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)

- The OP is not anti-democratic. If you're not interested in the topic of the thread I'm not sure why you are posting in it. Adios.

- Your answers are sidestepping the purpose of the OP. The OP wants to have a substantive discussion about immigration. Why not enter into that discussion? Why not be one of the democratic citizens who marshals arguments in favor of a real position?

Edit 2: To continue the line of thought that ↪Leontiskos, if let's say a culture simply had built-in (extremely) violent responses to injustices, and then someone was not from that culture but promoted (extremely) violent responses to injustices, but advocated it out of philosophical regard, if we determined the extreme violence was "bad", would the philosophical regard agent be worse than the cultural agent? — schopenhauer1

Yes, because there is a greater level of intentionality involved in the badness of the second person. They are doing the bad thing more purposefully and intentionally.

You deny entry when the immigrant does not meet the countries established laws for entry. — Philosophim

Think of it as a question about what the laws should be.

-

- :up:

- When the antecedent of a material conditional is false, the conditional itself is necessarily true. That's all that is happening here, and then the modus tollens draws 'G'.

We could add the implicit step:

~G→~(P→A)
~P
∴(P→A)
∴G

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

<"it is false that if I pray, then my prayers will be answered" translates to ~(P→A)>

We have scrutinized this sort of translation a great deal in the past months. This thread, for example:

However, what about ¬(A→B)? What can we say about this in English? — Lionino

However, I wouldn't take it as a badge of honor to be entirely ignorant of the basics of logic prior to the 20th century on account of this fact. — Count Timothy von Icarus

:grin:

The idea that there is "nothing but formalism" is the problem. — Count Timothy von Icarus

Yes, but as I said earlier, I don't see much support for it generally or on TPF. Most people who think about this for more than 15 seconds realize that "nothing but formalism" is a complete dead end. Frank wants his square circles and Banno wants his logical pluralism. I would need to see other voices taking up such bizarre positions before I would be interested in engaging, and I don't see any. The same cannot really be said for things like nominalism or logical pragmatism, which have a wider base of support.

Not having experienced it so far doesn't rule it out, though. — frank

Right, and it is very important that we keep our eyes peeled for square circles. They are probably lurking just around the corner.

The framing in the OP seems to lean towards the idea that "logic" is "formal logic." Thus, we speak of "languages," "systems," and "games" and difficulties within or between formalisms as problems for "logic." — Count Timothy von Icarus

Formal logic is about "ways of speaking," but logic is not about "ways of speaking" tout court. — Count Timothy von Icarus

Yes, very good. In my opinion this all gets a little tricky because what is at stake is a ratio, not a concept. For instance, to use a formal logical system is not thereby to commit oneself to the view that logic is formal logic. Lots of people who used and even created formal systems recognized that their formal system is not identical to logic itself.

Anyhow, to the extent that logical nihilism will tend to imply that things have no causes, that there is no metaphysical truth, etc. I think it's open to the criticism that:
A. This seems demonstrably false on all the evidence of sense experience, the natural sciences, etc.;
B. No one actually has the courage of their convictions on this matter and really acts as if causes and truth are "just games," and;
C. This makes the world inherently unintelligible and philosophy pointless. — Count Timothy von Icarus

Very good. :up:

Plus, to the extent that someone still tries to justify logic on "pragmatic" grounds it seems to be the case that any "pragmatic" standards bottom out in arbitrariness, there being no truth about what is truly a better standard or what truly ranks higher on any given standard. Hence appeals to the "usefulness of certain games," are unsupportable. — Count Timothy von Icarus

Agreed. :up:

(I am tagging @Srap Tasmaner given that we were talking about similar issues elsewhere.)

How do we determine which logic is appropriate for a given situation/problem? Sorry if this is a banal quesion. — Tom Storm

This is a fine question, but I want to say that the better question along these same lines is this: How do we differentiate an argument which is invalid from an argument which is merely pluralistically different? There is no differentiation between the two at the level of the object language, and this inevitably pushes the formalists into a metalanguage.

Stated more simply, if different approaches to logic are just different tools, are there nevertheless tools that won't work? Are there any bad arguments at all? And can someone who says that there are no bad (or good) arguments really call themselves a logician?

↪Leontiskos ↪Banno To what extent does your disagreement on this involve, perhaps, one being a conservative and the other liberal? — Tom Storm

It's an understandable trope, but in this case I think it is just that Banno is concerned with what I call metalogic/metamathematics and I am concerned with what I call logic. He was trained in that emphasis and so he thinks of it as logic. Would Banno actually bite the bullet and accept full-blown logical pluralism? I doubt it. I think he is just flirting with it as a contrarian who discovered an exotic idea. And I don't see enough support for that position on TPF or elsewhere to expend much effort critiquing it. Srap's logical pragmatism is an example of an approach which is much better represented.

But the substantive question relates to knowledge, which is why my first post in this thread concentrated on that topic.

(At the end of the day the principle of non-contradiction is the issue, and Aristotle showed long ago why attacks on the PNC can never succeed.)

