Until you accept that there is a difference here, further discussion is pointless. — Metaphysician Undercover

[/quote]

I agree that the present phase of our ongoing convo has reached an impasse. I just wanted to close the loop on a couple of things you said.

Yes, "2+2=green" has meaning. But I would reject this statement as inconsistent with the principles that I already understand and accept. — Metaphysician Undercover

What does it mean?

I don't know, the answer to these questions. "Meaning" is not an easy topic. That's why there's so many philosophical debates about it. I really do not know what meaning is, or how I know that something has meaning. Those are questions yet to be answered. — Metaphysician Undercover

Ok. I find that an extremely fair minded statement. But I want to make a finer distinction.

When I say that 2 + 2 = 4 has meaning, it's because I have defined '2', '4', '=', and '+' according to the standard mathematical conventions, either within the Peano axioms or ZF set theory. In other words from my viewpoint 2 + 2 and 4 and '=' all refer to something. The somethings that they refer to are abstract mathematical objects. And I will stipulate that when you challenged me to define exactly what I mean by those, I was stuck. I admit that! But at least by saying what these expressions refer to (in my mathematical ontology), I can thereby assign meaning and value to them. The meaning and value of these expressions derive from the referents I have assigned to them.

But you say that 2 + 2 and 4 don't refer to anything. So it is now incumbent on you -- not just for me, but for working out your own thoughts for yourself -- to figure out how to define the meaning and value of syntax tokens that you claim don't refer to anything at all! Do you take my point here?

By asking this question you indicate that you paid not attention to my explanation of what "=" signifies, or means in common mathematical usage, and what "is the same as" signifies or means in the law of identity. Since you still cannot see the difference here, after I've explained it countless times to you, it seems pointless to explain it again. It's actually a very simple difference, and very easy to understand. — Metaphysician Undercover

There is nothing simple about your point of view. Nor have you explained "what '=' signifies" in the least. I haven't seen you do it.

We learn values in school. If you still haven't learned the value of 4 yet, you could talk to a primary school teacher, or look it up on the web. You'll find there's a lot of educational stuff like that if you google it . — Metaphysician Undercover

It's funny. You can't answer the question I put to you: If 2 + 2 has no referent, how does it obtain its meaning or value?

You can't answer that, so instead of challenging yourself to clarify your own ideas, you make a childish insult.

But I have a perfect understanding of what the meaning and value of 2 + 2 are. Not only at the grade school level, but at a sophisticated mathematical level. The meaning and value derive from the REFERENT of the symbolic expression. But in your case, you DENY there is a referent. So in your theory, from where come the meaning and value?

You are cornered on this point, and instead of tossing out silly insults, you should take the opportunity to challenge yourself to respond intelligently.

Yes, that's a very real problem. We often do not know whether a word signifies something with thinghood or not. That is the case with quantum physics and wave/particle duality. Physicists cannot determine the "thinghood" of the described phenomena. — Metaphysician Undercover

Ok. I appreciate your admitting when you are stuck on your own ideas. Better than childish insults to avoid answering sharp questions.

Since you seem to have no idea of what "value" means I suggest you do some research into this topic, and come back to me when you get above the primary school level. — Metaphysician Undercover

LOL. As Ronald Reagan said to Jimmy Carter, There you go again.

I DO have a crystal clear understanding of how the meaning and value of 2 + 2 derive from the mathematical REFERENT of the expression. Whereas you DENY there is a referent, so you are STUCK trying to figure out how to derive the expression's meaning and value. Why don't you work on this and let me know if you have any fresh ideas on the matter.

Obviously you never looked into this, and haven't looked beyond your own nose to see what others say about what "=" signifies. The following is the opening paragraph from the Wikipedia entry — Metaphysician Undercover

Wikipedia isn't too far beyond anyone's nose. That's all you got?

The equals sign (British English, Unicode Consortium[1]) or equal sign (American English), formerly known as the equality sign, is the mathematical symbol =, which is used to indicate equality in some well-defined sense.[2][3] In an equation, it is placed between two expressions that have the same value, or for which one studies the conditions under which they have the same value.
— Wikipedia: equals sign[/url]

LOL. You're pasting that para to support some kind of argument? Your stuff is weak here. And you're agreeing with me. Because I can define the value of 2 + 2 very easily from first principles, based on the REFERENT that I assign to the expression. You on the other hand DENY there is any referent, so YOU are the one who can't figure out how to assign the expression a value.
— Metaphysician Undercover

Notice the mention of "the same value". — Metaphysician Undercover

Agreed on this point. But note that I can define what the value of 2 + 2 is, and you can't. Because you deny that 2 + 2 has any referent.

Do you accept that there is a difference between "is the same as" and "has the same value as"? — Metaphysician Undercover

I will stipulate that this is a tricky question. We agree that 2 + 2 and 4 have the same value (I think we agree on that). I claim that mathematically, they are literally the same thing. They have the same referent. They're two different symbol strings that point to the same mathematical object. And I'll stipulate that a long time ago you challenged me to tell you what a mathematical object is, and my response was not satisfactory even to me. So that's the point where I'm stuck.

But you deny the expressions have any referents at all, so I don't see how you're in a position to claim that they have the same value, or different values, or any values at all. How can we know their values if they have no referents? I, on the other hand, have a perfectly sensible way to define their values, based on the referents I have assigned them in PA or ZF. I can do this from first principles.

The former phrase is the phrase used by the law of identity. The latter phrase is what is signified by "=", as the Wikipedia entry indicates. — Metaphysician Undercover

I don't think the author of this particular Wiki pages had these distinctions in mind.

Until you accept that there is a difference here, further discussion is pointless. — Metaphysician Undercover

I do agree we're at an impasse for the moment. You claim that 2 + 2 has no referent. And you're stuck on your own theory here, because you can't tell me how to derive the meaning of a symbol string that has no referent. Can you see that this is problem for you? Why not think on it a bit. No hurry.

In fact I'll summarize as follows:

* You claim 2 + 2 has no referent, and since it has no referent, you can't tell me how to determine its value.

* I claim 2 + 2 has a referent, namely a particular mathematical object. But I can't tell you what a mathematical object is, other than "Whatever mathematicians think is a mathematical object," and I'll concede that this is not entirely satisfactory.

Would you call this a fair summary of the state of the discussion?

These two interesting. — tim wood

Thanks!

Nice. — Banno

I'm a big fan of hers.

That has nothing to do with whether physics has been "bad" for the last few decades. The OP isn't about funding science. — Xtrix

Ok. Suppose I phrased it somewhat differently:

I've been reading some books and articles, and watching some videos, in which professional physicists criticize the current practices of some areas of physics on the grounds that they have substituted abstract math for experimental contact with the world. I do tend to agree with this point of view; but of course the physicists being so criticized would disagree, and I lack the professional competence to have an authoritative opinion on the matter.

That said, I am sharing these links with the forum because they are interesting and educational in and of themselves, whether you agree or disagree with their point of view.


Would that be better?

I still would like to know, in your opinion, why I'm entitled to opinions about the work of some professionals but not others. I gave the examples of Wittgenstein, a philosopher that a lot of people around here have a lot of opinions about; and Ed Witten, a superstar mathematical physicist who, interestingly, is the only working physicist to have won math's greatest prize, the Fields medal.

It seems to me, if I'm reading you correctly, that I am entitled to opine (ignorantly as it happens in this instance) on Wittgy; but not on Witten. I wonder if you can help me understand the distinction.

Mentioning Ed Witten reminded me of my other favorite Witten: Jason Witten, the former longtime superstar tight end for the Dallas Cowboys, a professional football team.

Now Jason Witten is an incredibly skilled athlete, for many years at the absolute top of his craft in a difficult and dangerous activity that fewer than 1700 human beings are qualified to pursue at that level in any given year. To be a superstar of his longevity and accomplishments puts him in the top 0.000000014286 or so of humanity.

As it happens, many partisans of the Dallas Cowboys, as well as their many more passionate haters, as well as fans of professional football everywhere, have strong opinions about the performance of Mr. Witten, despite the fact that most of these opinionated amateurs never do anything more physically demanding than get up off the couch to fetch another beer.

By your logic, sports fans have no right to opine on the play of these gifted athletes who devote their entire lives from the time they're 8 years old to getting better at their craft.

And yet, Mr. Witten and all other professional athletes, as well as the league itself, absolutely want beer-swilling couch potatoes to have strong opinions on the play of their athletes. Why? Because the opinionated couch potatoes watch the ads on tv and buy the merchandise sold by the league. We are talking about an almost fifty billion dollar industry in global merchandise sales (across all sports), plus the massive television and streaming revenue from the ads.

Without sports fans not only being allowed, but being mightily encouraged, to have strong opinions on the skill of professional athletes, there could be no professional athletes! At least none making the kind of money they make now.

What do you make of this? If pro physicists sold jerseys would it be okay to cheer your favorites and boo your rivals?

I am asking you: Given a professional, when am I allowed or not allowed to hold an opinion on their work, given that I can have no real understanding of what it is they do?

Wittgenstein yes, Ed Witten no, Jason Witten yes?

Do you at least take my point? Your own position doesn't seem consistent. You haven't given me a standard that I can apply.

What's interesting about this is that whereas it is quite easy to see how mathematics (at its extremes) makes no sense — synthesis

I totally agree. Bertrand Russell nailed it:

Mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true..

Tru dat.

You're welcome to your delusions. — Xtrix

Did I say something that bothered you? By way of conversation, I'm wondering why you think the public is entitled to a voice in which highways to build, which public projects to fund, but not which scientific projects to fund? Or am I misconstruing your concerns? I thought you might find my links of interest to your own knowledge. After all it's true that we are not physicists, but you seem to be saying that we shouldn't even bother to read popular accounts of the work of physicists.

But then why have a philosophy forum? Are we armchair philosophers allowed to have opinions, informed or not, on the philosophical issues of the day? After all philosophers work a lot cheaper than physicists. Are we allowed to opine on Wittgenstein but not Witten? Where do you draw the line?

To presume I have any idea that its "bad physics" is delusional. Ditto for you — Xtrix

I can't speak for you. But I'm entitled to (and do in fact have) an informed opinion on the matter. I can refer you to some recent books by physicists on the subject. And since the work of modern physics is primarily supported by government grants and I'm a taxpayer, I most definitely have say.

You may remember the Superconducting Super Collider, a massive particle accelerator in Texas that would have been far more powerful than the current Large Hadron Collider, but killed by Bill Clinton in 1993 for budgetary reasons. As the bureaucrats said to the astronauts in the film, The Right Stuff, "What makes the rockets go up? Funding. No bucks, no Buck Rogers."

Review of Sabine Hossenfelder's book:

https://www.wsj.com/articles/lost-in-math-review-the-beauty-myth-1529703982

Lee Smolin's book:

https://en.wikipedia.org/wiki/The_Trouble_with_Physics

Peter Woit's article. He has a book too.
https://blogs.scientificamerican.com/cross-check/why-string-theory-is-still-not-even-wrong/

Also see these vids by Sabine Hossenfelder. She's terrific on explaining physics and also on explaining these methodological and philosophical issues with contemporary physics that I'm referring to.

https://youtu.be/9qqEU1Q-gYE

https://www.youtube.com/watch?v=HwTkBkb94Rc

Note that all these books and articles, and others like them, are intended for mainstream audiences. So these authors are physicists who understand the physics; and who also believe that it IS the business of the public to make informed judgments on the validity of the work currently being done by the physicists.

We are a long long way from when Isaac Newton returned home during the London plague to invent calculus, develop his theory of optics, and conceive of the law of universal gravitation. He did all that with paper and quill pen. Today, science is a massive public works project, and its funding is not all that different from a vote on a referendum to float a bond to repair a highway. It's all public money, and quite a lot of it.

Yes: understanding physics takes work. Hard work. — Xtrix

What explains the recent (past several decades) of bad physics from the hard-working professional physicists?

After having read the following quote, I came to the conclusion that the agnostic stance on the matter of God's existence might be the most reasonable: — spirit-salamander

Yes. That is my position.

* First, it's absurd that there's a Causeless Cause (CC) that created everything; let alone that the CC has a beard, a white robe, and cares a lot about how people have sex.

* Second, it's equally absurd that the universe either began to exist or has always existed, along with its apparently exquisitely intricate design, without any cause at all.

* Finally, I do not have the arrogance or self-importance to imagine that I could ever be personally possessed of the answer -- as so many others on all sides (the Intelligent Design proponents, the traditional Christian believers, the "New atheists); -- believe themselves to be.

I truly have no idea. In fact I go further. I don't believe the question is answerable. This belief of mine has a name: the New Mysterianism.

As Wikipedia, says:

New mysterianism—or commonly just mysterianism—is a philosophical position proposing that the hard problem of consciousness cannot be resolved by humans. The unresolvable problem is how to explain the existence of qualia (individual instances of subjective, conscious experience). In terms of the various schools of philosophy of mind, mysterianism is a form of nonreductive physicalism.

I go further. I say that not only consciousness, but also the origin of the world is in the same category. A mystery outside of human ability to resolve or understand or know.

As I put it, somewhere on earth there is a forest. In that forest is a tree; and on that tree is a branch. The branch has many leaves; and on one of those leaves is a caterpillar. And that caterpillar has an ontology. It knows what to eat, and what wants to eat it. It knows when to sleep and when to wake. It knows night from day. It knows when it's warm and it knows when it's cold. It knows, deep in its cells and its DNA, that someday it will ascend to become a beautiful butterfly. But it can never know about the branch and the tree and the forest and the earth, let alone the quarks and the gluons.

Likewise we humans, who think so much of ourselves, are stuck at our own level of perception and understanding. The difference between me and Laurence Krauss is that neither of us knows how the world got here, but he thinks he knows and I know I don't. And he's wrong, and I'm right.

The tedious tide of theological threads appear to have been replaced by a population of piss-poor physics posts. — Banno

You mean here, or on the Internet in general? Personally I'm much more interested in bad physics than in bad theology. And in bad math most of all. It's the Internet, not the Royal Society. Then again when Newton was president of the Royal Society he ordered the burning of the the last surviving portrait of his great rival Robert Hooke. If these guys showed up on the Internet today they'd flame with the best.

I always viewed physics as just another form of advanced math, like calculus and whatnot. Am I wrong on that? — James Riley

Yes you are wrong. Math is to physics as hammers and nails and wood and bricks are to construction. Tools and materials of the trade, essential to the enterprise, but not the enterprise itself.

In logic, a statement need only be logically correct. "If A implies B and A is true, then B is true." This is a logical truth because it's a valid statement true under any conceivable assignment of meanings to A and B.

In math, a statement needs to be logically valid AND mathematically valid to be true. "If 2 + 2 = 5 then I am the Pope." That is a mathematical truth. Note that it's NOT a logical truth, because it depends on the meaning of "2 + 2 = 5". We need to know that mathematically, 2 + 2 = 5 is false. At that point, the implication becomes true; but in the real world, meaningless.

In physics, a statement must be experimentally true about the world, not just mathematically correct. Mathematical models that are not physically confirmed (string theory, eternal inflation, etc.) are labeled as speculative. They are not physical truths even if they are mathematically correct.

There are many such speculative theories floating around in physics these days. In fact that's one of the great criticisms of contemporary physics. "The Trouble With Physics" by Smolin, "Lost in Math" by Hossenfelder, etc. The complaint is that since the physicists have been stuck for decades, they're now reduced to churning out one speculative mathematically correct but physically unverifiable theory after another; while publicly making ever more grandiose claims of knowing how the world works, ie "A Universe from Nothing" by Krauss.

The notion of an actual infinite makes zero sense if, as per my assumption, actual means what it seems to mean to wit, completed in one sense or another for it flies against the definition of infinity as being necessarily that which can't be completed.

Maths, set theoretical infinities, kind courtesy of Georg Cantor, is an altogther different story as maths is essentially an axiomatic system, anything goes so long as you don't contradict yourself within one. — TheMadFool

I am in agreement with this. Whatever it is that physicists mean by infinity, they surely don't mean mathematical infinity. The set of positive integers is infinite by construction in Peano arithmetic, or by the axiom of infinity in set theory. But I do not believe such an infinite set can be instantiated in the real world.

I have another idle thought ... that the next revolution in physics will be the discovery of the actual infinite in the real world. By analogy, non-Euclidean geometry was thought to be a mathematical parlor trick of no use to physicists. Then Einstein came along and non-Euclidean geometry became real to the physicists.

Physically realized actual infinity has the same status in physics today as non-Euclidean geometry had in physics in the 1840s. The future genius to make this next breakthrough hasn't been born yet. Perhaps.

See recent thread here. And call me God.

https://thephilosophyforum.com/discussion/10727/pronouns

Is it clear that a field of study can ever be fully understood by reducing it to another? — Gregory

Provisionally yes, meaning yes but I could probably think of counterexamples if I tried. I guess I didn't understand your post.

ps -- Did @Banno's response to me above address your concerns? He explained what I said better than I did.

Memory is simply the mind's record of the past — TheMadFool

That's far from true. Numerous experiments show how unreliable our memories are.

So the powder using its force in a way that is different from gravity, — Gregory

This makes no sense. A gunpowder explosion is a chemical reaction that's perfectly well understood. You might as well say that fire violates the law of gravity. Or that cooking violates the law of gravity. The world is full of chemical reactions that have nothing to do with gravity. I don't follow your thesis at all. Chemistry operates at a level above the fundamental forces of physics.

You just said I may be right. I am. You only grabbed that one sentence of mine out of context and you haven't read most of the thread. — James Riley

Since I already confessed to that crime you can't prosecute me for it a second time. Isn't that double jeopardy? Or is this a state prosecution followed by a federal prosecution, as is commonly done in this great bastion of constitutional freedom of ours?

So, to satisfy your curiosity on that point, we're not arguing the merits of any given political position. We're talking about gatekeepers, and whether or not "arguments" or "facts" deserve equal time. — James Riley

I say let everyone speak and let the market decide. I don't believe in gatekeepers. They have the worst track record of all.

Or we could just tune in to that bastion of "fair and balanced" Fox News? Yeah, that's the ticket. — James Riley

You just said you fundamentally agree with me, and now you want to pick a fight about Fox News? I don't watch cable news and certainly not broadcast news. I'm not sure if you want to argue politics or agree with me about something. Intellectuals and mainstreamers have an awful track record. You were advocating if not the "rule," at least the primacy of -- who exactly? The "public intellectuals," certified morons like Sam Harris and the so-called New Atheists? Who exactly? That's what I asked you. Or perhaps by intellectuals you really mean the mainstream neocon/neoliberal coalition that's run the country so well the past 30 years.

Here's a nice clip that summarizes it all. Max Keiser and Stacy Herbert (if you're not watching them on Youtube you should be) pointing out that Bill Clinton did three things: He repealed Glass-Steagall, he passed the Commodity Futures Modernization Act, and he granted China most favored nation status in the WTO. Keiser calls this, "the trifecta of the disembowlment of the American middle class." Starting at 4:45 here but the whole thing is well worth watching. as is everything Max and Stacy put out several times a week. Turn off the tv news, turn on Youtube and other streaming services. That's where honest journalism is these days. Lester Holt ain't it.

https://www.youtube.com/watch?v=HZcQtp-qCRU&feature=youtu.be

you and I are in accord. — James Riley

You may be right. I only grabbed that one sentence of yours out of context and haven't read most of the thread. FWIW, intellectuals have a terrible track record in the 20th century to the present. The "right kind of people" seem to do all the wrong kinds of things. My apologies if I misconstrued your sentiments.

I think we were talking about Holt. — James Riley

Holt works for NBC News, does he not?

NBC News Deceptively Edits Bodycam Footage So Viewers Don’t See Knife in Ma’Kiyah Bryant’s Hand Moments Before Officer Shoots Her Dead

Lester Holt works for a network with a demonstrated pattern of not believing in fairness.

As a columnist on PJ Media, a scurrilous conservative website I enjoy wrote:

I can’t be the only one who didn’t have “Liberal America Doesn’t Want Cops to Stop Black Girl From Stabbing Another Black Girl” on my bingo card.

I'll leave it at that this morning.

We are the gatekeepers. — James Riley

Can you give an example of the ones over whom you are entitled to rule? Name names and justify your claim to be among the gatekeepers.

On a broader theme, it's the "best and the brightest" who got the US into Vietnam, Iraq, Afghanistan, Syria, Libya, and all the other futile wars we can't win. You may know that there was a book, The Best and the Brightest, about how the so-called "whiz kids" of the Kennedy administration blundered into Vietnam.

Intellectuals have quite a lot to answer for over the past sixty years of American history.

Here's a piece I just happened to read this afternoon by the great Chris Hedges about what the intellectuals you revere have done with the US as it thrashes about in the violent throws of its status as a failing empire.

https://www.salon.com/2021/04/20/unraveling-of-the-american-empire-a-series-of-military-debacles-point-toward-a-tragic-end/

Imperial ineptitude is matched by domestic ineptitude. The collapse of good government at home, with legislative, executive and judicial systems all seized by corporate power, ensures that the incompetent and the corrupt, those dedicated not to the national interest but to swelling the profits of the oligarchic elite, lead the country into a cul-de-sac. Rulers and military leaders, driven by venal self-interest, are often buffoonish characters in a grand comic operetta. How else to think of Allen Dulles, Dick Cheney, George W. Bush, Donald Trump or the hapless Joe Biden? While their intellectual and moral vacuity is often darkly amusing, it is murderous and savage when directed towards their victims.

Hedges is a radical leftist, a former foreign correspondent for the New York Times, and a man who tells it like it is.

I didn't watch the vid but I know the argument. I have three comments.

* Everything that "begins" to exist has a cause. So the conclusion that there must be an uncaused cause, which we name God, is baked in to the assumptions. But who caused God? How can there be an uncaused cause? Well in the argument, it's because God has always existed. God did not "begin to exist." So there's a bit of sophistry or word play at work.

* The negative integers ..., -4, -3, -2, -1 provide a model of causality in which (a) every event has a cause; and (b) there is no first cause. How do you know causality in the world doesn't work like that? It's turtles all the way down.

* Causation in the world is not at all like one thing causing another. Any event has many causes. A million different things had to happen for your parents to be born and meet and create you. Causality is more like a network and not like a linear chain. So the whole model of causality in the argument is wrong.

The argument is sophistry. It doesn't prove the existence of God. It's not even a coherent argument. It's wordplay. William Lane Craig makes a living off it but that's as far as it goes.

Suppose that the KCA was sound — Walter Pound

The argument is unsound. If we suppose it's sound we can conclude anything we like.

Right, "2+2=4" has meaning without referring to anything, just like "green is a colour", and "the acceleration of gravity is 9.8 metres per second per second" have meaning without referring to anything. — Metaphysician Undercover

I have a quibble about that. You say 2 + 2 = 4 has meaning even though you assert that neither 2 + 2 nor 4 refer to anything. And you've said that green doesn't refer to anything. Questions so that I can better understand:

* Does 2 + 2 = green have meaning? If no, then why does 2 + 2 = 4 have meaning? None of 2 + 2, 4, and green refer to anything by themselves. So why can we combine 2 + 2 and 4 on either side of an equal sign, but not 2 +2 and green?

* Does 2 + 2 = 5 have meaning? What does it mean? If none of 2 + 2, 4, or 5 have meaning; then how can you distinguish 2 + 2 = 4 from 2 + 2 = 5?

These are generalizations, abstract rules or laws, which have a broad application without referring to any particular thing. But even though they don't refer to any particular thing, they still have meaning. — Metaphysician Undercover

If they don't refer to anything, how do you know they have meaning and what that meaning is? Does dfslkjf have meaning? Does it refer to anything? What gives 2 + 2 meaning; and what exactly does it mean, if it doesn't refer to anything?

The law of identity states that a thing is the same as itself. — Metaphysician Undercover

Yes. And you assert that it only applies to "things." So that Joe Biden = Joe Biden is an instance of the law of identity; but 4 = 4 is not.

And I asked you, how do we determine thinghood?

So when it is expressed using = then "=" signifies is the same as. So if the law of identity is expressed as "A=A", then A=A is supposed to signify that an object is the same as itself. I wouldn't say "4=4" is necessarily meaningless though, because "=" in mathematics signifies "has equal value to". — Metaphysician Undercover

Well now you have introduced a brand new term, "value." What does it mean? If 4 does not refer to anything, how do I know what it's value is? If fglfdkjgldj does not refer to anything, how can I determine what its value is?

Do you recognize the difference between "the same as" and "equivalent to"? — Metaphysician Undercover

Of course. I wonder if you do. Equality is a special case of equivalence. But there are equivalences that aren't equalities. For example 4 = 4 is an equality. $4 \equiv 6 \pmod 2$ is an equivalence that is not an equality. Is that what you mean? That's the mathematical sense of the word but perhaps you have something else in mind.

In general, two things are equivalent when they live in the same equivalence class of some equivalence relation. For example if we say two people are equivalent if they live in the same state, then the equivalence classes are the states, and I am equivalent to Gavin Newsom. That's equivalence.

Equality is a special case of equivalence in which each equivalence class contains exactly one element.

I fail to see how equivalence has anything to do with what we're talking about, though.

As for your question of who decides what a true thing is, that's what the law of identity is the criteria for. If it has its own identity as unique particular, it is a thing. — Metaphysician Undercover

Isn't that circular? The law of identity only applies to things. And how do we know if an entity (if I may use that word to mean something that might or might not have thinghood) has thinghood? It does if the law of identity applies to it. That's circular!

Given an entity, like Joe Biden or 4, how do I know that the former has thinghood, so that Joe Biden = Joe Biden is an instance of the law of identity; and 4 DOESN'T have thinghood, and 4 = 4 is NOT an instance of the law of identity?

Yet in the latter case you assert that although 4 = 4 is not an instance of the law of identity, it does nevertheless have meaning. And what is its meaning, exactly? Does 4 = 5 have meaning? If so, what is its meaning?

@Meta you are tying yourself into knots trying to make sense of your claim that 4 does not refer to anything.

Of course you do not have to agree with the law of identity, many philosophers have argued against it. — Metaphysician Undercover

I'm not disagreeing with the law of identity, you are. You claim that 4 = 4 is not an instance of the law of identity. That is a radical claim that requires much more evidentiary support than you've so far provided.

And you THEN claim that even though 4 = 4 is not an instance of the law of identity, it nevertheless has "meaning," by virtue of the "value" of 4. But you haven't defined these terms and clearly seem to be using them in a nonstandard way. If 4 has a value but doesn't refer to anything, you have some 'splainin' to do.

The law of identity is not about symbols, it is about things. That's why it is quite difficult to grasp, and also why many argue against it. — Metaphysician Undercover

But I'm not arguing against it. I'm asking you to give me a coherent account of your idea that 4 = 4 is not an instance of the law of identity, yet 4 = 4 has "meaning" by virtue of the "value" of 4. If 4 doesn't refer to anything, how can it have a value?

By the way philosophers of mathematics have long settled on perfectly sensible answers to this question. We can define 4 as the class of all sets of cardinality 4 (which was the original definition, but suffers from the drawback that this class is not a set); or we can use the modern definition, which isthat we choose a canonical representative of 4-ness, namely 4 = {0, 1, 2, 3}. This was von Neumann's clever idea..

The intuitive response to "identity" is to think of the name of the thing as the thing's identity. — Metaphysician Undercover

I am not making that error, this is a strawman argument.

But this is not what the law says, it says that the identity of the thing is the thing itself. This creates a separation between the identity which we assign to the thing, (it's name, description, or whatever we say about it to identify it), and its true identity, which is itself. — Metaphysician Undercover

More strawmen. You claim that 4 = 4 is not an instance of the law of identity; yet it has "meaning" by virtue of the "value" of 4. I am asking for a coherent account of that claim.

You might say then, that to have "thinghood", is to have independent existence, separate from whatever we might say about the thing. This is to have an identity, to be something. — Metaphysician Undercover

How do I know that Joe Biden has thinghood and that 4, 2 + 2, and green, don't?

And if 4, 2 + 2, and green don't have thinghood, how can you claim that 2 + 2 = 4 has "meaning," but 2 + 2 = green doesn't?

No, this is not what I am saying at all. What I say, is that "=", when used in mathematics, does not mean "the same as", as dictated by the law of identity. — Metaphysician Undercover

You're just flat out wrong about that. In math, = means "the same as" as dictated by the law of identity. As I've been telling you for three years.

But the problem is that having denied that, you can't give a coherent account of "meaning" and "value" by which 2+ 2 = 4 has meaning and 2 + 2 = green doesn't.

So it's not that you're not allowed the opposite opinion. It's that your account of the opposite opinion is not coherent. I'm not just disagreeing with your position. I'm asking you to make sense of it.

So these uses of "=" have meaning, but the meaning is not "the same as", as dictated by the law of identity. — Metaphysician Undercover

As I say. Give me an account of your idea so that I too may see why 2 + 2 = 4 has meaning but 2 + 2= green does not, even though none of the terms have thinghood and neither equality (according to you) is an instance of the law of identity.

I don't agree with this. Many philosophers argue against platonic realism. Saying that "4" refers to an object which is a number is nothing other than platonic realism. — Metaphysician Undercover

I'd be willing to accept that 4 doesn't refer to anything, since my claim is that it refers to the "abstract number 4" which has much less claim on thinghood than a rock or Joe Biden. Mathematicians get around that problem either by defining 4 to be the proper class of all sets of cardinality 4; or else they choose a canonical representative of that class, {0, 1, 2, 3}, to stand in for the number 4. Although as Benacerraf points out, 4 "can not possibly be" {0,1,2,3} and of course he is right about that.

So I'm willing, for sake of discussion, to grant you that 4 has a rather tenuous grasp on thinghood.

But then 4 = 4 is not an instance of the law of identity, yet you say it has MEANING by virtue of the VALUE of 4. That's where your thesis is in need of support.

It's easier to just take 4 as {0,1,2,3} so that we can have a sensible theory by which 4 = 4 IS an instance of the law of identity. That's what I do and that's what most philosophers of math do.

What you have done is propose an alternative but you are stuck on "value" and "meaning." If you can explain these, please do.




No, philosophically I believe in a correspondence type of truth, so strictly speaking these statements are valid within a logical system, but it doesn't make sense to talk about truth here. [/quote]

This was in response to my question of whether you think "4 is an even number" is true. I agree that if one is a strict formalist then it's not a true fact about the world. But that's an argument against strict formalism, and not an actual stance one should take if one wishes to be sensible.

I might in common speaking, say that such things are true, but I would be using "true" in a less rigorous way. — Metaphysician Undercover

As I say, I take this as an argument against formalism, and not as a sensible position to take. Even on my formalist days I am stuck on "5 is prime." That seems to be a true fact of the world no matter how we fight against Platonism.

No, "=" as it is used in mathematics means to have the same value. It does not mean "the same as" as dictated by the law of identity. — Metaphysician Undercover

As I've noted, you're wrong about that. But if you're not, then you need to give a coherent account of "meaning" and "value."

This has always been the heart of our disagreement. So "2+2=4" has meaning, it just does not mean that "2+2" refers to the same thing as "4", it means that they have equal value. — Metaphysician Undercover

Once you explain to me what meaning and value are, I'll be in better position to understand your viewpoint. If 4 and 2 + 2 don't refer to anything, how can they have meaning or value? And how can I know that 4 has meaning and value but dflsklsjlslds doesn't?

* 4 = 4 is meaningless because the law of identity only applies to "true things" and not to properties, and 4 is a property and not a "true thing." — Metaphysician Undercover

You've been saying it has meaning, even though it's not an instance of the law of identity because 4 lacks thinghood. Now you say 4 = 4 is meaningless.

In fact in your very first sentence of the post I'm replying to you said: "Right, "2+2=4" has meaning without referring to anything, ..."

And now yuou say 4 = 4 is MEANINGLESS. Can you see that you contradicted your own position? And how could you not? You are claiming that 4 doesn't refer to anything, and that 4 = 4 is therefore not an instance of the law of identity, and now you are hard pressed to give an account of 4 = 4. You say it has meaning and then you say it's meaningless. And then you wave your hands and say that I don't understand the law of identity, as if that would make your position coherent.

These I think I've already addressed. — Metaphysician Undercover

Not to my satisfaction. But I'll settle for a coherent account of 4 = 4. Does it have meaning? Does 4 have value? Does kfkdfjkdjdkd have meaning or value?

I've studied philosophy for many years. Have you not heard of platonic realism, and that some philosophers are opposed to it? — Metaphysician Undercover

I take your point, but even a Platonist has to come to terms with the truth of "5 is prime" and "4 is even." And "4 = 4".

So am seeing this quote now days quite a lot. — RBS

That's why they call it virtue signaling. The worst people spend the most time telling you how good they are.

Keep the masses as uninformed about their reality as possible. — Bitter Crank

Perhaps we can convince everyone to let the government run the schools, and then have the federal government to use financial incentives to exert top-down control of state and local school authorities. That would get the process started, and the media could do the rest. Can it all really be such a dastardly plot? Or did it more or less happen by accident?

I'm not sure, but perhaps that post is a parody? — j0e

No, this is the new generation of young adults in the US. They are deadly serious. A couple of people did mention that "it" is a slur against transgenders.

Look at what you say above, "2+2" says something about 4. What is 4? It is a quantity, or a value, it is not a thing. Remember, my argument is only applied to a strict definition of "thing", in which a thing has an identity according to the law of identity. — Metaphysician Undercover

For the first time I understand what you're saying. If you've been explaining this all along and I didn't understand, that's on me. But you haven't been explaining your position this clearly, well now you have. What you say is interesting. Still extremely wrong IMO but at least you have staked out a position that is coherent, and I would say very interesting.

Let me say this back to you. In the past I thought you were saying that 2 + 2 and 4 refer to different things. But what you are saying in fact is that 2 + 2 and 4 don't refer to anything at all. Because they are properties, or attributes. 4 is a property of a string quartet, for example. There is no number 4 by itself as an object. So it's wrong to say that 4 refers to anything at all.

Do I have that right? I disagree but I will put that aside so we can catch up to each other.

Your position: 4 and 2 + 2 are qualities or attributes or properties of things; but they do not refer to a specific thing. 4 is a property of a string quartet. But 4 by itself is a "potential property," if I may call it that, but it's not any particular thing and it does not refer to any particular thing except something that enjoys thinghood, like a string quartet. Have I got this about right?

As I say I will defer my objections to the end and for now content myself with merely understanding you after all this time.

If for example, you assume that green is a thing, you might say yellow and blue make green, so that you might argue that "yellow and blue" refer to the same thing as "green". But this is what I deny. "Yellow and blue", might as you say above, say something about green, but neither "yellow and blue" nor "green" refer to a thing. Green is a property, something we attribute to a thing. Likewise 4 is a property, something we attribute to a group of things. — Metaphysician Undercover

I don't like the color mixing example because color theory, additive and subtractive, is relevant to painters and physicists but not to philosophers or mathematicians. But I will take your point that green does not refer to anything except the "things" it does refer to, like houses and traffic lights. But there is no color green. There are green houses and green traffic lights but no green by itself. Forget the color mixing, that's not a good analogy IMO.

The intent of the law of identity is to distinguish true things, which have a real identity, from concepts, platonic ideas, which have no true identity and are therefore not things. — Metaphysician Undercover

Ok! I understand you. The law of identity x = x only applies to "true things," things that are deserving of thinghood; and not properties, which can apply to things, but are not themselves things. A green house is green, but green by itself is not a thing. Therefore green = green is meaningless. Is that your point? I wish you had said this earlier, and I suppose you'll say you did. But I understand you now. Green is not a thing and 4 is not a thing. 4 does not refer to anything at all. It's a property. 4 = 4 is therefore meaningless.

Do you assert that 4 = 4 is meaningless? Can you please explicitly confirm this and don't skip over it?

You assert that 4 = 4 is meaningless because 4 does not refer to a "true thing."

May I ask, who decides what is a true thing. But nevermind, I said I'd defer my objections to later.

So it makes no sense to say that "4" refers to a thing, or "an object" in any sense, as 4 has no true identity. It has an infinite number of representations, 2+2, 3+1, etc., and none can be said to be the true representation. If we affirm that 4 is the true representation, then the others must refer to other true objects, represented by 1 and by 2 and by 3. — Metaphysician Undercover

I would never say that 4 is the "true representation." All representations are equally NOT the thing they represent. 4, 2 + 2, 3 + 1, 3.999..., and 47 - 43 are all representations of the number (represented by) 4. I'm sorry I can't actually name the thing itself! Tricky, that. But YOU say that none of those representations represent ANYTHING. I bizarre belief but like I say, I'm happy I finally understand what your belief is.

Yes, this is exactly what I am saying, 2+2 does not refer to the same thing as 4 because neither refers to a thing. — Metaphysician Undercover

I really don't think you've ever been as explicit. I understand your point of view perfectly. 2 + 2 and 4 are properties that can apply to string quartets and, um, gallons of milk that contain 4 quarts of milk. But by themselves, they don't refer to anything ... and that therefor you claim that:

2 + 2 = 4 is MEANINGLESS.

Is that what you say? Please give me a clear yes or no on this. You assert that 2 + 2 = 4 is meaningless because neither expression refers to anything.

Are you SURE this is a position you want to defend?

They refer to properties, which are not things, by the law of identity. — Metaphysician Undercover

Can you point me to a discussion of the law of identity that explicitly confers thinghood on some symbols and not others? Do you call them symbols? There are "true things" and "false things," by what word do you call things in general? Entities perhaps? An entity can be a true thing or a property? What is your terminology?

So, take my example, "blue and yellow" does not refer to the same thing as "green", because neither refers to a thing. — Metaphysician Undercover

Color theory isn't a good example but I don't know, maybe it is. It's not resonating with me so I'm skipping over it.

Notice that there can be many green things in the world, just like there are many groups of 4. But through the application of the law of identity we see that "green" itself does not refer to a thing, otherwise all the distinct instances of green would be the very same thing in violation of that law. Likewise "4" does not refer to a thing. — Metaphysician Undercover

Yes I get that. So green = green is meaningless; and 4 = 4 is meaningless; and 2 + 2 = 4 is meaningless. Is this the proposition you're prepared to go forward defending?

To make up an imaginary object, a platonic idea, called a number, and say that this is the object referred to by "4" does not resolve the problem, as I've explained to you already. — Metaphysician Undercover

Let's not argue about whether you've explained it before. Let's just say I understand your point. When mathematicians say that 4 and 2 + 2 refer to the abstract thing called the number (that we call) 4, you are disagreeing. You say there IS NO number 4. That the symbol '4' does not refer to anything.

You do know you're kind of out of step with pretty much everyone, right? Not that this is an argument against your idea. You could be right and everyone else wrong. But you do agree that virtually all philosophers and mathematicians believe in abstract numbers as "true things."

Tell me, do you believe that "4 is an even number," or "4 represents an even number," have truth values? If so, what would you say the truth values are?

Then, "2" must also refer to such an imagunary object. So, when you write "2+2", you denote the object, the number two twice. By what principle do you say that this object, the number two, when denoted twice actually refers to the number four? — Metaphysician Undercover

I could go nominalist and invoke the Peano axioms, or empiricist and note that 2 pebbles and 2 more pebbles is 4 pebbles. But why bother, i'm sure you've thought of this. For now I will defer direct argument with your ideas. I just want to confirm I've got your ideas right.

That's completely nonsensical, to say that two instances of occurrence of this object which we call the number two, magically becomes the object called the number four. — Metaphysician Undercover

I must say it seems rather commonplace to me. But let's defer that for the moment.

You must respect the object actually referred to by "2", just like if you say that the colours are this type of platonic object you must respect the colours actually referred to by "blue" and "yellow", and not falsely conclude that "green" is being referred to when someone says "blue and yellow". — Metaphysician Undercover

Ok. I am not going to write anymore in this post. I just want to make sure that I understand your position.

* 2 + 2 = 4 is meaningless because neither 2 + 2 nor 4 refers to anything. You would agree that 2 fish plus 2 fish is 4 fish, but you would NOT go so far as to agree that 2 + 2 = 4.

* 4 = 4 is meaningless because the law of identity only applies to "true things" and not to properties, and 4 is a property and not a "true thing."

* You would NOT agree that 4 represents an even number, because you don't think 4 represents anything at all.

* You do understand that you haven't got much if any agreement in the math or philosophy communities, yes?

* Who is the arbiter of "true thingness?"

Ok very interesting. I eagerly await your comments.

Can you tell me (I've asked this before) where you came up with these ideas? Are they written down somewhere? I've never heard it said that abstract numbers are not "true things" deserving of being equal to themselves. The Wiki page on the law of identity does not mention any distinction between "true things" and properties.

I think we're talking past each other. No worries. — RogueAI

Yes but could you just tell me specifically how your day to day life would change?

That's weird. My response posted before your question. Maybe God did that.

So you're telling me Fish, that if you knew for certain that a god exists (and here I mean some powerful supernatural being capable of creating a universe like ours), you would have no follow-up questions? Really? You would just take it in stride? — RogueAI

Yes. What else can I do? Can you please give me a specific example of how you think my life would change? I'm not a criminal nor a violent person. I don't have much about my life that I think is bad or ungodly in the sense of going against the purpose or will of the universal intelligence or spirit. I'm asking you (third time I think) to give me a specific example of what you are talking about. It doesn't have to apply to me in particular, just give me an example of what you are saying because I honestly have no idea. Watch fewer pro-football games? Have different political opinions? Eat fewer animals? Maybe that last one has something going for it. But then why did God make cheeseburgers taste so good? If it were up to me when I die I'd like to have them toss my body in a cow pasture to complete the cycle, but cows don't eat people. Next choice would be to toss my body, my whole body and not my ashes, into the ocean so the fish can eat me, as I've eaten so many fish in my life. But I feel this way right now, I don't need proof of God to feel that way. So tell me what you are talking about. Give me an example. Please.

How do you think the world and scientific community would react to definitive proof of theism? — RogueAI

I truly have no idea. I watch the world react to the latest doings of the British royal family or the butt sizes of the Kardashians so I don't have a very high regard for the opinions of the general public. And the scientists? What would they think? Who cares? They wouldn't stop doing science.

I really think you need to give me an example of how you think people would change because I don't know what you're talking about. Would we all go to church more? That's religion, not God. The biggest Holy Roller televangelists are always robbing the till and consorting with rent boys. I truly have no idea what you are getting at.

I think people would completely lose their shit. Because once you know some god exists, it becomes pretty important to find out what its plans are for you and whether you're in its good graces. — RogueAI

People lose their shit over everything and anything. What does "lose their shit" mean in this context? Tweet about it? Post a selfie? Do you pay any attention to the popular culture? People got worked up over Oprah's interview with Megan and Harry, so I guess for a few weeks they'd get similarly worked up over God, but nothing much would change. People are always "losing their shit" over one thing or another. News tease: "God proved to exist. News at 11." What would change? I genuinely disagree with you that anything would change long term. And I still challenge you to give me a specific example. "Lose their shit" is not a specific example.

If you knew for certain that god exists, that wouldn't change your life in any way? — RogueAI

Not in the slightest. I'm asking you to explain how it would make any difference in my life. Explain this so I can understand what you mean. I do think there's some kind of universal spirit, maybe an active intelligence of the universe. I don't discount the possibility. And I do have a humble reverence for the miracle of life and the universe and all that. But I don't alter my behavior in any way as a result of my beliefs.

I think you're conflating the difficulty of proving "god did it" with "god did it". Simulation theory and "god did it" are both very similar in that they're impossible to prove, but if true, have staggering implications. — RogueAI

Name one. If I'm a brain in a vat or God made me or the great programmer in the sky made me or I'm a Boltzmann brain, exactly what will I do differently today than I would have done before I found out? And how would I find out? They're all propositions without any hope of proof.

And all these explanations explain nothing. If God made the universe who or what made God? If we're designed, as in Intelligent Design, who designed the designer? If we're programs running in the cosmic computer, who programmed the programmers? In fact only the Boltzmann brain explanation actually explains anything. It's pure random statistical chance, actually far more likely than that the entire universe exists. But I say that NONE of the things you mention has the slightest implication whatsoever, let alone staggering ones.

I just see that you both come from different perspectives, and it is related to the wording of the question as 'Should..' I don't see the matter as being how we should see, because it is being prescriptive. — Jack Cummins

I think I personally use the term God the way Einstein did. Nature, or the cosmos, or the Great Everything and all its mysteries. Certainly not in any religious sense.

Fishfry, if we discovered for sure that God did something, wouldn't it become of paramount importance to figure out the nature of this god? — RogueAI

Hasn't that been the basis of too many violent religious wars over the centuries? That's one of the New Atheist arguments against religion: that it's not just a benign and harmless set of beliefs, but that it's actively harmful. I mean sure, if we could confine the figuring out of the nature of God to academic journals that would be great, as long as we can leave the holy wars out of it.

And then try to communicate with it? — RogueAI

Like SETI but aimed at God? How would that work exactly? I'm ok with personal prayer, if that's what you mean.

Of course. Let me give you an example: suppose one night the stars move around to spell out: "god is displeased with you all". Wouldn't the "god did it" explanation then be a heavy favorite? And wouldn't it succeed in explaining the phenomena? — RogueAI

I'll reserve judgment till that happens. On the other hand one might be tempted to say that the evidence of God is all around us in the world. What more do we need?

I'm not sure if you're asking rhetorical questions or making a serious theological point.

Why is "God did it" useless as an explanation? Doesn't it tell you why something happened? God did it! — RogueAI

It's not helpful as a scientific theory. It doesn't help us make predictions or develop deeper understanding. I'm probably not the best person to offer a detailed critique of the unsatisfactory nature of religious explanations. The new atheists (Krauss, Dawkins, Harris, et. al.) do a fine job of that. It's their excesses of scientism that I object to.

I wanted to mention to you that I did read that Quanta article and die a little web research. I convinced myself that we had yet another classic case of a speculative scientific idea, simplified and misconstrued by Wikipedia, and finally completely misrepresented by a pop-science writer who was not in a position to ask the right questions and substituted gee-whizzery for insight. I was going to write it all up but didn't. I wonder if I can challenge myself to say it in fewer than 3000 words (my first draft, which I abandoned). Bottom line is that eternal inflation is a highly speculative idea. The multiverse, if it even exists, is finite today, finite tomorrow, finite a billion years from now, and finite at every moment of time for all eternity That's something the Quanta author missed and that you have to dig into the literature to figure out. It's only when you assume that inflation is truly eternal -- that it lasts literally forever -- that you get infinite universes. The cosmologists perfectly well understand that, they just enjoy not making it explicit when they're impressing the public.

Secondly, the cosmologists perfectly well understand the point I made about asymptotic density, that we can in fact sensibly say that half the positive integers are even, by taking the limit of finite calculations as you go to infinity. What the article (and the measure problem in general) are about, is a description of the various approaches cosmologists take in calculating that limiting process. In that respect, the article is excellent. What's wrong is the gee-whiz attitude of the "mystery of doing statistics on infinity," which is actually a perfectly well understood process by mathematicians AND these cosmologists. It's really mostly the blurb at the top of the article that says, "Infinity does a number on statistics," that implies mystery where there is none. The article's not even about that. It's about how cosmologists try various approaches to calculating the infinite limits.

Hey that came out pretty well. I did actually write 3000 words last week in response to the article, then abandoned the project, and this morning it came out just fine in a couple of paragraphs. If there is one takeaway, it's that eternal inflation is literally that. They assume time goes on forever; and that at each moment there are finitely many new universes, so that over eternal time you get an infinite multiverse.

Sounds more like theology than science.

Fundamental physics tells us energy is indestructible and that there is no single place in the universe where energy hasn’t got it’s fingernails dug in- it has a “finger in every pie” so to speak. It is every object that occupies the universe as well as all interactions between said objects. — Benj96

Darn good questions. My Youtube feed has lately been serving me up a lot of creationist-oriented critiques of science, so this subject is on my mind.

It turns out that there's quite a lot we don't know about the universe and its origins. We're told that the big bang came out of the original quantum field; that there was "nothing," defined by Laurence Krauss (author of A Universe from Nothing) as a quantum field devoid of time, space, matter, and energy. One day it all explodes into existence, and we can "do the math" and make the theory work. Critics note that the quantum field and the laws of physics are not "nothing," they're something; and all we've done is shove the question deeper. Where did the quantum field come from, where did the laws of physics come from?

It turns out also that we can't actually explain the origin of even so familiar a thing as the solar system. We're told the planets coalesced out of spinning gas, but the model doesn't actually work to explain the various planets and their anomalies.

Now the creationists say, "God did it." To me this is unsatisfactory. Even if God did do it. this doesn't explain anything. It just says we're giving up trying to understand, and just invoking a supernatural explanation.

But the new atheists are wrong too. They say, "Science proves there is no God," when in fact science proves no such thing. We have better and better explanations, but in the end all we have is mysteries.

So I object to both the new (and militant) atheists, Krauss and Sam Harris and Richard Dawkins and all the rest of them. They don't know what dark matter is, they don't know how the world got started, they don't know how life got started. They have theories but only to a point, and often no proof. And none of their theories say God doesn't exist.

I object also to the scientific creationists, the people who say that since we have all these inexplicable scientific mysteries, that "God did it" is a logical conclusion. It's not. Especially because it's so often the God of the Christian Bible. These folks will outline a brilliant critique of the (borderline nonsensical) theory of eternal inflation, and then "answer" it with a quote from the Bible. As if the Buddhists and Zoroastrians have no say in the matter.

I suppose that makes me an agnostic, "one who believes it impossible to know anything about God or about the creation of the universe and refrains from commitment to any religious doctrine." That's my belief.

What I do oppose is scientism, the popular belief that science has already explained everything. Truth is it hasn't. We have far more questions than answers. Our own theories say that it's statistically far more likely that I'm a Boltzmann brain than that the universe exists. In fact there was recently a thread here in which @RogueAI linked a popular article on the measure problem in eternal inflation. From the Boltzmann brain article we find out:

One class of solutions to the Boltzmann brain problem makes use of differing approaches to the measure problem in cosmology: in infinite multiverse theories, the ratio of normal observers to Boltzmann brains depends on how infinite limits are taken. Measures might be chosen to avoid appreciable fractions of Boltzmann brains.[20][21][22] Unlike the single-universe case, one challenge in finding a global solution in eternal inflation is that all possible string landscapes must be summed over; in some measures, having even a small fraction of universes infested with Boltzmann brains causes the measure of the multiverse as a whole to be dominated by Boltzmann brains.

Our best cosmologists can only come up with absurdities to avoid believing "God did it." Yet "God did it" is useless as a scientific theory or an explanation of anything.

We simply don't know. Which is fine. What's not fine is so many "public intellectuals," in well-deserved quotes, going around telling the public that we do know. That's wrong intellectually and morally. It's wrong intellectually, because in fact we don't know; and it's wrong morally, because it leads the public to believe "science" has all the answers. And we've seen enough of that this past year to last a lifetime.

tl;dr: Up with science; down with scientism. Up with a healthy respect for the miracle of creation; down with the glibness of "God did it."

As you yourself have repeatedly stated, in this thread, your proof is that 2+2=4. And, you've also stated that you recognize that I do not dispute the fact that 2+2=4. — Metaphysician Undercover

I was listening to a podcast on Frege, and the speaker mentioned his insight into sense and reference.

She (Patricia Blanchette) said that Frege noted that 2 + 2 and 4 refer to the same thing; but they have a different sense. 2 + 2 = 4 tells us something about 4 that merely saying 4 = 4 does not.

I believe this is the point you have been making, and in fact I might almost agree with you about this

However as I understand it, you are on record as saying that 2 +2 and 4 do not REFER to the same thing. And in this, you are wrong. You're wrong mathematically, and you're wrong according to Frege.

Is it possible for you to clarify your thinking here? Are you saying that 2 + 2 and 4 don't refer to the same thing, in which case you're wrong; or rather that 2 + 2 and 4 tell you different things about 4, in which case Frege would say you're right, and I myself am still on the fence.

Frege published this work in 1882 and Peano's axioms date from 1889. In terms of Peano arithmetic, 4 is just another name for 2 + 2 once we break everything down to the successor function. Which is why I don't even think they have a different sense. But if we drop the Peano formalism, I can indeed see that 2 + 2 = 4 gives more information about 4 than 4 = 4 does. So I can go both ways on this.

But regardless, 2 + 2 and 4 do REFER to the same object, namely the number that we call 4. So if you are saying they refer differently, you're wrong about that. Can you please clarify your intent?

I have no idea but that "anything" would be impossible to detect as detection requires some form of interaction but transparency means none of that. Good day. — TheMadFool

Dark matter fits the bill. It doesn't interact electromagnetically at any frequency, it's only detectable as extra gravitational attraction.

https://en.wikipedia.org/wiki/Dark_matter

Let me leave you with this.

I agree with you in this point, that sounds insane. — Amalac

That's what I thought you were talking about. I don't know the diff between that and whatever Leibniz thought about the subject.

Good! If I got you curious about something, then our exchange about possible worlds wasn't entirely fruitless. — Amalac

I glanced at the SEP article on possible worlds and my eyes glazed. Never could get into this subject I'm afraid.

I mean the part of the universe we can't observe at present, but may be able to observe in the future. We may never see those parts, but it's not logically impossible to see them. But then we're back to modal logic, and there we disagree. — Amalac

Well we can see out another light year per year. Not very much in the scheme of things.

If we could see them, then eventually (if space has some ultimate limit, even if we could never see it) we would have to reach something that is not transparent and not translucent by logical necessity. — Amalac

Whatever we can see at any given moment is part of the ever-expanding observable universe. I don't see how we can reason past that.

I'll answer a few of your other points later, right now I've some work to do. — Amalac

You're far better off. I'm truly puzzled nobody else jumped in here about modal logic or possible worlds.

Ok, but I'm not talking merely about the observable universe, I'm talking about both the observable universe and the parts of the universe we have not observed yet (that's why I said I meant “universe” in an all-encompassing sense). — Amalac

We can have no possible information about the part of the universe we can't observe. For all we know, in the unobservable universe, bowling balls fall up. There, I just contradicted my own position on this matter. I'm willing to accept that bowling balls might fall up in the universe at large, but not that there's a Newtonian possible world. My own ideas are clearly not well considered.

I use the term in the same sense as the one suggested by Bertrand Russell in this passage:

Space and time appear to be infinite in extent, and infinitely divisible. — Amalac

Two nonsensical premises, at odds with all of contemporary physics. Russell of course did not know about quantum physics or the Planck length.

If we travel along a straight line in either direction, it is difficult to believe that we shall finally reach a last point, beyond which there is nothing, not even empty space. — Amalac

False (or at least unproven and highly doubtful) premise hence unsound argument. But you already know this, right?

Again, I don't use the word “transparent” as it is used by physicists, but rather in the sense Wittgenstein uses it in my OP. You can substitute “see through” (meaning: such that you can see through it) every time I say “transparent” if you like. I guess it's a sense more akin to phenomenology than to physics. — Amalac

But the CMB is already transparent to visible light, to the human eye. Its color temperature can only be seen by powerful radio telescopes. You're refuting your own premises.

At any rate, what is wrong with this definition of transparent object?:

An object such that when a human sees it, through it some other object that is both not transparent and not translucent can be seen with clarity. — Amalac

Because by that definition, the CMB is indeed perfectly transparent. It can only be seen with a radio telescope.

I already told you I'm talking about Leibniz's doctrine of possible worlds, not Lewis' strange claims (if he does in fact claim what you say he does, which I don't know). I don't agree with Lewis, I don't believe “possible worlds” (other than the actual world) exist. — Amalac

Modal realism is the view propounded by David Kellogg Lewis that all possible worlds are real in the same way as is the actual world: they are "of a kind with this world of ours."[1] It is based on the following tenets: possible worlds exist; possible worlds are not different in kind from the actual world; possible worlds are irreducible entities; the term actual in actual world is indexical, i.e. any subject can declare their world to be the actual one, much as they label the place they are "here" and the time they are "now".

https://en.wikipedia.org/wiki/Modal_realism

I'm afraid I don't know anything about Leibniz's views on the matter except that he said that we live in the BEST of all possible worlds. I'd hate to live in the other ones!

I did address it, I said if there is nothing logically contradictory about a world where Euclidean geometry holds or one where it doesn't, then by definition they are both possible worlds. If you are going to say that there is no possible world in which Euclidian geometry and newtonian physics are wholly true, then that must mean that their truth implies a logical contradiction, in which case you just have to tell me what that logical contradiction is. — Amalac

I don't need to do any such thing. I have already said several times that I agree that a Newtonian world is logically consistent, but still impossible.

The root problem here is that you insist on arguing with someone who rejects the doctrine of possible worlds in the first place. I don't know why your thread didn't attract any Wittgenstein or Leibniz scholars, since I am neither. I am totally the wrong person for you to be continually hammering with these irrelevant points.

Perhaps you could say that Euclidian geometry contradicts some basic axiom of mathematics or logic, in which case there are no possible worlds in which that's the case. — Amalac

I say again, for the fourth or fifth time: I accept that Euclidean geometry is logically consistent; and I reject the idea that there is a possible Euclidean world, except in our imaginations. But you wouldn't believe the stuff I have in my imagination. Everything is up there EXCEPT a Newtonian possible world. So again you are simply arguing with someone who already disagrees with your premise. Why don't you get that? I'm sorry your OP didn't attract any higher quality responses than mine, because I can't discuss this subject using your premises.

If you are asking: Assuming that the current laws of physics don't change in the future, is there any possible world in which the whole of newtonian physics is true? Then the answer is no, since as you pointed out newtonian physics were, at least partially, falsified by observation. — Amalac

Right.

But the thing is, logic is not limited by the laws of physics. — Amalac

Why are you explaining to me that which I have stipulated many times over already? It's like you're not reading what I'm writing.

When saying that there is some possible world in which newtonian physics is the case, what one means is that we can conceive of a world where newtonian physics wasn't ever falsified, and in which the behavior observed that falsified newtonian physics simply didn't happen. That's possible, since there is nothing logically selfcontradictory about such a state of affairs. But then you may still go back to determinism and deny this. — Amalac

I understand what you're saying. I disagree with your premise that whatever is logically possible is actually possible. Once you get that you'll stop hammering me with what I already understand and disagree with.

You say I'm just making you repeat yourself, yet you have asked me the same thing again about newtonian physics. — Amalac

Then we understand each other. I truly can't be of any assistance here. I don't know why there aren't any modal realists jumping in to have a better conversation with you than I'm capable of.

Well, I simply don't agree with you in the least about what you say here, so there's no point in discussing the matter of possible worlds further. — Amalac

Ahhhh, yes now we are in agreement. And I mean it when I say I am disappointed that no modal realists, Wittgenstein scholars, or Leibniz fans jumped into this thread. I'm the last person here who can be of any use to you because I find possible worlds incoherent. There are things that are logically possible yet still not possible. I'm not sure if there's a name for that position but if there is, that's what I am. I'm curious about that now. Maybe I'll google around.

There's no common ground. Perhaps the Stanford Enciclopedia of Philosophy can do a better job than I did: https://plato.stanford.edu/entries/possible-worlds/ — Amalac

A better job at what? At explaining something I understand and (without having studied the matter much) reject? Like I say, I actually share your frustration at my own limitations in this area. I'm totally unqualified to be having this conversation with you. Mostly I"m responding because you seem confused about the CMB, which is not transparent in any conceivable or even logically consistent world, and is by definition the limit of what we can see at any wavelength at all.

Ok then, if that's what you meant by “perfect window” then there are no problems. I accept that definition. — Amalac

I already noted in my first post that space is essentially perfectly transparent (except for some minor amount of interstellar dust) and that we can perfectly well see to the limit of the observable universe, namely the CMB.

It's not irrelevant, I was trying to clarify what I meant by “transparent”: When the average person speaks about X object being transparent, they probably have in mind something very different than what physicists have in mind. When saying «a window is transparent», they usually don't mean that it lets X,Y or Z amount of light To pasa through, they mean simply: you can see through a window. — Amalac

What average person? In some possible world? This is the most irrelevant point imaginable.

To quote Wittgenstein again: The meaning of a word is its use in a particular language game. The language game of describing things in daily life is not the same as the language game that results from doing physics. — Amalac

I'm not familiar enough with Wittgenstein to comment.

Human eyes. Have I defined it well enough for you now? — Amalac

Well then the CMB is indeed transparent or invisible to the human eye. Its color temperature is far far outside of our range of vision. It's visible only by powerful radio telescopes. You've just refuted your own premise.

So modal logic is not serious philosophy according to you? I disagree — Amalac

Model logic is not the same as possible worlds, but I haven't studied it. But what's wrong with disagreeing? We do disagree. I'm sorry there are no modal realists around here to engage with you.

Well, the doctrine of many possible worlds is just taken for granted in modal logic, for example. ]/quote]

I'm saying the whole idea is incoherent to me, notwithstanding all the smart people to whom it's coherent. I'm just not one of those smart people.
— Amalac

When saying X is logically possible, all one means is that the existence of X does not violate any of the laws of logic. That's just the definition of a “possible world”, there's nothing incoherent about it. When asserting that there is some possible world in which X exists, one does not assert that such a world literally exists in some alternate reality (at least most people don't), rather one merely asserts that reality could have been that way, or could be that way, depending on what the assertion is. — Amalac

David Lewis claims possible worlds are real. That, I find clinically insane.

But you didn't address my question about non-Euclidean geometry. Is there a world where Euclidean geometry holds (Newton) and one where it doesn't (Einstein)? There are a lot of technical problems with that belief.

But then you are doing physics again, while I'm trying to do logic. This seems to me like a case where you are confusing one language game with another. — Amalac

I already said that I am not sure whether physics is contingent. Is there a possible Newtonian world?

For example, Wittgenstein said this in his Remarks on Colour:
We are not doing physics here(...) — Amalac

I can't comment on Wittgenstein.

As you yourself pointed out before, a universe where the CMB were transparent would have different laws of physics, and there is at first no logical impossibility in it having laws which would allow it to be transparent, not until you start considering what that logically entails. — Amalac

Is Newtonian physics logically possible? Yes, since Euclidean geometry is consistent. But there is no possible Newtonian world. In my opinion. I don't know what philosophers would say. It's a question I'd like to put to them.

Again, is there some possible world in which the CMB had the necessary physical properties to be transparent, or were the Big Bang happened differently? Yes, so long as that does not involve a logical contradiction. That's all the doctrine of many possible worlds asserts. It does not claim that there are in fact alternate realities or multiverses, one in which that's the case (at least most interpreters of the doctrine don't, it seems to me). — Amalac

Then they're wrong. In my opinion. Just like there is no possible Newtonian world. It would violate experiment. And Newtonian physics contains singularities, since two point masses can be arbitrarily close together, making their gravitational attraction unbounded.

I mean, it's quite simple in a sense: I can imagine/conceive that if I jumped of the roof of my house I started floating upwards instead of falling. I can imagine/ conceive of the sun not rising tomorrow, and these events imply that physics is contingent. And since I can conceive of them, they are possible, they involve no contradiction. — Amalac

Well you're making me more convinced of my belief that possible worlds that violate known physics are indeed incoherent. Sure we can imaging a world where bowling balls fall up, but if we take that fantasy seriously, that's the worst kind of philosophy.

On the other hand, I can't conceive of me counting one orange, and then only another orange, and then somehow having altogether 50 oranges (1+1=50), because that contradicts the most fundamental and most self-evident axioms of mathematics. I can't conceive of seeing something that both was and was not a tree (at the same time and in the same sense), because that would violate the Law of Contradiction. — Amalac

Maybe you just can't conceive well enough. I do understand the point you're making between logical and physical necessity, I just don't agree.

3.0321 We could present spatially an atomic fact which contradicted the laws of physics, but not one which contradicted the laws of geometry.
— Ludwig Wittgenstein — Amalac

Newtonian physics. Wittgenstein is wrong.

However, supposing one takes the route of determinism, then I ask: Do you agree with Leibniz's Principle of Sufficient reason as interpreted in his esoteric system, according to which every true proposition is analytic, including empirical truths? If so, I suppose there's no sense in arguing with you about possible worlds in which the laws of physics were different. — Amalac

I plead ignorance, so I can't answer the question. But there is no point arguing with me about this because I understand the point you're making and I disagree with it. There is no Newtonian possible world, except in our imagination. It would make a fun science fiction story, but NOT serious philosophy.

To answer that we need to answer the question: Does such a state of affairs (a possible world in which Einstein's famous prediction failed and Newtonian physics reigns supreme) involve a logical contradiction? If it does, then there is no possible world in which that's the case. If it does not, then there is such a possible world. — Amalac

I agree with your premise but not your conclusion. Newtonian physics is logically consistent but false in THIS world; and, I contend, false in ALL possible worlds. I'm not misunderstanding your conclusion, I'm simply disagreeing with it.

It seems clear to me that such a scenario does not involve or imply a logical contradiction, but if you think otherwise, then tell me what the logical (not physical) contradiction that such a scenario implies would be. — Amalac

I'm perfectly happy to agree that Euclidean geometry is logically consistent. It just happens to not be the right geometry for physics, in this or in any other world. We're flogging a deceased equine now. I already said many posts ago that I find possible worlds incoherent, and now you're just trying to get me to repeat myself over and over. I find logically consistent possible worlds an incoherent idea, as it posits the existence of a world in which bowling balls fall up. Helium-filled bowling balls maybe.

Would you say this proposition does not give us knowledge about the world then?:

If the universe has a boundary, then such a boundary must not be transparent when seen by a human by logical necessity, since it is impossible for a human to see anything that does not have any color, in the sense in which black and white are also colors. — Amalac

You're wrong about that. We can't by definition see beyond the boundary of the OBSERVABLE universe. We know that's not all there is, but it's all we can possible see under any circumstances.

Notice that assuming that the universe were in fact finite with regards space, then we could have knowledge about the boundary from the truth of the proposition above, without the need of experience (such as the experience of observing the boundary), merely by logically analyzing the meanings of words. — Amalac

Nonsense. We can see to the limit of the observable universe, and we can have NO KNOWLEDGE of what's past that. Multiverse theory, for example, is purely speculative. It's proponents well understand that point. We can not see or measure or observe anything past the limit of the observable universe. Information simply hasn't had enough time to get here since the universe started.

And although in that case it would be perhaps considered an analytic proposition, nonetheless it seems to gives us knowledge about the world. — Amalac

You haven't made your point. We can't see past the observable universe.

Well, that's not the question but it is related to it somewhat. I would like to confirm: if a clear glass window (which according to physics apparently does have a color: blue) was in a world were the only other objects in it were other transparent objects, then is it correct to say that they would all look monochromatically blue? — Amalac

To whom? To a bat? Bats perceive the solidity of a window because they rely on sound and not light. So you need to define transparency, which I should have challenged you on many posts ago.

Some reddit user answered the question about what color is a window:

if you stack up enough windows you'll see that window glass is actually usually a blue/green color. It's just so translucent that with only one pane it's pretty much impossible to see — Amalac

Those are of course physically made, imperfect window. I have for several posts already stipulated to a PERFECT window. You could have one ten miles thick and it would be perfectly transparent to visible light.

And apparently the same is true for clear water: — Amalac

You're conflating physical things with conceptual ones. I have for sake of discussion granted you purele transparent windows, water, and so forth.

But that is relevant for the physics definition of transparent. I am using a different sense of that word, the one most commonly used in ordinary life by ordinary people. — Amalac

I am granting you perfectly transparent glass and water, which does not exist in the world but serves as a limiting case for our discussion.

I did in my OP: such that through it some other object (at least one object) that is both not transparent (not transparent= such that you cannot see through it with clarity) and not translucent can be seen through it. — Amalac

Humans or bats? Human eyes or radio telescopes? Cameras or sonar? Cameras or radar? You haven't defined transparency at all.

The important aspec

t of that definition is that it is not a physics definition of «transparent», but rather one which defines the word according to our visual experience. — Amalac

What about bats? Radio telescopes? Sonar? Radar? Heat? Sound?

If a window would indeed look monochromatically blue/green if it was surrounded only by other windows, then the average person who is not knowledgeable about physics would not call it transparent in the sense I gave in the OP. — Amalac

You're going quite far afield now. What the average person would see of the real world is irrelevant to your point.

They would not be wrong, they would in that case only use the word with a sense that is not the physicists' sense (the meaning of a word depends upon its context, and the way it's used in a particular language game, as Wittgenstein would put it). — Amalac

Bats, radio telescopes, radar, sonar, heat. Define transparency. And try to stick to your original point. I'm willing to stipulate to theoretically perfect windows, perfectly transparent to visual frequencies of light. They're still not transparent to heat and sound. And in any event, you can't see past the observable universe no matter what.

My point was more like: If the universe has an edge, then such an edge must not be transparent by logical necessity (not merely physical necessity), because otherwise we would be able to see what is beyond the universe. — Amalac

I don't think I agree. The edge of the observable universe is as far as we can see. It doesn't matter what's beyond it. We can't see it in any event. It would appear black I assume.

The argument would be: anything we see is part of the universe. Therefore, if we could see something through it, that thing would be both in the universe and beyond the universe, which is absurd. Therefore, it's impossible for there to be anything beyond the edge of the universe (in an all-encompassing sense, not in the sense some physicists speak of “multiverses”). — Amalac

We already know there's part of the universe past the observable universe. We can't see it because light from there hasn't had time to get to us in the age of the universe.

And yet, if nothing could be seen through the transparent object, then the transparent object would not have any color when we looked at it. But that's also absurd: since we impose color onto all that we perceive, it's impossible for us to see something that has no color. — Amalac

A perfect window is transparent and has no color. But as @TheMadFool notes, it's not transparent to heat, sound, etc. What exactly do you mean by transparent? Bats can detect windows by echolocation. To a bat, a window is not transparent. So you need to "define your terms" as they say.

Therefore, in view of the 2 previous conclusions, we conclude that it is logically necessary that such an edge is not transparent/translucent. — Amalac

No, you haven't made that case at all. We simply can't see past the edge of the observable universe, period. Nor have you defined transparency. We see invisible (to visible light) things all the time via radar and sonar for example.