even on the questionable assumption that methodological naturalism was born metaphysics-free). I think it would require an enormous amount of energy to prevent methodological naturalism from hardening into a metaphysics, culturally speaking. On this account physicalism is just the most prominent metaphysics that methodological naturalism has gestated.

Basically I see the appeal of Aristotle and common sense as a mistaken appeal -- it makes sense of the world, but need not hold for all empirical cases: There are times when a person is in contradiction with themself, or an organism has a contradictory cancer, or a social organism is composed of two opposite poles (hence Hegel's use of contradiction in attempting to understand a social body or mind). — Moliere

But these are so far from counterexamples to Aristotle that they are all things he explicitly takes up.

And I, for one, take up the liar's paradox as a good example of an undeniable dialetheia: A true contradiction. — Moliere

Every time I have seen someone try to defend a claim like this they fall apart very quickly. The "Liar's paradox" seems to me exceptionally silly as a putative case for a standing contradiction. For example, the pages of <this thread> where I was posting showed most everyone in agreement that there are deep problems with the idea that the "Liar's paradox" demonstrates some kind of standing contradiction.

logical impossibility isn't all it's cracked up to be — fdrake

Well, your post would appear obtuse to the layman, and maybe it just is. Maybe the argument is much simpler than you are making it:

• Circles are round
• Squares are pointy
• What is round is not pointy
• Therefore circles are not square

Or even simpler:

• Circles are circular
• Squares are square
• What is circular is not square
• Therefore circles are not square

These arguments are not any less powerful for their simplicity, and most objections would be little more than quibbles. For example, someone might offer the counterargument of a shape like 'D', and claim that it is both circular and square. That quibble of course could be addressed, but need not be.

More formal:

• The points of a circle are all equidistant from some point
• There is no point from which the points of a square are all equidistant
• Therefore no circle is a square, and no square is a circle

It is very odd to question such arguments. If these are not good arguments, then there probably is no such thing as a good argument. There seems to be a point at which trying to be charitable towards a dubious thesis crosses over into sophistry, no? Logicians have a difficult time saying that some claim or argument is false or unsound, as opposed to merely invalid. In these cases one must recognize that falsity can enter into a concept; that someone can simply fail to understand what a circle or square is.

Material logic — Count Timothy von Icarus

Is this what you mean by material logic?

Historically logic is the thing by which (discursive) knowledge is produced. When I combine two or more pieces of knowledge to arrive at new knowledge I am by definition utilizing logic. — Leontiskos

Or we could say that logic is that by which correct inference is achieved.

word searches are neither good arguments nor good ways of informing yourself about philosophy. — Count Timothy von Icarus

Indeed! It is also a symptom of conceiving everything in terms of technicalities, technical terms, and stipulations.

- Yep, exactly right. :up:
That is literally the best AI-generated content I have ever seen. :smile:

(Edit: When I said, "We have scrutinized this sort of translation a great deal in the past months," that was a nice way of saying that the translation is problematic.)

I disagree you can disregard the "not S" step, because the statement in its entirety must be false. If I say "if I pray then my prayers are answered", stating "I don't pray" says nothing about the consequent of that statement so we don't know what it means. Q is merely implied because if there are no prayers, they cannot be answered. — Benkei

Did you read my post <here>?

Do you agree with this:

~P
∴(P→A)

Q is merely implied because if there are no prayers, they cannot be answered. — Benkei

I don't think that is quite right. Q is merely implied because of the way a material conditional works. The inference <~P; ∴(P→A)> is different from, "If there are no prayers, they cannot be answered." It says, "If there are no prayers, then it is true that (P→A)."

So I agree this is valid — Benkei

Okay, good.

But the logical structure and the argument are not necessarily the same. — Benkei

I agree.

At what point though is it incumbent upon the person with the "bad (cultural) habit" to change them, ethically? When it leads to harm? When should a cultural habit that leads to possible harm be excused? — schopenhauer1

You seem to be conflating the questions of self-correction and other-correction, which I want to keep distinct. I already answered your first question: "when it is self-consciously recognized to be a bad habit and the necessary resources to make a change are available." What is bad and what is harmful are not identical notionally, but if someone thinks that only harm is bad then they will only self-consciously recognize something to be a bad habit if it is harmful.

(We can only self-excuse when we lack the available resources to change, for the very fact that we are considering excusing shows that we already see the habit or action to be bad.)

Physicalism in relation to methodological naturalism seems to me like an empty suitcase taken on a plane. — Baden

This is a great OP. I need to chew on it a bit more, but one aspect of this is the question of how metaphysics relates to science. Awhile back I was reading parts of Thomas Nagel's The Last Word with @J, and I came to realize that Nagel is interested in this question particularly as it relates to theism. I haven't yet read the last chapter of that book, but @Wayfarer links to publicly available copies of it here and here. That chapter is called, "Evolutionary Naturalism and the Fear of Religion."

3. Physicalism’s close association with methodological naturalism and the confusion there engendered risks denigrating the latter. — Baden

If I am following, the idea is that physicalism, as a form of metaphysical naturalism, imposes metaphysical commitments that methodological naturalism should be free of. These commitments are somewhat tendentious, and given the way that physicalism is bound up with methodological naturalism, methodological naturalism becomes burdened with a kind of guilt by association.

I think that's all correct, but I lean towards disagreeing with this claim:

[Methodological naturalism's] justification as a method rests on its results rather than any metaphysical presumptions. — Baden

I do see methodological naturalism being presented as justified based on results, but it is an open question whether the success of modern science is independent of metaphysical presuppositions.

The other question is whether a robust methodology can perdure independent of metaphysical presuppositions.

Of course, this might have less to do with culture than political arrangements — schopenhauer1

Yes, I think it is widely recognized that it flowed from political arrangements, namely because the aftermath of WWII was different from the aftermath of WWI in precisely the respect you identify. In fact the political arrangements that followed WWII were a recalibration of the failed political arrangements that followed WWI. It therefore seems more likely that the difference was due to postwar political arrangements rather than the nature of German culture.

Now, the more complex question though, is when does it become incumbent upon people of a certain culture to evaluate a possible negative cultural trait/feature to see if it needs to change?

...

At what point might one take the new cultural feature and change the previous culture, if at all? — schopenhauer1

I don't think there is an easy answer to this, but I would say that a bad habit should change when it is self-consciously recognized to be a bad habit and the necessary resources to make a change are available. This applies to individuals and cultures.

The flip side of this has to do with external judgment and external influence. We can ask about the self-reflective question of self-change, or we can ask about the question of changing another. For example, the interventions into World War II on the part of the Allied powers were in part motivated by a judgment of German actions which was external to Germany itself. That is, when speaking of the war, Germany did not seek to change itself. Instead, an external set of agents sought to change Germany.

If not P, then not Q (if R, then S)
Q equals if R, then S
Not R
Therefore, not S
Therefore, Q (through double negation)
Therefore, P — Benkei

Nope. This is your mistake:

Not R
Therefore, not S
Therefore, Q

(Another mistake is that Q does not follow from ~S)