And that is where we stand. Presuming that there is one true logic is no longer viable. — Banno

Lol. I suppose that's where things stand if you just ignore the rest of the article and/or appeal to SEP as some sort of normative source, setting out what is allowed and what is not, even though it doesn't present itself that way. (Michael has that difficulty as well). In your case it is less excusable given what I have already pointed out to you. Dialetheism qua dialetheism is the flat-earthism of the logical world. Yet the inquiries of dialetheists can and have been interesting, even if they don't ultimately achieve their purported aim.

I don't consider this at all unique. I take it that logical pluralism (and nihilism) is just the logical extension of what has occurred in all other areas of discourse, i.e. pluralism and/or nihilism. Historically speaking, such developments look to be inevitable given our overarching ideation. This all perhaps began when religious pluralism was baptized with modern liberalism. The hold-outs seem to be things like scientific and physical pluralism, but maybe that will eventually come too.

Logical pluralists seem to argue that different contexts require different logics and this seems to be determined by the kinds of reasoning or the goals of inquiry involved. — Tom Storm

No, that's really not it. See:

Logical pluralism takes many forms, but the most philosophically interesting and controversial versions hold that more than one logic can be correct, that is: logics L1 and L2 can disagree about which arguments are valid, and both can be getting things right. — SEP | Logical Pluralism

For example, someone who believes in deductive, inductive, and abductive reasoning is not a logical pluralist. It is in no way controversial that there are different ways of reasoning.* Even SEP's phrase, "getting things right," is weasel language. The controversy and uniqueness of logical pluralism arise with the idea that there are conflicting logics that are all correct.

Each time I look into these theories they turn out to be smoke and mirrors. It looks a lot like the pseudoscience of the logical world. But even on TPF this is largely acknowledged, so there seems little reason to argue.


* Similarly, someone who utilizes different logical languages or formalisms for different arguments is also not a logical pluralist.

- Not just you, but there are also fewer up there than you suppose. Most people recognize that contradictory conclusions cannot both be the result of sound arguments—even and especially laymen.

Sounds fair. Is there a risk with pluralism that one might simply select the logic one wants to suit ourselves? How do we determine which logic is appropriate for a given situation/problem? Sorry if this is a banal quesion. — Tom Storm

Banno looks like the cat who has climbed and climbed and now cannot get down, and does not know where he is. What is logic? Banno thinks it is something like the arbitrary manipulation of symbols - and of course there are many ways to arbitrarily manipulate symbols. But that's not what logic is.

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. If logical pluralism were true then you could know X and I could know ~X, and we would both have true knowledge, which is absurd. When, "two logics over the same domain reach opposite conclusions," we do not arrive at an "interesting question." We arrive at contradictory conclusions and conflicting arguments, one of which must be wrong.

- If you managed to read my posts it wouldn't be necessary. You're a pro at talking past people.

Not one logic, but many. — Banno

The foundational topic here relates to the Meno, which you are welcome to weigh in on:

Here's how I would start a thread about logic. I would post the dilemma of Meno 80b. I would basically say that if that dilemma can be overcome then logic exists, and if it can't then logic does not exist. Per Rombout, someone like Wittgenstein doesn't think logic exists. But the thread would not use the word "logic," for that word is an equivocal quagmire. — Leontiskos

On the one hand, it's a ridiculous point because you can't *say* one word on top of another -- gotta say them in order. But on the other hand, spoken language is pretty much always accompanied by gestures, so you can imagine an accompanying gesture to convey the "on". On the third hand (the gripping hand), this won't work over a telephone. But on the fourth hand, language is spoken in person long long long before telephones, and pretty damn long before writing. And even writing has its own story, a little different from the story of speech. — Srap Tasmaner

Rombout has a nice section on linguistic differences, such as Frege's spatial notation. For example, the author she appeals to considers the difference between the Roman and Arabic numeral systems. I would say it's not ridiculous, because written language is not somehow limited to linear left-to-right symbols. Even spoken language can have similar things, such as tonal languages like Vietnamese where inflection becomes centrally important.

Well, no, I didn't, — Banno

Well, yes, you did:

Have you ever noticed that when someone sets out a state of affairs, they do it by setting out a statement?

It's far from obvious that states of affairs are helpful, rather than just yet another thing to puzzle over. — Banno

Well, yes. What a statement sets out is a particular situation in the world. Do you then have three things, the true statement, the situation in the world and the fact? Or are we multiplying entities beyond necessity? — Banno

-

Folk are welcome to talk about states of affairs, but might do well to remember that they are a turn of phrase, not a piece of ontology. — Banno

I don't know what it would mean for state of affairs to be a "piece of ontology." In all likelihood you don't either.

This is a classic Analytic move of claiming that natural language has gone astray and "states of affairs" is unnecessary. In natural language "state of affairs" and "fact" do not mean the same thing. I'll stick with natural language rather than the artificial simplifications.

- Yes, @Banno began by claiming that talk of states of affairs is redundant and superfluous, and then went on to continue conflating states of affairs and statements in subtle and not so subtle ways. For example:

SO how does a state of affairs differ from that which a statement sets out? — Banno

A statement and what a statement sets out are not the same thing, and it is not redundant or superfluous to talk about what a statement sets out. Thus Banno is arguing for a different thesis here than his original one (i.e. equivocating). Even if we agree that a state of affairs does not differ from what a statement sets out, it does not follow that a state of affairs does not differ from a statement. A statement is a locution; a state of affairs is not.

---

- Good posts. :up: