These are different uses of "1", in different contexts (language-games).
(Iadded this later, to try and clarify). Compare a traditional example:- "John came home in disgrace, a flood of tears and a wrecked car." "In" is ambiguous, because "disgrace", "flood of tears", and "wrecked car" are different kinds of thing, are pieces of different language-games and "in" is polymorphous and has different senses, or uses" in each of them. That's the theme of this whole argument. — Ludwig V

Earlier you said there was something off about using 1 as a probability and that .999... = 1. But that's two uses of the same number 1. So I don't see your point. Of course 1 has many different uses. Why is this nontrivial or interesting?

Applying numbers to objects in the solar system is one kind of language-game. Applying numbers to probabilities is quite another. — Ludwig V

It's another. It's not "quite" another. You seem to be saying that it's not only a different usage; but a super-different usage, if I'm understanding you. And it's not. It's just different.

In fact let me tell you what a probability is. It's just a real number between 0 and 1, inclusive. So it's the same real number one in the context of probability or anything else.

Actually, there are (at least) two ways of using numbers in the context of probabilities. There are 6 probabilities (I prefer "possibilities" or "outcomes" as less confusing) when throwing a die, each of which can be assigned a probability of 1/6, and if the 6 comes up we can, I suppose, assign a probability of 1 to that outcome. — Ludwig V

Yes ok. You don't have to suppose. Probabilities are additive. That is, if the events are independent (meaning that one is not dependent on the other) then you can add the probabilities. It's one of the axioms of probability. Or one of the consequences of the axioms, depending on how you state the axioms.

So I would prefer to say that probability is not applicable to either 2+2=4 or (x=3)&(x+1=4). Why? Because there are no other possibilities. Probability of a specific outcome is only meaningful if there is a range of possible outcomes. — Ludwig V

I see the point you are making but it doesn't seem right. If we roll a die the probability that it's either 1, 2, 3, 4, 5, or 6 is 1. There is no other possibility. In fact that's another one of the probability axioms: That the total probability of the entire event space is 1.

1 is conventionally used as the range of the outcomes. — Ludwig V

1 is a probability. 0 to 1, inclusive, is the range of probabilities.

Assigning a probability to one outcome and then to another without outside that context is meaningless. 1 isn't counting or measuring anything - it's just the basket (range) within which we measure the probabilities (in relation to the evidence and if there is no evidence, then equally to all). (fdrake is right to emphasize the role of evidence - especially in the context of Bayesian probability) We use 100 as a basket in other contexts when it suits us. In the case of the die, P(1v2v3v4v5v6)=1 is just reasserting the rules. — Ludwig V

Well, "evidence" is a term in the philosophy of probability, I suppose. But it's not a word in the formal mathematical theory of probability. In any event, I don't think that's right. Evidence can change the credence of an event -- your subjective degree of belief. But it doesn't change the probability.

I'm in way over my head on the philosophy of probability actually.

In the case of truth, the language-game that provides the context is different. In a sense, when we assign 1 to truth, it is not a number at all. We can equally well use "T" or a tick if it suits us. This reflects the point that "true" is one of a binary pair. Probability isn't. I want to say that probability and truth are different language-games. — Ludwig V

Well I certainly agree with you. I am not the one trying to apply probability theory to true/false propositions. @fdrake is doing that. I'm a bit baffled by the attempted connection.

But that would be too quick, because they are related. Probability is what we retreat to when we cannot achieve truth, one might say. There are others - "exaggerated", "inaccurate", "vague", "certain", "distorted", "certain". I would be quite happy to say that truth is not binary, but multi-faceted; the language game of truth has more than two pieces - probability is just one of them. Probability itself has more pieces than are usually recognized. In the context of empirical probability, we find ourselves confronted with "likelihood" and "confidence" and, sometimes, "certainty" and, of course, in the context of Bayesian probability, "credence" - "degree of belief" turns up from time to time, as well. — Ludwig V

Are you perhaps referring to credance, or the degree of belief? I can't really debate these issues, I know nothing about them. Truth in mathematics is binary. In real life, not so much. Also in intuitionist logic, where we reject the law of the excluded middle. That's another complication.

@fishfry There's one other point I would like to make, in the context of our previous discussion about time in mathematics. — Ludwig V

Uh-oh. Was all the preceding not for me? Probably wasn't since it's not about anything I can sensibly talk about. To me a proposition is true or false. That's the definition of a proposition.

Given that, probability is a bit of a problem, because it seems to me that it has time, or at least change, built in to it. (I have seen it said that probability is inherently about the future). — Ludwig V

Philosophical probability, I suppose. Mathematical probability has no time element in it. A probability measure is a function from some event space to the set of real numbers between 0 and 1, inclusive, satisfying some additional rules. That's it. No time involved.

We build the table around the outcome, in the context of a thought-experiment such as tossing coins or throwing dice or drawing cards lotteries or roulette wheels. (I expect you know that Pascal built the theory around a desire to help his gambing friends) We expect an outcome, when everything changes. Time isn't essential. The outcome could be unknown, for example. Even if it is known, we can pretend that we don't know it. But there is an expectation of change, without which probability makes no sense. So the timeless present does not describe what is going on here. — Ludwig V

The mathematics of probability is abstracted from all that. No time element.

This article gives the mathematical definition of probability.

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

You don't need to follow the symbology. The point is that time is not mentioned. Probability is a mathematical function that outputs a real number in the range [0, 1] and satisfies some rules.

Now particular applications of probability often involve real life, temporal events, such as tomorrow's weather or the next card dealt from a deck. The underlying theory is abstracted from that.

One could regard probability theory as applied mathematics, but probability isn't a prediction. Probability statements are neither confirmed nor refuted by the actual outcome. (That's not quite black and white, because we do use deviations from probability predictions as evidence that something is wrong. But still...) — Ludwig V

Probability theory is abstract. Applied probability is applied.

I prefer to say, however, that the probability table does not change when the outcome is known. It describes a situation and that description is correct even after the outcome is known - it just doesn't apply any longer. So probability = 1 doesn't really apply. — Ludwig V

I don't know why you have that hangup about probability 1. Probability 1 is just the probability of the entire event space. It's the claim that out of all the possible outcomes, one of them will occur. After all, in any situation, something must happen, even if we don't know what. The probability that something, anything at all will happen, is 1. That's one of the rules of probability in the Wiki article.

Ok. That will do. Maybe some of that is helpful. — Ludwig V

You have thought a lot more deeply about the real-world meaning of probability than I have. The math is just math, as in the article I linked. It's very mathy as you can see.

Full disclosure - I haven't formally studied probability either, any more than I've studied mathematics. But I have discussed both and thought about both a good deal, in various philosophical contexts. — Ludwig V

It's the philosophical contexts that I don't know much about.

I agreed with you about "pure math", for the sake of discussion, so that we could obtain some understanding of each other. But I will tell you now, as came up one other time when we had this discussion, I do not agree that there is such a thing as "pure math" by your understanding of this term. So I agree that if there was such a thing as pure math, that's what it would be like. However, I think your idea of "pure math" is just a Platonist/formalist fantasy, which is a misrepresentation of what mathematics is. In reality, all math is corrupted by pragmatics to some degree, and none reaches the goal of "pure math". You criticize me to say, it's not a goal, it's what pure math is, but I say that's false, it is a goal, an ideal, which cannot be obtained. Therefore "pure math" as you understand it, is not real, it's an ideal. — Metaphysician Undercover

Those corrupt math professors. Something must be done. Pure math is math done without any eye towards contemporary applications. That's a decent enough working definition. Mathematicians know the difference.

I think the issue being exposed here is a difference of opinion as to what mathematics is. — Metaphysician Undercover

Not really. Nailing down a definition is unimportant. Mathematics is whatever mathematicians do in their professional capacity. Circular, but as good a definition as any. What difference does the definition of mathematics make?

Since this is a question of "what something is", the type of existence it has, I think it is an ontological issue. Would you agree with this assessment? — Metaphysician Undercover

No. Mathematics is a historically contingent human activity. It's different every day, every time someone publishes a new paper.

For example, the head sophist refers to "mathematical logic", and I find this defined in Wikipedia as the study of the formal logic within mathematics. So we have a distinction here between the use of mathematics (applied mathematics), and the study of the logic used by mathematicians (mathematical logic). "Mathematical logic" would be a sort of representation, or description, of the logic used in mathematics. What you call "pure mathematics", I believe would be something distinct from both, applied math and mathematical logic, as the creative process whereby mathematical principles are developed. But I think that this process is not really "pure", it's always tainted by pragmatics and therefore empirical principles. — Metaphysician Undercover

You must think I'm sticking to some pure/applied distinction. I'm not.

The issue I have with the head sophist — Metaphysician Undercover

Repeatedly calling a fellow forum member that makes you look like an asshole.

is with the way that mathematical logic represents the use of the = symbol as an identity symbol. In applied mathematics, it is impossible that "=" is an identity symbol because if both sides of an equation represented the exact same thing, the equation would be absolutely useless. — Metaphysician Undercover

This is a standard complaint. If math follows from axioms, then all the theorems are tautologies hence no new information is added once we write down the theorems. But that's like saying the sculptor should save himself the trouble and just leave the statue in the block of clay. Or that once elements exist, chemists are doing trivial work in combining them. It's a specious and disingenuous argument.

This I've explained in a number of different threads. — Metaphysician Undercover

Repeating a mistake is no virtue.

In reality, as any mathematics textbook will show, "=" means "has the same value as". — Metaphysician Undercover

We agreed long ago that 1 + 1 and 2 are not the same string; and many people have explained the difference between the intensional and extensional meanings of a string. Morning star and evening star and all that.

Therefore we can conclude that any mathematical logic which represents "=" as an identity symbol is simply using a false proposition. When a "textbook in mathematical logic" states that "=" is an identity symbol, this can be taken as the false premise of mathematical logic. — Metaphysician Undercover

What math teacher hurt your feelings, man? Was it Mrs. Screechy in third grade? I had Mrs. Screechy for trig, and she all but wrecked me. It's over half a century later and I can still hear her screechy voice. I hated that woman, still do. When I'm in charge, I'm sending all the math teachers to Gitmo first thing.

I have conceded the point regarding what you call "pure math". However, I am now qualifying this concession to say that "pure math" is just an unreal ideal. — Metaphysician Undercover

You are the one making a big deal out of the distinction. Besides, in my last post I ended up talking myself out of my entire thesis due to the structuralist turn in mathematics.

There is no such thing as pure math. It's a term which people like to use in an attempt to validate their ideals. In reality though, such ideals are fiction, so all that I have really conceded, is that within the fictitious conception which you call "pure math", this is the way things are. Of course, I'm not going to argue about the way things are in your work of fiction, but I will argue about the way that your fiction bears on the real world. — Metaphysician Undercover

I really haven't made a big deal of the distinction; and if I did, I shouldn't have.

Sure, there are thousands of people who might call themselves "pure mathematicians". In reality though, these people are not engaged in "pure mathematics", as I believe you understand this to mean. As I said above, all mathematics is tainted by pragmatics (applications), and there is no such thing as "pure" mathematics. — Metaphysician Undercover

A piece of math without any known application is pure math. A hundred years from now it could be applied. The most striking case is number theory, which was totally useless for 2000 years then became the basis of public key cryptography in the 1980s, the basis of online commerce.

This is very evident in our discussion of the meaning of "=". In what you call "pure mathematics", we might say that "=" signifies "is the same as". This would remove the basic fact that what mathematicians work with are values. To make the mathematics "pure" we must remove this content, what the mathematicians work with, values. We remove the inherent nature of the thing represented by the symbols (i.e. that the symbols represent values) to allow simply that the symbols represent things without any inherent nature, no inherent content. Then we might claim the left side of the equation represents the exact same thing as the right. However, this type of equation would be totally useless. We could do nothing with an equation, solve no problems. — Metaphysician Undercover

I just think you're working yourself up over nothing. I'm losing interest. Can you write less? This is tedious, I find nothing of interest here.

Furthermore, there would be a disconnect, an inconsistency between the mathematicians practising "applied" math, who use "=" to represent "is the same value as", and those "pure" mathematicians creating mathematical principles which were inconsistent with the applied mathematics. Since the supposed "pure mathematicians" actually produce principles which are compatible with, and are actually used in applied mathematics, we can conclude that the supposed "pure" mathematics is not really pure, and the principles they are using and developing do not really treat "=" as meaning "is the same as". That's just a misrepresentation, supported by the misrepresentation that these people are doing "pure" mathematics. — Metaphysician Undercover

Whatevs. I can't follow you. And I've already noted that the difference between pure and applied math is often a century or two, or a millennium or two.

I can't say I understand everything you wrote following this, but it mostly makes sense to me. I'll have to work on these ideas of "mod 4", and "cyclical group". — Metaphysician Undercover

Sorry. Nevermind all that. Point being that two groups are essentially the same even though their presentation as sets is entirely different. Just like the real number 5 and the integer 5 are essentially the same even though they are different sets. Now what do I mean by "essentially the same?" Well now we're into structuralism and category theory. Sameness in math is a deep subject. I'll take your point on that.

What I mean, is that if you recognize that two things are different from each other, then that difference has already made a difference to you (in the subconscious for example) by the very fact that you are recognizing them as different. So for example, if you see two chairs across the room, and they appear to be identical, yet you see them as distinct, then the difference between them must have already made a difference to you, by the fact that you see them as distinct. So to say that the difference between them is a difference which doesn't make a difference must be a falsity from the outset. We might even say that they are identical in every way except that they are in different locations, but this very difference is the difference which makes them two distinct chairs instead of one and the same chair. — Metaphysician Undercover

Ok. They're two instances of chair-ness.

I knew you wouldn't agree, but i wouldn't agree that the real number 5 is an instance of a real number. — Metaphysician Undercover

I can't even imagine how it isn't.

The problem I think has to do with the statement "a real number". "The real numbers" is a conceptual construct in itself. — Metaphysician Undercover

Yes.

This conception dictates the the meaning of "a real number". So in reality any supposed instance of "a real number" is just a logical conclusion drawn from the dictates of "the real numbers". — Metaphysician Undercover

Even so, 5 is one of the real numbers. What do you call it if not an instance? What WOULD be an instance of a real number?

In other words its not a distinct or individuated thing, which would be required for "an instance", it's just a specific part of "the real numbers". Can we agree that the real number 5 is a specific real number? — Metaphysician Undercover

I agree that 5 is a specific real number. But ok, instance means something else. Still a bit fuzzy but sort of seeing your point.

You haven't lost any debate, you just made a post with some mistakes. You seem ready to acknowledge them, which is winning in my book. — flannel jesus

I make many misteaks :-)

Thanks! Again a fine article, fishfry, that I have to read. — ssu

It's relatively short. You can skip most of the technical bits. I did.

I've been listening to Youtube lectures that Joel David Hamkins gives. They are informative and understandable. — ssu

He's awesome.

Sure, it looked bad, but the two cases are not the same. Obama was not separating every family. The Trump Admin was. Obama was not doing it as a deterrent. The Trump admin was. Those are crucial differences, don't you agree? — RogueAI

Absolutely. Obama is a saint and a lightbringer. Trump is Orange Hitler. That's the distinction you are making.

I knew about Obama's cages in 2014, so when the left went wild over Trump putting kids in the same cages, I recognized them for the ignorant hysterics that they so often are. Eventually Jeh Johnson, Obama's Homeland Security guy, had to explain to reporters that those cages were had indeed been built by Obama. The left literally did not believe it. Willful denial of reality along with hysteria. Not a good look for the side I'd always considered myself to be part of.

As always with Trump, you conflate his often artless rhetoric with reality. The truth is you don't actually know that his motives were different than Obama's. Only that Obama can do no wrong, and Trump can do no right. And that Trump's words often inflame the left. I think he does it on purpose, like the taco bowl tweet. He's a troll. I watched the cage story develop from 2014 to 2018 and it does not reflect well on the left. Ignorance and hysteria. That's their style.

Except when it’s about racism and some property is damaged. — Mikie

Racism? Not catching the reference. The Floyd riots? J6? Something else.

Then it’s screamed about for years. Meanwhile, a few months later a bunch of white people storm the Capitol building in an attempt to stop the electoral college vote, and they were “let in” — and after years of spin, we should deny what we all saw that day and tell ourselves it’s no big deal. — Mikie

Maybe you didn't see the videos of them being let in. I did.

Because if it were the Black Lives Matter crowd, I’m sure we’d be saying the same thing. And I’m sure only one insurrectionist would have been shot. — Mikie

Um ... what? The Floyd riots killed 20 people. A black cop shot unarmed Ashli Babbitt. Reverse the races and the left would still be hysterical about it.

The hypocrisy is laughable. — Mikie

On your side, most certainly.

So maybe it's something else. — TonesInDeepFreeze

My deficiency, I'm sure.

Most glaringly of all, what accounts for you recently claiming that I hadn't specified 'identity theory' when I had specified it multiple times in this thread, including multiple times addressed to you, and even twice quoted by you? Your claim is bizarre. — TonesInDeepFreeze

I'll retract it then, as an alternative to arguing the point. Or if you consider the second clause as adding fuel to the fire, I'll retract it.

P(X=1|X+1=2). Where X is a random variable. That'll give you probability 1. — fdrake

Yes ok, a true proposition has prob 1 and a false one 0. I don't see how intermediate probabilities could apply. Unless, say, we could poll a bunch of mathematicians and ask them to assign a probability to the Riemann hypothesis being true. That would be one example I suppose. But I think that's credence (degree of belief) rather than probability (whatever exactly probability is).

It is the same article as the reading for my Metaphysics of Mathematics thread. Tones didn't love it. — Lionino

So many articles, so little time.

you kind of contradict the first half of your post here with the second half. In the first half, you speak as if something being deterministic is basically synonyms with it being predictable, but in the second half you acknowledge that a chaotic system could be deterministic but unpredictable. — flannel jesus

I believe I'm losing this point. I do know about chaos.

If a chaotic system can be deterministic but unpredictable, then you should be able to imagine software that is chaotic, and thus deterministic and unpredictable, no? — flannel jesus

Yes, I think I have lost this debate to @Tarskian. Except that he thinks programs have "free will," and of course they don't.

I think there's a subtly shifting meaning for the word "unpredictable" that's at play there. — flannel jesus

Agreed. But also, chaotic deterministic unpredictability is not the same as Halting problem deterministic unpredictability, and Tarskian is trying to make some kind of connection.

But I concede the point that programs are inherently unpredictable in the sense of Turing. Not in the sense of chaos, and they certainly don't have free will, except for alternative definitions of the phrase.

Perhaps you should stick to the part I quoted? — Benkei

I am actually confused about what you wrote. I outlined the basic facts about the sepaations and the cages, and you responded by complaining about my reading habits (and getting it wrong. Breitbart yes, RedState and Townhall no). I fail to see how what I read alters the fact that Trump put kids in the cages Obama built for the same purpose. All the rest is partisan rhetoric. You say that when Obama put kids in cages he was noble, and when Trump put kids in the same cages he was Orange Hitler. I fail to understand your point beyond partisanship.

If am missing your point, feel free to clarify.

But they don’t cut it mate. I’ve said before, I respect your intelligence, I’ve learned things from you about philosophy of math (mainly, how little I know.) I have to say that you’re completely wrong about Trump, he’s malignant, mendacious, and a threat to the American Republic. Until you’re willing to acknowledge that, we have nothing further to discuss about it. — Wayfarer

I was influenced by your kind words and I did my best to at least explain and justify my political feelings. Especially since I'm no Republican nor a conservative, but rather a fallen liberal. Still a registered Democrat. One of the seven to ten million Americans who voted for Obama and then Trump. The Democrats have no interest in who we are, which has been a great frustration these last eight years. The left just stopped listening. Just Russia Russia Russia and then J6. Lawfare and propping up Biden, both of which have failed spectacularly. It's the Dems who are a threat to the American republic, and I did not used to feel that way. They talked me into it over the past couple of decades and especially in the past eight years.

I enjoyed our Trump chat, and as I said, I appreciate your writing prompts so that I could express some of my thoughts. For some reason, Trump just doesn't trigger me the way he does others. And I do believe that if the Dems had totally ignored Trump, skipped the lawfare entirely, and held a competitive primary, Newsom or Whitmer would be beating DeSantis today.

Now it's up to the American people, such as they are, and our electoral system, such as it is.

You will never predict correctly what thwarter is going to do. — Tarskian

I'll concede you the Halting problem, but certainly not that programs have free will, if that was the claim.

When you put thwarter in that chaotic system, you suddenly have something freely making decisions while you can impossibly predict what decisions it will make. — Tarskian

Nothing is "freely making decisions." That's a complete misunderstanding of what programs are. I know you know that, so you must be using free will in a different sense than I understand.

Free will is a property of a process making choices. If it impossible to predict what choices this process will make, then it has free will. — Tarskian

Oh for gosh sake. That's not true. A coin doesn't have free will when you flip it. And if you say that deep down coin flips are deterministic, so are programs.

The first statement explains the second. And, it’s more than ‘a little’. But there’s no way to make someone see what he or she doesn’t want to see, so let’s leave it for now. (Although how a forensic retelling of an attack on the American people could be a fraud on the American people beggars logic.) — Wayfarer

You have swallowed the psyop. The J6 committee was a total fraud.

Although as this is the Election thread, not the Trump thread, I’ll add I still don’t believe Biden will be the eventual Democratic nominee. I just wish folks would say that he should ‘pass the baton’. It sounds a lot less hostile than that he should resign or quit. It is really what he must be persuaded to do, and, I believe, will be. — Wayfarer

Yes back on topic. The election. I don't see how the Dems have much leverage. Biden is president. Biden is dug in. Biden has 3896 pledged delegates, with only 1,991 needed to win. Biden has Jill and Hunter in his corner; and crack and hooker jokes aside, Hunter is a smart and tough ally.

The Dem civil war is also a race war. All the Dem pols coming out against Joe are whitebreads (except for Obama in the background). Joe has the support of the Congressional Black caucus. AOC and Omar came out for Joe. Tellingly, black NYT columnist Charles Blow just came out with support for Joe. The Strongest Case for Biden Is His Resilience in the Face of the Onslaught. This is noteworthy because the Times editorial board and many of its other (white) opinion writers have called for Joe to "pass the baton" as you say.

Labor is behind Joe. Old people are behind Joe. I read that after the debate, his poll numbers went UP with women. They must have felt sorry for him.

Is the DNC going to screw over all the Biden supporters and primary voters? Dumping Joe is fraught with risk.

Also, Kamala has many negatives. As a former northern Californian I've watched her finger-to-the-wind brand of politics for a couple of decades now. She polls about the same as Biden against Trump. She's been a worthless VP and her approval ratings have been terrible. She is no panacea. And of course nobody else can leapfrog her because of Democratic identity politics.

There are also technical issues. Some states have strict filing rules that limit how long the Dems can wait. The WSJ published a story today saying that Biden can't transfer his campaign account to Kamala until he's formally nominated.

When Nixon was told by the party honchos that he had to resign, he was facing certain impeachment and conviction. What leverage have the Dems got? A strongly worded editorial from George Clooney, who just raised $30M for Biden three weeks ago and publicly claimed Biden was fit as a fiddle when he privately saw Biden's infirmity? Well today Rosie O'Donnell called for Biden to "pass the torch." That oughta do it.

I'm on record saying Joe is the nominee. Biden's press conference was not good enough to quell any doubts, but it wasn't bad enough to make his position any worse. He made some flubs but he also made his foreign policy points. He bought himself more time, and time is of the essence for the anti-Joe Dems. They are stuck. Nobody can make Joe leave but Joe. And he is a stubborn, selfish old guy who, despite his sad recent cognitive decline, was always pretty much like this.

The Dems made their bed and now they have to lie in it.

You do. — Wayfarer

You should read what I wrote. And take it to heart.

And I do thank you for the writing prompts. I've had these thoughts in mind for a long time. You wondered how I could be for Trump. I'm explaining.

You know that Trump on multiple occasions has sucked up to Putin? — Wayfarer

Ah, Russia Russia Russia, another symptom of TDS. Let us take a brief walk through history.

FDR joined up with brutal dictator Stalin to defeat the Nazis in World War II. I do not recall anyone criticizing FDR fo "sucking up" to Stalin. Well actually some people did. I read once that Herbert Hoover said at the time that the US should stay out of the war and whichever of the Nazis or the Soviets were winning, we should help the other one till they both destroyed each other. So I imagine that at the time, there must have been some voices questioning FDR's alliance with the bloody commie dictator Stalin. But it's not the prevailing view of history. It's regarded as a pragmatic decision to beat the Nazis, in retrospect a very good thing.

After the war Truman and the Dulles brothers got the cold war started, no sucking up to Russia there.

Ike had a summit meeting with Khrushchev in 1959. Why not? They were trying not to blow up the world. They were going to meet again in 1960, but Francis Gary Powers got shot down in his U-2 spy plane and the meeting got cancelled. Was Ike "sucking up" to the Soviets? Or negotiating with his geopolitical opponent with the aim of achieving peace? As a soldier of war, he knew the importance of peace.

JFK famously met with Khrushchev; and towards the end they had back-channel communications to establish peace. In his American University speech on June 10, 1963, JFK called for peaceful coexistence with the Soviets, saying:

So, let us not be blind to our differences--but let us also direct attention to our common interests and to the means by which those differences can be resolved. And if we cannot end now our differences, at least we can help make the world safe for diversity. For, in the final analysis, our most basic common link is that we all inhabit this small planet. We all breathe the same air. We all cherish our children's future. And we are all mortal.

Five and a half months later he was dead. Killed, some say, by the CIA on behalf of the very warmongers whose profits were threatened by peace. Or if you prefer the Lone Nut theory, the warmongers just got lucky. Somehow they always do.

Would you say JFK was "sucking up" to the Soviets? Or seeking peace, with deep wisdom?

I could go on. A lot of presidents met with their ideological opponents. Nixon went to China, for gosh sake. The arch anti-communist of the Alger Hiss case, the man who built his entire political reputation on fighting the Godless commies. "Only Nixon could go to China." Sucking up, I guess, is that how you would put it?

And so we come to Trump. He's a businessman. He doesn't have mortal enemies. He has competitors. He negotiates with his competitors. You call that sucking up. I call it international diplomacy, the only alternative to nuclear war. Biden comes in, and we're today closer to WWIII than at any time since the Cuban missile crisis of 1962.

When, exactly, did talking to our geopolitical rivals become sucking up in the leftist worldview? The left used to be for peace. Now they regard geopolitical negotiations as sucking up.

That he stood on the world stage with him and said he trusted Putin above his own intelligence agencies? — Wayfarer

Indeed. Not the most politic thing to say in public, but surely true. Reminds me of another story from the JFK days. The JFK assassination and the history and politics of that era are an interest of mine.

When French president Charles de Gaulle survived an assassination attempt by the right wing OSA (see the film The Day of the Jackal), de Gaulle knew that the OSA was closely allied with the CIA. De Gaulle called Kennedy and asked if the US was behind the assassination plot. Kennedy said that he certainly had nothing to do with it; but that he could not vouch for or control his own CIA.

So its hardly news that American presidents can't trust the CIA and don't trust the CIA. The only thing that's new is that Trump said it in public. Probably shouldn't have. You'll note that in the past couple of weeks, Trump has learned to keep his mouth shut. He may be starting to learn how to play the game of politics. If so, that's why the left is frightened. Imagine Trump being Trump, but no longer his own worst enemy.

That he thinks Kim Jong Un is a really neat guy, even saying once that they were 'in love'? — Wayfarer

You just don't like the guy's negotiating style. As someone said, as a New York City builder Trump always thinks he's negotiating with the sheet rock union.

Instead of lobbing missiles and starting a war, Trump went over there and buddied up with the leader of one of our country's "enemies." Are the North Korean people really the enemies of you and I? Or are they merely a tool for the military-industrial complex to keep the bucks flowing? Trump is a man of peace. He's a negotiator. No wonder the establishment hates him.The establishment gorges on the profits of war. Trump is dangerous to them.

The only thing I don't understand is why the left, with whom I marched against the war in Vietnam long ago, has now aligned itself with the defense contractors and the intel agencies in the cause of war.

If I had one wish, it would be for every leftist in the world to snap out of their trance and see how they are being played by the war machine. Hate Russia! Hate Russia! Hate Russia! A horde of mindless TDS-addled zombies.

Peace, man, Peace. Ike was a man of war and he worked for peace. JFK worked for peace, you see where that got him. Nixon worked for peace. Every president works for peace.

And when Trump works for peace? The left hates him for it.

I pray to the deities that be, for the liberals to snap out of their warmongering, deep-state loving trance and recognize that malignancy in our government; and that Trump, for all his flaws and faults, is trying to fight that malignancy.

Why is it that the only political leaders he's ever expressed admiration for, if not because they're role models for him? Not that he's got anywhere near the guts or the guile to actually pull it off. Fortunately. — Wayfarer

Like I say. You just don't like the guy's style. Why don't you look at his results? Only prez in my lifetime not to start any new wars. Look at the dangerous condition of the world with senile Biden and his feckless, incompetent, and neocon-influenced foreign policy team that have us on the brink of nuclear war.

Wake up. Peace is possible. But not by worshipping the neocon deep state that has a stranglehold on the Democratic party.

Computability may be deterministic but is fundamentally still unpredictable too. It is generally not possible to predict what a program will be doing at runtime: — Tarskian

I am not sure if Rice's theorem means what you say it does.

If you give me a program, say its listing printed out on paper; and you give me its inputs; and you give me a lot of pencils, paper, and time; I can deterministically and with no ambiguity determine exactly what it's going to do. I can not imagine this being false, and therefore Rice must be full of beans! :-)

A deterministic system is unpredictable when its theory is incomplete. There is no need for randomness for a system to be unpredictable. Free will is essentially the same as unpredictability. — Tarskian

Not how I understand this. A chaotic system is deterministic yet unpredictable. Nothing to do with incompleteness. There's no free will, none whatsoever, in a chaotic system.

Trump says border bill ‘very bad’ for Lankford’s career — Wayfarer

Oh it turns out I DIDN'T miss this story. This was the bogus border bill that would have codified Biden's disastrous border policies, while bringing the Republicans on board so they could no longer criticize Biden over it.

I do remember this completely, did not realize this originated with a Republican, for some reason hadn't registered the name Lankford with it.

So I was with Trump on this. This was the bill that would have allowed in, what was the number, 5000 or something undocumented crossers every day, massively exacerbating the humanitarian crisis at the border and in the blue cities that have to absorb the newcomers, while giving the Dems the ability to blame it all on the Republicans.

I was massively opposed to this bill at the time. It codified the ongoing disaster and made the Republicans complicit.

So that was the Lankford bill. Somehow I missed that detail, but I definitely followed the story of the bill. Very glad the Dems blocked it. Bad bill as I understand it.

I will grant that if I have been misinformed about the details of this bill, I could be wrong. But the high-level bullet point was that 5000 a day would come in, a massive number that was far more than what Jeh Johnson, Obama's Homeland Security secretary, said would lead to humanitarian disaster. So this bill deserved to go down.

Thanks for the update, anyway. I recalled this bill as being a couple of months ago, but it was February. Time flies.

As mentioned, Lankford was then censured by his own party. This for a straight up-and-down Republican who has toed the party line on every single issue. — Wayfarer

I will concede that it is POSSIBLE that I may be misinformed about the badness of this bill. I confess that my media diet is a little skewed to the right these days. I've actually gone back to reading the NYT lately. So it's possible that you are right and I'm wrong on this issue.

But now that you've refreshed my memory about which bill this was, I most definitely remember that I had the impression that it was a bad bill, because it codified a lot of the bad stuff that was already going on, while making it impossible for the GOPs to complain. So AFAIK Trump was right on this issue.

Poor Lankford, though. No good deed goes unpunished, and the GOP are a hopeless and confused lot these days.

And I just don't know how you can say that. He's on the record suggesting, for instance, that the constitution ought to be suspended, that he plans to purge the civil service and stock it with his operatives, and intends to use the Department of Justice against his enemies. — Wayfarer

If only.

It won't happen. You know what I think is going to happen? The massive financial crash that people have been predicting since 2008 is finally going to happen on Trump's watch, and he's going to go down in history as the second coming of Herbert Hoover. Trump is being set up to take the fall for the coming economic crash.

Exact revenge on his enemies, put Pelosi and Cheney and Garland and Wray in prison? I wish. Never going to happen.

Suspend the Constitution? More TDS. Where do you get this stuff?

Again: You confuse suggesting with actually doing. They are not the same. As is typical for the left, you confuse Trump's style of rhetoric with his actions. Watch what the guy does, not what he says. You know the saying: Trump's opponents take him literally but not seriously. His supporters take him seriously but not literally. Liberals overreact to his words and never notice what he actually does.

The last few weeks, there's been a lot of press over Project 2025, which likewise plans to implement plainly authoritarian policies - Trump has been trying to disassociate himself from it, but it is almost entirely composed of ex-Trump aides and staffers, and he's spoken at the Heritage Foundation on a number of occasions. — Wayfarer

Yeah yeah yeah, Project 2025. Another TDS hysteria. You know Trump put out his ACTUAL platform, and it's extremely middle of the road, basically 1990's Clintonian policies. I posted this link recently. Here's Brit right-of-center website Spiked on the subject.

The truth about Trump? He's a moderate

That's Trump's platform. Project 2025 is yet another leftist hysteria. TDS is a genuine psychological disorder. Trump is not going to suspend the Constitution, he's not going to be a dictator. And if he does get a measure of justice for the wrongs that have been done to him and to the J6 political prisoners, I support him in that.

Here's NPR's take on Trump's platform, along with the platform. Why don't you read it and comment on Trump's ACTUAL platform, not the Project 2025 boogyman the liberals are using to distract from their laughable yet incredibly dangerous for the country Biden fiasco.

https://www.npr.org/2024/07/08/nx-s1-5033015/rnc-republican-party-platform-2024

But then, you know, but seem to downplay or rationalise, that Trump sicked his mob on the Capital Building, leading to multiple deaths and hundreds of arrests and jail sentences, one of the darkest days in American history. Why you're OK with that I can't fathom. — Wayfarer

What happened to "A riot is the voice of the unheard" as the Floyd rioters killed 20 people and caused two billion dollars in documented insurance payouts?

Most of the J6'ers were invited in by the Capitol police and wandered around peacefully, and now they're sitting in prison for three years. It's a shameful incident in American history. If there is any justice in this universe of ours there will someday be justice for the wrongly imprisoned J6'ers.

The J6 committee was a fraud on the American people. Why did they destroy their records? Why are thousands of hours of video still under lock and key?

When you say "mathematical truth" do you also refer to axioms? Me and another user had a disagreement about the definition of logicism as it seems hard to source — no surprise. SEP presents both a "weak logicism" and "hard logicism":

The strong version of logicism maintains that all mathematical truths in the chosen branch(es) form a species of logical truth. The weak version of logicism, by contrast, maintains only that all the theorems do. — Lionino

I am definitely not authoritative on that. I know that Russell wanted to develop math from logic, and Gödel busted Russel's dreams. Beyond that I am totally ignorant.

The article The Three Crises in Mathematics: Logicism, Intuitionism and Formalism says:

The formulation of the logicists' program now becomes: Show that all nine axioms of
ZF belong to logic.
— https://www.jstor.org/stable/2689412?seq=1 — Lionino

I should read that. Will dispatch a clone.

I just checked on this past week's papers in logic posted at ArXiv.org . Four are from American universities and 13 are from foreign countries. FWIW — jgill

Does that make Americans illogical? :-)

You really do come up with amazing twaddle. — Mikie

We saw the videos. Unjustly locking people up for three years does not a crime make. It makes an illegitimate DOJ. Shamefully so. Else how explain the leniency to the Floyd rioters who killed 20 people and did two billion dollars in documented, insurance-covered damage, and cheered on by the left? "A riot is the voice of the unheard." Except when the unheard are the deplorables. There's a reason Trump is about to be reelected in the greatest political comeback in American history. Enough people see what's been going on.

I don't understand you. I gave you an example of how equivocation of "same" has a considerable effect. Of course it has no effect in "pure mathematics", because by definition "pure" mathematics maintains its purity, and the purity of its definitions. — Metaphysician Undercover

Then you DO understand me perfectly.

1) With regard to math, "same as", "=", and "is identical with" are synonymous. Period.

2) With respect to everything outside of math, you are probably right, but I take no position on it whatsoever. So if you're right about photons, that's great. Not any point I'm making or anything I care about in the context of this discussion.

Pure mathematics is not applied, and therefore has no effect in relation to the physical world where "same" means something else.. We live in the physical world, our cares and concerns involve the world we live in, it is impossible that anything in the fantasy world of "pure mathematics" could actually concern us. This is known as the interaction problem of idealism. However, in reality we apply mathematics and this is where the concerns are. — Metaphysician Undercover

This is of course true, but irrelevant to my part of this discussion. If you have some point to make about sameness as it pertains to playgrounds and photons, I'll concede the point without even thinking about it. Because I don't care about the issue. So if you're right, you're right. And even if you're wrong, I don't care, so I won't bother to try to prove you're wrong. Therefore I concede that you are right about a discussion I'm not even having with you.

You seem to misunderstand the issue completely. — Metaphysician Undercover

You agree with me about pure math. And I'm entirely agnostic about any other aspect. I can't misunderstand what I have no interest in understanding. I can be ignorant; but I can't be wrong, because I haven't even taken a position.

You appear to understand that there is a difference between the use of "same" by mathematicians (synonymous with equal), and the use of "same" in the law of identity (not synonymous with equal). — Metaphysician Undercover

Not as it's understood in math. You're just trying to argue with me about something that I have no opinion on and no interest in having an opinion. I know, for an opinionated guy like me that's unusual. But there are a lot of things I have no opinion on.

You said that this difference has no bearing on anything you know or care about. The things included in the category of what you know and care about, are not limited to principles of pure mathematics, because you live and act in the physical world. The law of identity applies to things in the physical world which we live and act in. — Metaphysician Undercover

I don't get worked up about this at the grocery store. For example one onion is pretty much the "same" as any other, and the ways in which they are the same and the ways in which they are different may be of interest to a philosopher. But I don't trouble myself with it. I just pick out some onions.

So, to make myself clear — Metaphysician Undercover

If only.

I do not claim that there is a problem with using "same" as synonymous with equal, within the conceptual structures of mathematics. — Metaphysician Undercover

Well then we are DONE. You have agreed with my point, with my ONLY point. I have no other point. I have no other opinion. I have no other thesis. I concede everything you say about the subject, not because you're necessarily right, but because I just don't care one way or the other.

So we're done. You agree with me about the only point I'm making. Which I appreciate a lot, actually. It's taken me a long time to get you to agree that "same" and "=" are synonymous in math.

The problem is in the application of mathematics, as inevitably it is applied, and this use of "same" is brought into the world of physical activity, and taken to be consistent with the use of "same" when referring to physical objects. — Metaphysician Undercover

I care not about applications. Nor do I believe that you are correct on this point. Math is math, whether you apply it or not.

That is where the problem occurs. Sophjists such as Tones enhance and deepen the problem by arguing that the use of "same" in mathematics(synonymous with equal) is consistent with the use of "same" in the law of identity (not synonymous with equal). — Metaphysician Undercover

I can't comment on the thoughts of others. Nor do I understand much of what @TonesInDeepFreeze says. But he did clarify a point of longstanding confusion on my part about the axiom of extensionality, for which I'm grateful to him, even if he thinks I'm still misunderstanding.

This is exactly the issue, the reality of the situation is that we do have it both ways. There are two very distinct ways for understanding "same". You can dictate "you cannot have it both ways" all you want, but that's not consistent with reality, where we have both ways of using the term. If you think that we ought to reduce this to one, (insisting "we cannot have it both ways"), the two cannot be combined, or reduced to one, because they are fundamentally incompatible (despite what the head sophist claims). This means that we have to choose one or the other. If we choose the one from pure mathematics, then we have nothing left to understand the identity of a physical object in its temporal extension. If we choose the one from the law of identity, then we simply understand "equal" as distinct from "same", and the problem is solved. Obviously the latter makes the most sense, and doing this would support your imperative dictate: "You can not have it both ways." — Metaphysician Undercover

You have conceded my point regarding math. I have no other point. I don't worry about sameness for onions or photons. I can chop up an onion like nobody's business; and I can flip on a light switch. That's as far as I go with onions and photons.

It is very clearly you are the one who does not understand how math "works". — Metaphysician Undercover

Sadly I came to this conclusion in grad school.

Math only works when it is applied. — Metaphysician Undercover

I don't know why you make demonstrably absurd claims like that.

"Pure mathematics" does nothing, it does not "work", as math only works in application. — Metaphysician Undercover

Tens of thousands of professional pure mathematicians would disagree.

You are only fooling yourself, with this idea that pure mathematics is completely removed from the physical world, the world of content, and it "works" within its own formal structures. — Metaphysician Undercover

Yeah yeah.

That is the folly of formalism which I explained earlier. — Metaphysician Undercover

I'm only a formalist sometimes, when it helps clarify an argument. Clearly math is "about" something. Just not clear exactly what.

To avoid the interaction problem of Platonist idealism, the formalist claims that mathematics "works" in its own realm of existence. But the claim of "works" is sophistic deception, and the formalist really digs deeper into Platonism, hiding behind the smoke and mirrors of the sophistry hidden behind this word "works". That is when the term "mathemagician" is called for. — Metaphysician Undercover

I agree with you that most mathematicians are Platonists. A group theorist does not believe he's merely pushing symbols. He's discovering facts about groups. I concede your point. But I'm not concerned with it.

I believe, the concept of "five" in my mind is completely different from, though similar to, the concept of "five" in your mind. There is a number of ways to demonstrate the truth of this. The first is to get two different people to define the term, and see if they use the exact same expression. — Metaphysician Undercover

Any two set theorists will give {0, 1, 2, 3, 4} as the definition of 5. That's due to John von Neumann, who invented game theory, worked on quantum physics, worked on the theory of the hydrogen bomb, and did fundamental work in set theory. Now there was a guy who blended the applied with the pure.

Another way is to look at what "five" means in different numbering systems, natural, rational, real, etc.. Another is from the discussions of mathematical principles in general. There is always difference in interpretation of such principles. You and I have significant differences, You and Tones have less significant differences.[/quotet]

You raise an interesting point. The integer 5 and the real number 5 are completely different sets. They are NOT the same set at all. They are not equal as sets. But they are the "same" number, for the reason that we can embed the integers inside the reals in a structure-preserving manner. This raises issues of structuralism in mathematics. Lot of interesting issues. Point being is that sameness as sets is NOT actually the basis of sameness in mathematics, entirely contrary to what I've been claiming. There are structural or categorical ways of looking at sameness. I concede your point.

I'll give an example. The set of numbers {0, 1, 2, 3}, along with addition mod 4, is a cyclic group with four elements. Addition mod 4 just means that we only consider remainders after division by 4, so that 2 + 3 = 1. Hope that's clear.

Now you may know the imaginary unit $i$, characterized by the property that $i[&2 = -1/math]. Then <span class="plush-jax" style="font-size:15px"><script type="math/tex">i^3 = -i$, and $i^4 = 1$. So the set of complex numbers $\{i, -1, -i, 1\}$, with the operation of complex number multiplication, is also a cyclic group of order 4. But as any group theorist will tell you, there is only one cyclic group of order 4. Or to put it another way, any two cyclic groups of order 4 are isomorphic to each other.

So these two groups, the integers mod 4 and the integer powers of $i$, are the exact same group, even though they are ridiculously different as sets.

This is a pretty good introduction to structuralism in math. What mathematicians are studying is not the particular sets; but rather, the abstract structure of which these two sets are each representatives. What group theorists care about is the idea of a cycle of four things. How we represent the cycle doesn't matter. Now that's Platonism too, because the cyclic group of order 4 is "out there" in the abstract world of patterns. It's real. It's not a set, it's merely represented in various ways by sets.

So you are right that sameness is a tricky business, even in math. Perhaps I will need to retreat to saying that sameness and set equality are synonymous for sets. For groups, that's not true. Different sets can represent the same group.

Maybe I just talked myself into your point.
— Metaphysician Undercover

Nevertheless, the differences exist and are very real. There is a principle which I've seen argued, and this is to say that this type of difference is a difference which does not make a difference. — Metaphysician Undercover

I like that.

Aristotle called these differences accidentals, what is nonessential. The problem with that expression though, "difference which does not make a difference", is that to notice something as a difference, it is implied that it has already made a difference. So this argument is really nothing other than veiled contradiction. — Metaphysician Undercover

Can you give an example? I might have not followed you.

Anyway, this is the issue with identity, in a nutshell. When we ignore differences which we designate as not making a difference, and say that two instances are "the same" on that basis, we really violate the meaning of "same". The meaning of "same" is violated because we know that we are noticing differences, yet dismissing them as not making a difference, in order to incorrectly say "same". Therefore we know ourselves to be dishonest with ourselves when we say that the two instances are the same, by ignoring differences which are judged as not making a difference. — Metaphysician Undercover

Like the two ways I showed of representing the cyclic group of four elements? So are you talking about structuralism? Two things can be the "same" if they have the same structure, even if they are very different as things.

So when you say that you think the 5 in my mind is the same as the 5 in your mind, I think that this is an instance of dishonesty, you really know that there are differences, and if pressed to argue such a claim, you'd end up in contradiction, dismissing the obvious differences as not making a difference. — Metaphysician Undercover

Well ... no. There is only one Platonic 5. We may all think of it different ways, but we all have the same concept of fiveness. So yes and no to your point.

Right, particulars are instances, specifics are not. — Metaphysician Undercover

Particulars versus instances. I take your point there too. I think. Fruit and apples, colors and red. Two subtly different concepts. Which is which?

The concept "red" is not an instance of colour, it is a specific type of colour. — Metaphysician Undercover

Ok. I accept that.

A particular red thing is an instance of red, and an instance of colour, exemplifying both. — Metaphysician Undercover

\

Hmmm. Ok.

The concept "apple" is not an instance of fruit, it is a specific type of fruit.[/quote[

Ok
— Metaphysician Undercover

A particular apple is an instance of both. — Metaphysician Undercover

Ok. Like apple is a subclass of fruit, but a specific apple in my hand is an instance of the class of apples. Is that right?

The concept "5" is not an instance of number, it is a specific type of number. — Metaphysician Undercover

A type of number. No, don't agree. Real numbers and complex numbers and quaternions are types of numbers. The real number 5 is an instance of a real number hence an instance of a number. It must be so, mustn't it?

A group of five particular things is an instance of both. — Metaphysician Undercover

I do not agree that five apples is an instance of the number 5. The collection of five apples has cardinality 5. That is, 5 is an attribute of the group of five apples. Numbers are pure, they are not apples. A group of apples is not an instance of 5. It might be a representation of the number 5, I could live with that, in the sense that xxxxx is a representation of the number 5.

Hey fishfry, do you not remember what you said to me? You said " I don't make a distinction between "same as" and "is equal to." In math they're the same. If you have different meanings for them, it does not bear on anything I know or care about." Now you've totally changed your position to say "it makes quite a big difference to me", if the taxi driver took you to a house which had an equal fare as yours, but was not the same house. — Metaphysician Undercover

I already addressed this point.

I said in the context of doing math blah blah. When I'm not doing math, the subtleties of sameness matter. Of course the subtleties matter in math too, as I just showed. Two different sets can represent the same group. These days structuralism is how we think about things in math. Two things are the same when they have all the same relationships to all the other things.

Just finished reading it. It is very informative. I must say, though, that it is heavily vested in logic connected to the arithmetical hierarchy. It is still doable but admittedly an obstacle of sorts if you do not use that framework particularly often. — Tarskian

I enjoyed it.

Hamkins acknowledges that the contemporary version of the proof is arguably preferable to Turing's original "detour":

Turing thus showed that the symbol-printing problem is undecidable by mounting a reduction to and through the undecidability of the circle-free problem. But let us illustrate how one may improve upon Turing with a simpler self-referential proof of the undecidability of the symbol-printing problem in the style of the standard contemporary proof of the undecidability of the halting problem. There was actually no need for Turing’s detour through the circle-free problem.

I have tried to turn Hamkins' phrasing of the standard contemporary proof into a narrative:

[... details omitted]
— Tarskian

You have made an impressively detailed reading of the article, way more than I did.

I think that humans have a soul while programs do not. — Tarskian

I am in complete agreement. But just try to explain that to the simulation theorists, the mind-uploading freaks, the singularitarians, the AGI proponents, etc. They have the mindshare these days.

However, since programs also make choices, they can just as humans appear to be "free" in making them or not. That is why I think that it is perfectly possible to analyze free will as a computability problem. — Tarskian

Hmmm. Let me mull that over. I don't agree. Computability, by its nature, is deterministic. Whatever free will is, it is not computable.

Motives matter. Separating families for the good of the kids is one thing. A zero tolerance policy separating all families to deter would-be immigrants is evil, unprecedented, and was quickly stopped when the public found out what was going on. — RogueAI

You made my point for me. In 2014 when Obama was separating families and putting kids in cages, the MSM did not widely report the story. People were not outraged because they didn't know it was happening. When images of kids in cages covered in foil space blankets "like baked potatoes" started circulating on social media, Obama dialed back the cages and loosened the vetting of families. Even the WaPo was forced to report on the kids Obama was losing to traffickers.

I have already conceded to you that if Trump said what you you say he did, that was not a good look. Trump is a very flawed man, but the only alternative to the wrong turn the Dems have taken the past couple of decades and especially the past eight years. So if he did bad, I'll grant you the point.

But as I mentioned in another post just now, if your point is that Obama put kids in cages it was good because he's Saint Obama; and when Trump put kids in the exact same cages Obama had built for that exact purpose it was bad, because he's Orange Hitler, you are just being partisan.

How do we know Trump wasn't just being Trump, and saying something inartfully that could be twisted by his opponents? Maybe just trying to send a message to prospective immigrants? As the saying goes, Trump 's opponents take him literally but not seriously. And his supporters take him seriously but not literally. Like when he jokingly asked Putin to find Hillary's emails. I thought that was hilarious. The left went hysterical; and for the most part, disingenuously so.

Also, a little off-topic: Like the taco bowl tweet. I thought that was hilarious too. "Trump is a brilliant performance artist and troll." That was my reaction. The left went hysterical over that too. For whatever reason, Trump's personality doesn't trigger. me. I get the guy. He's Queens, the establishment is Manhattan. They look down on him, and he is alternately insulting them and enviously wishing he could belong, which he never will.

When a Dem says, "Oh Trump put kids in cages," I know I'm talking to someone utterly ignorant of the issue. Which includes pretty much everyone on the left.

And yes, Biden's record on the border is awful. — RogueAI

Ok, well I'm glad you see that. But I'm not even talking today about Biden's open borders and the massive humanitarian crisis he's dumped on blue cities like NYC, Chicago, and Denver. I'm talking about the lesson Biden's administration learned about the separations and cages. Those are bad optics; turning kids over to traffickers keeps the issue out of the MSM. That's a moral outrage. I do predict this story will eventually become known. Like Biden's cognitive condition became known. Way too late, and only when it became impossible to keep covering up.

We're not doing people any favors when we make it easy for them to come here illegally and then live in the shadows and be exploited. — RogueAI

We leave them to die of thirst in the desert, and then give them driver's licenses, social welfare programs, and jobs if they make it over alive. A bipartisan moral atrocity that got started with FDR's Bracero program in the 1940s. I'd love to see some sensible immigration reform in my lifetime. I'm not holding my breath.

Just an aside. You probably know this stuff. But others might not. This is not a rigorous presentation. — fdrake

Actually I never formally studied any probability theory. I've seen measure theory but not the fine points of probability.

When you talk about the probability of something, that needs to be defined as an event. Which is a particular kind of mathematical object. It does not tend to be the kind of mathematical object that a formula in a mathematical argument is. Eg the probability that it will be raining in 2 hours given that it is raining now makes sense. The probability that 2+2=4 doesn't make too much sense.

However. If a statement A is provable from a statement B and concerns a quantity *, the probability of A given B is 1. As an example, what's the probability of X+1=4 given that X=3? Probability 1.

Another fact like this is that if A and B are mutually contradictory, the probability that A occurs and B occurs is 0. That also works with entailment. Like the probability that X=3 given that X+1=2 is 0, since X+1=2 implies X=1, and there's "no way" ** for X to be 3 given that assumption. — fdrake

I've never seen probabilities assigned to mathematical facts like that. Not sure what it means.

The same holds for statements *** you can derive from B using classical logic and algebra and set operations. eg if the probability that X=3 is 0.3, what's the probability that (X=3 or X!=3)? 1, since those are exhaustive possibilities. The latter does have a connection to truth, as if you end up asking for the probability of something which must be true, its probability is 1. — fdrake

Same remark. Don't follow this at all. If you pick a random real in the unit interval, the probability that it's between 0 and 1/3 is 1/3. That I understand, from measure theory. But I don't follow assigning probabilities to equations at all.

For folks like Fishfry, I'm sure you can make the amenable sense I've not specified precise. Logical, algebra and set operations which can be represented as measurable functions on the sample space work like the above. "no way" corresponds to the phrase "excepting sets of measure zero". Which is the same principle that stops you from asking "What's the probability that clouds fly given that x=2?", as there's no way of unifying both of those types of things into a cromulent category of event. — fdrake

You are giving me too much credit. I have no idea how to assign a probability to an algebraic statement. I've never seen that.

The latter also blocks a more expansive connection to truth. Since the kind of things that humans do while reasoning from premises typically aren't representable as measurable functions. Maths objects themselves also have plenty of construction rules that behave nothing like a probability - like the ability to conjure up an object by defining it and derive a theorem about it, there's just nothing underneath all maths that would take take a probability concept which would usefully reflect its structures I believe. — fdrake

I don't know if reasoning from premises is amenable to probabilities. I may have missed much of what you said in this post.

:rofl: I see you're thoroughly misinformed nowadays. — Benkei

Perhaps you can explain what I'm misinformed about re the family separations and cages.

If I'm understanding you correctly, when Obama separated families and put the kids in cages, he did it for saintly reasons, him being Saint Obama. And when Trump separated families and kept the kids in the very same cages Obama had built for that purpose, he did it for dastardly reasons, because he's Orange Hitler.

That is the only way I can interpret your claim that I am "misinformed" regarding widely known matters of fact. If you didn't know about Obama's cages in 2014 that's understandable, because the story was not widely reported in the MSM. If you claim it's not true today, it's you who are misinformed.

I'm open to your explaining exactly what I am misinformed about regarding this situation.

Love the cavalier attitude to the use of armed force. — Benkei

Not cavalier at all. If you can't see the difference between lobbing a few missiles onto an airport tarmac (if I recall the details correctly, didn't bother to look it up) and starting new wars, as every president of both parties since Ike has done; then I just don't know what to say. You draw an equivalence between the tarmac bombing and Biden's two major proxy wars? Or Clinton's bombing of Serbia, a war Clinton's voters ignored because it was a Dem war. It bothered me, and I was a big Clinton fan and voter at the time. Yet another one of the datapoints in my growing estrangement from the Dems. The antiwar left is strangely silent when they're Democratic wars. The left hated Bush's torture program but they didn't mind that Obama institutionalized it by failing to hold the Bush regime accountable (for understandable political reasons, to be sure).

So Trump bombed a tarmac and killed one Iranian. That's a remarkable lack of bloodshed for an American president of any party. I don't see how you can pretend not to understand that point.

This really underlines my point. Let's pretend it's not a war and then it's ok. No matter that "war" isn't the appropriate legal term any more. No matter that the President can unilaterally decide to put soldiers, e.g. US citizens, into harm's way because "technically" it isn't a war. No matter that it's still armed aggression, which is prohibited under the UN Charter so the President is unilaterally deciding to breach treaties Congress signed up to. It's authoritarian and it was his primary M.O. with respect to international relations. Of course, other US Presidents have done the same thing but presenting Trump as a peace candidate is silly and not borne out by the facts. — Benkei

The tarmac and the terrorist. That's it. You don't seem to be able to understand the difference between using massive violence, as most president do; and bluster and the threat of violence to avoid violence, as Trump did.

I think you actually do understand; but just want to pretend you don't to make a partisan point.

(1) The symbols I used are common. The formulas I gave are not complicated. If one knows merely basic symbolic logical notation, then one can read right from my formulas into English. For example:

AxEy yex

reads as

For all x, there exists a y such that y is a member of x. — TonesInDeepFreeze

That is not my point. For whatever reason, I've always had difficulty with your posts. Maybe it's the symbols. Maybe it's the words. I don't know.

(2) I did give lots of explanations in certain contexts. — TonesInDeepFreeze

I'll concede that either I'm too dense to follow your arguments, or I just lack the logic background. I appreciate your efforts.

(3) You complain about the length of my posts, but also say I should give more explanation. You can't have it both ways. And you're hypocritical since your own posts are often long, and often enough have not merely a few symbols. — TonesInDeepFreeze

Guilty as charged on all counts.

Senator James Lankford is a strict conservative GOP member who was on a bipartisan committee tasked with addressing border issues. He drove a very hard bargain and got many more concessions out of the Democrats than anyone had expected, getting them to agree to what many of them thought were overly harsh measures that the GOP had been demanding for years. But then before it went to a vote, Trump got wind of it and said he didn’t want it to go ahead. Why? Because it would take away his talking points about the country being flooded with Mexican rapists. So Lankford was then pressured to vote against his own hard-fought legislation, rather than bring it to the floor - because it might have been a solution. Trump would rather keep his talking points than actually solve the problem. For his trouble, Lankford was then censured by the Oklahoma Republican Party, for the mortal sin of working with Democrats. — Wayfarer

Thanks for that summary. I apparently missed this story. I did a quick search and evidently the GOP Senators rejected his bill. I looked at a couple of articles and they didn't mention Trump's influence, even though "Trump" was one of my search terms.

If you happen to have a reference to Trump's influence on the GOP abandonment of Lankford's bill I'd appreciate it. Pending that, and taking your word for it, I'll grant you your point. I've never said Trump isn't a flawed man. I've only said that he's the only alternative to the wrong turn the Dems have taken the past couple of decades and especially the past eight years.

I agree that the GOP are useless. They get nothing done at all. I'm saddened but not surprised to learn they killed a chance at sensible immigration reform, with or without Trump's pressure.

That probably also explains why 24 previous aides and allies went on the record saying he was unfit for office and a danger to democracy. — Wayfarer

The word authoritarian is lacking in your talking point. For sure he's a danger to the status quo in Washington, so it's not difficult to find people to throw rocks at him. I just don't see how a guy who got so easily subverted by his underlings could be an authoritarian. Joe Stalin was an authoritarian. He killed his enemies and friends alike. His critics didn't go to the press, they went to the Gulag.

At least, if you are ever interested in a formula, but you don't know the use of the symbol, there you have it. Of course, if you're not interested in formulas, though they are the most exact and often the most concise communication, then I can't help that. — TonesInDeepFreeze

Symbols need explanatory words to go with them. This is probably more true in math than in logic.

The core business in that era was pillaging someone else's farmland. — Tarskian

Coming soon to a bankrupt empire near you! :-)

The narrative above is pretty much the gist of Alan Turing's proof for the halting problem. — Tarskian

Tarskian, You may be interested in a recent paper by Joel David Hamkins. Turing never proved the impossibility of the Halting problem! He actually proved something stronger than the Halting problem; and something else equivalent to it. But he never actually gave this commonly known proof that everyone thinks he did. Terrific, readable paper. Hamkins rocks.

https://arxiv.org/pdf/2407.00680

In fact, there is no app that can tell minute by minute what even any other app will be doing. — Tarskian

That's too strong a statement. If an app is halted, I can write a program that, given any time t, says, "The program is halted at time t."

Likewise if I'm dead, a program can exactly predict what I'm doing. But of course in that case I wouldn't have much in the way of free will.

The real requirement here, is incompleteness of the theory. — Tarskian

Penrose thinks free will might be a quantum effect in the microtubules of the brain.

https://philosophy.stackexchange.com/questions/3322/the-emperors-new-mind-and-free-will

By the way, humans may or may not have free will.

Programs, by their very nature, do not have free will.

False. Look it up. Military intervention and threat was his primary foreign policy tool. — Benkei

Threat. He's a negotiator. He lobbed a few missiles at Syria. Drone strike against Soleimani. No new wars. He used threats to keep the peace. I didn't call him a milquetoast. I called him a peacemaker. Big difference. Based on results. No new wars. First prez in my lifetime who can say that. No new wars.

I do not believe he initiated any military interventions. You say that's false. Names and dates please. Trump started no new wars. As far as I know, no new military interventions at all. Did a quick lookup, couldn't find any.

And yes, Republicans are more authoritarian than Democrats even if they both are. Only Republicans have had sitting presidents and advisors argue in favour of it and the unitary executive theory. Most recently in court. Or did you miss that? — Benkei

Unitary executive is a little inside baseball. It doesn't mean "all powerful president." According to Wiki: "The unitary executive theory is a controversial legal theory in United States constitutional law which holds that the president of the United States possesses the power to control the entire federal executive branch."

It does not say anything about going to war. It says essentially that the prez is in charge of the people who work for him. I think you might be conflating different things. If you're referring to the recent Chevron decision, it's a good thing. The underlying case was a fisherman who had to pay $700 per day to have government inspectors on his boat. If Congress wants to pass a law to make him do it, let them pass a law. The agencies don't have the right, so say the Supes. Tell it to Ruth Bader Ginsberg, she's the one who stayed too long, expecting Hillary to win. Not my fault, not Trump's fault.

Who can argue with who's more authoritarian? The Supreme court told Biden he couldn't transfer student loan debt to the taxpayers. He did it anyway. Obama bragged about ruling "with a pen and phone." He held weekly Kill List meeting where he decided which American citizens to drone-bomb without due process. Going back in time, LBJ lied the country into the Vietnam war. There was no attack on a US ship in the Gulf of Tonkin and that was known at the time. Reagan sold arms to Iran to fund his secret war in Nicaragua. Ok a GOP you got me there. I mean, you look at recent history, it's hard to tell one authoritarian from another. Trump was arguably less authoritarian than any of them, simply because he knew so little about how the government works that he got rolled by the bureaucrats and betrayed by the people who worked for him.

So you'd know the name Senator James Lankford, and why he made news a couple of months back. — Wayfarer

Had to look that one up, perhaps I missed your point.

So you think Mike Pence should have hung? — Wayfarer

Along with the fly.

Depending upon the quality of the university to some extent. With the exception of a 12 month post-graduate program I took at the U of Chicago for the USAF, my entire education was in large state universities (4).

I checked at what Harvard has to offer and they have two undergraduate courses in mathematical logic (and probably foundations), but at my last Alma Mater there is nothing of that kind offered at any level. — jgill

I don't think it's just quality. My grad school was high quality but no logic or foundations to speak of. The one set theorist when I was there didn't get tenure and left. I think logic is concentrated in a few places but not that widely. Seems that way anyway.

It sounds like you're getting your information from places like Townhall, TheFederalist, Breitbart, and Redstate. Am I correct on that? — RogueAI

Decades of interest in Mexico, traveling in Mexico, living in Mexico, paying attention to border politics. If you don't know about Biden's trafficking operation, hardly anyone does. If you don't care now that I've drawn people's attention to it, you should demand more of yourself re this moral atrocity.

I haven't read Townhall in years. Redstate, maybe the occasional article if it's linked from an aggregator. Don't recall last time I read it. Breitbart most definitely never writes about the cages and separation policy the way I've explained it. Don't recall The Federalist writing on immigration. Most of my political orientation these days comes from the disaffected liberals (like I am). Greenwald, Dore, Maté, lot of Substackers. They don't write about border issues either.

In the immigration issues as I explained them -- the cages and the separation policy -- I got that on my own from factual reporting on the subject. I was living in Mexico in 2014 when Obama had a terrible humanitarian crisis down there and built the cages. I followed the issue. I don't recall where it got reported. The MSM barely reported on it till the photos of the kids in cages covered in foil blankets started hitting social media. A lot of information not in the MSM is nonetheless true. That's a problem in itself. You can always say, "Well XXX is a scurrilous right wing rag." And maybe it is. But a lot of alt media covers stories the MSM won't touch.

Such as Biden's senescence. People were calling Jill Biden Edith Wilson in 2020. But in the alt media, not in the New York Times. But the alts were correct, and the MSM were lying. I hope there's a reckoning about that soon. You can't run a decent society without a truly free press.

And if the New York Times doesn't tell the truth about the border (or anything else), why is that? I read very widely, from the left-wing wackos to the right-wing wackos. But my knowledge of the border comes from a very long personal interest and involvement with the subject.

From the Reuters piece you linked: "In June, Trump abandoned his policy of separating immigrant children from their parents on the U.S.-Mexico border after images of youngsters in cages sparked outrage at home and abroad."

Exactly the same reason Obama and Biden decided to stop the caging and just turn the kids over to traffickers. Cages generate bad optics. Nobody sees the trafficked kids. That scandal's waiting to explode.

I'll stipulate that Trump said what the Reuter's piece says. Not a good look, I agree. It doesn't detract from my point. Obama put kids in cages till the optics got bad. Trump put kids in cages till the optics got bad. Biden just let everyone in and is running a massive trafficking operation. He'll be out of office before people come to find out what he's done.

Nearly all of these text symbols are quite common: — TonesInDeepFreeze

Not quite my point, but thanks.

I stated the axioms of identity theory in multiple posts. Not funny, but true. — TonesInDeepFreeze

Not true, but funny.

I did not say that it's not.

I'll say again:

First order logic with identity provides:

(1) law of identity (axiom)

(2) indiscernibility of identicals (axiom schema)

(3) interpretation of '=' as standing for the identity relation (semantics)

Set theory takes (1) - (3) and adds:

(4) extensionality (axiom) — TonesInDeepFreeze

I'm sure you're right. Just a little beyond my awareness.

Actually I'd say alot of them would be relieved if Biden were replaced right now. Like I said alot of Dem voters didn't want Biden to run again and the debate has been spread around so much that people know what's going on with Biden. Most of the in person takes from Democrats I've seen seem to be "yeah I'll vote for Joe over Trump because Trump, but honestly I think I will prefer anything else". — Mr Bee

Chuckie Schumer is said to be "privately" open to opposing Biden. Pelosi gave an ambiguous statement coded to mean she's sticking in the knife, but very subtly.

But the big news of the day was that the Democrats brought out their big gun. Their nuclear weapon. Their neutron bomb. Yes, I mean George Clooney. A few weeks ago Clooney organized a $30M fundraiser for Biden complete with Julia Roberts and all the other beautiful people. Today, Clooney stabbed Biden in the back with a NYT op-ed. I tell you it's sickening to watch. I hope never to have "friends" like that. And Clooney said that when he saw Biden three weeks ago, Biden was not the same man as he was in 2010 or even 2020. So Clooney knew. And Clooney still raised the thirty mil. And today Clooney jumped on the Judas bus and stabbed his former friend in the back. These people are lower than low.

But in the end, the Dems have no leverage. And as I say, they can swap in Kam and they'll have a whole new set of problems.

Part of what makes me see the debate as a blessing in disguise. I thought Biden's campaign was a dying campaign that was gonna lose before anyways so a disastrous debate performance was just the sort of jolt needed in desperate times. I mean Biden may still stay in but if things were going in a bad direction already then hey gotta take a chance right? — Mr Bee

Right. Some say the Dems deliberately set him up to get him out. But it's not quite working the way they thought it would. I don't think they planned on Joe digging in and daring them to move him out.

I'm not gonna argue policy but politically Kamala would be wise to try to distance herself from the unpopular policies of Biden's administration and tie herself to the more popular aspects. — Mr Bee

She's way further left than Biden, and Biden has governed from the left. Are you saying Kamala should turn into Milton Friedman and Ayn Rand? Ain't happenin'. She's a hard core leftist and would be a disaster for the country.

The Gaza issue for instance is something that is splitting the base right now for Biden, so another candidate who isn't as tied to Biden's actions would be better, if simply for the fact that they won't be seen as having Palestinian blood on their hands as the chief director of an administration's foreign policy. — Mr Bee

No, they'd have Israeli blood on their hands. Kamala is married to a nice Jewish guy but she's a Hamasnik all the way. Just yesterday she said she "understands" the Gaza protesters. That's code for Death to Israel in my book. By the way I stand with Israel, just so you know. And I will say, this issue has split a lot of people. Some of my favorite political commentators have horrified me with some of their rhetoric. Glenn Greenwald, Jimmy Dore, Aaron Maté. The Gaza war has been a terribly divisive issue. And Kam is way on the wrong side of it IMO. But we can agree to disagree on that. I don't talk about it much, it's just so emotional and so divisive for everyone. The Middle East has been a bloody mess all my life and I don't have any answers.

I don't think alot of Democrats would disagree with that, particularly on the progressive left (the "Bernie would've won" types). — Mr Bee

I wish that were true. The TDS brigade would not take any responsibility for the Trumpenstein of their own creation. I wish Bernie and his supporters had been a lot more vocal when the DNC screwed them over in 2016 and again in 2020.

The Dems utter incompetence in running an effective candidate against an easily beatable buffoon like Trump is what got us here and may get us to another Trump term. — Mr Bee

It's funny. In 2016 the Dems found the only candidate in the country who could lose to Trump. In 2024 they're about to do it again.

Hilary was unpopular but the DNC decided it was her turn and she was the nominee. Biden was also uninspiring but the DNC decided it was his turn and pulled alot of strings to get more popular candidates like Buttigieg to drop out and endorse him before Super Tuesday, winning him the nomination. And now the DNC is again ignoring the will of it's voters by putting up a man the majority of the country think is too old. — Mr Bee

They didn't think he was too old when they gave him 3986 delegates. And why not? Because the Dems and the media gaslit the hell out of them. And again -- my ongoing thesis -- Kam would be worse. And nobody can leapfrog Kam. So in the end they stay with Biden. There is no alternative.

It's funny how apart from Biden the two candidates who won the general elections since 2008 were dark horse candidates in Obama and Trump who genuinely built up a base of support from the ground up. Maybe the Democrat party should take some lessons from that or maybe they'll try to force Kamala down our throats in 2028 since it's her turn next. — Mr Bee

By then Gavin and Gretchen will be fresh and ready. Kam will be yesterday's news. She's never been very popular and she's a terrible politician.

I'd say the GOP also bears some of the blame too for what happened post Jan 6. They condemned Trump and what he did, rightly so. They could've impeached and gotten rid of him forever but they chickened out, perhaps because they thought that he was gonna go away on his own. The Dems thought the same and also did nothing too. — Mr Bee

I better take a pass on J6. I regard it as the Democrats' Reichstag fire. Bunch of unarmed, peaceful protesters were invited in by the Capitol police, things got out of hand and a riot ensued. What ever happened to, "A riot is the voice of the unheard?" That was the Dem line when the Floyd protesters caused $2B in property damage and killed 20 people. The Pelosi and Cheney J6 psy-op was a fraud. Trump has called for military tribunals. I disagree about that. In this country we use the civilian system of justice. But I do hope Trump gets some revenge on the Dems who have so abused our system of justice. Garland and Wray for two. The impeachments were totally fraudulent. It was Biden who was seen on video extorting the Ukrainians to get rid of the prosecutor investigating his money laundering scheme there. We better not get onto this topic, you know how I feel now.

You may have your own ideas on why it took Garland so long to start an investigation into Trump but I think it's just because they had the same mindset as the GOP: That Trump would simply go away and disappear because there's no way the people would flock back to a loser who tried to pull off that, right? There was no need to start a politically charged investigation into a highly controversial figure which would probably just anger the people at Jan 6. It was just pure incompetence and trust in the public to move on when they clearly seem unable to. — Mr Bee

I want Garland and Wray in jail. Let's agree to disagree on that. J6 was a psy-op, a fraud, a Reichstag fire for our time and place. You can't have an insurrection with a bunch of unarmed people peacefully wandering around an office building. Compare and contrast to the Floyd riots. Voice of the unheard and all that. If anyone's unheard in this country it's the rank and file middle Americans. The people Trump has activated and drawn to him.

Like I said before, courage is a rare thing for elected officials, and nobody has the guts to actually go after Trump effectively and snuff him out for good, causing him to come back as he always has. It's not that Trump is invincible but everyone else is a coward. — Mr Bee

The Democrats have disgraced themselves. Trump is a reaction to that. He has many flaws but he is the only alternative to the corrupt, warmongering status quo that the Democrats (and Republicans!) have turned into. Let's agree to disagree again. We're not doing policy here, only the politics of the Biden dilemma.

Well at this point they have to talk as much sense into Jill as they do to Joe. — Mr Bee

Jill does not strike me as someone amenable to logic. Or political pressure. She's dug in. The Dems can impeach Joe or 25A him or they can pound sand. George Clooney's not going to do it.

And just now we have Pelosi coming on to Biden's favorite show Morning Joe and laying out that this issue is clearly not over right to Joe's face. She is still saying Biden "needs to make a decision" after he decided to stay on, which is essentially code for "we'll let you do it on your own terms, but get the hell out or else more people will lose confidence in you". — Mr Bee

Right. Caught that. But she's wrong too. Joe is not "making a decision." He's made his decision. Now the Dems have to make theirs. Impeach, 25A, or stab him to death on the floor of the Senate à la Julius Caesar. Strongly worded editorials and vaguely worded statements on Morning Joe aren't going to cut it.

And George Clooney. That really cracked me up today. What a slime ball. Joe's best friend three weeks ago.

Well that's the idea. He clearly has a tendency for dangerous ideas given Jan 6, but was stopped by some of the people who were working for him like Mike Pence. I guarantee you whoever he picks for his running mate and his administration won't be professionals who would keep him in check like last time. — Mr Bee

I'd hang Mike Pence AND the fly he rode in on. 'Nuff o' J6.

Professionals? Milley is a treasonous bastard who belongs in prison. Mattis, useless. Barr, useless.

The reason the Dems are afraid of Trump is that they realize he's probably learned a few things about how Washington works. I truly hope so.

I assume we probably are gonna disagree here but I'll just leave things there. I'm not looking to debate Trump's policies or Project 2025 right now. — Mr Bee

Likewise. I really do try to avoid policy in this thread. But P2025 is not Trump's platform. P2025 is yet another TDS hysteria. Trump's platform is his actual platform. And it's surprisingly centrist, moderate, and popular. Here's Brit right-of-center website Spiked on the subject:

The truth about Trump? He’s a moderate

And here's The Guardian making the same point.

The Republicans’ new party platform is scary – because it can win

They made the point that Trump's platform is very 1990's Democrat centrist in nature. Jobs. Border control. Peace.

P2025 is another left wing hysteria. It's not Trump's platform at all.

Similarly nobody in the Biden White House can truly stop the congressional Dems from coming out and distancing themselves from the president, which is clearly something Biden is working hard to avoid. Both sides are lobbing threats at each other and Biden according to one article is promising mutually assured destruction if he is attacked. Of course if the Dems are in a sinking ship anyways then why not pull a mutiny? — Mr Bee

Attacks on Biden weaken him if he's the eventual nominee. Some Dems see that. Kamala is no panacea.

LBJ stepped aside and a chaotic primary ensued where RFK was assassinated. — Mr Bee

That was a bad bad day. If one is conspiratorial-minded, one would say that they killed Bobby because as president, he was going to get to the bottom of his brother's murder at the hands of the CIA. I'm conspiratorial-minded in that regard. More shots were fired at Bobby than Sirhan's gun held. The coroner said he was shot at close range from behind, but Sirhan was several feet away, in front.

Terrible day. Awful. So many hopes were on Bobby. Making me sad now for what might have been.

The average voter just cares about who is at the top of the ticket and a bit about who is running with them. They're not gonna think that far ahead like you are. In fact I imagine alot of them are ignorant of how succession works. Plus it's very unlikely a narcissist like Biden would just hand over the presidency to Kamala as soon as he is inaugurated. He will be in the office most likely until he dies partway through the term at 85. — Mr Bee

Yeah you're right. A career politician does not give up power willingly.

I don't think the party will spin it that way. Biden won't make a speech saying "Yeah I've been lying about having dementia for 2 years now so I'm stepping aside", but probably saying something along the lines of "I believe I can serve another 4 months, but not another 4 years, so I'm renouncing my candidacy". The GOP will probably continue with the narrative but as far as the Dems are concerned, they didn't lie and they Biden is just making a personal decision about his next 4 years. — Mr Bee

I don't think they'd say it out loud, but many voters will read it that way. They shut down competitive primaries, foisted Joe on the Dem voters, and now this? What a mess.

Also more would stay home if given the choice between Biden and Trump. Sure people hate Trump but the DNC is essentially making them walk through glass to vote against him by making the alternative just as despised and with crippling flaws of his own. — Mr Bee

Anything can happen.

My perception is people would just be relieved that they won't have to vote for a criminal geriatric and a senile one. — Mr Bee

The TDS crowd thinks Trump's a criminal. The other half of the country sees the Bragg prosecution as totally illegitimate. Nelson Mandela spent 28 years in jail but they didn't call him a felon when he became president. They recognized the legal process against him as unjust. Trump same, for half the country.

But I do agree that Trump is old and leads an unhealthy lifestyle. He could keel over too. I wonder what this is like for the young people of this country. They must be appalled.

You can say the scandal and the coverup is a bad look and the right wing circles will certainly go wild with that, but in an election full of conspiracies and scandals about laptops and documents that people seem to care very little about, at the end of the day the inattentive swing voter will just care about who they're voting for at the top of the ticket. Kamala isn't great, but she's not a corpse or a convicted felon. — Mr Bee

In 2020 a poll showed that 17% of the electorate would have changed their vote if the'd known that the laptop was authentic. And that's another thing. "51 former intelligence officials" said the laptop was Russian disinformation. It wasn't.

Why do people support Trump? Because he is the only alternative to the culture of official corruption that's seized this country. When the CIA and the FBI lie to the public to help a political candidate, that is a very serious problem. Trump stands opposed to that. A lot of people, such as myself, support Trump for what he stands for, not for who he is. He stands in opposition to this massive corruption of our government.

Yeah Biden has been in politics for 50 years but that has made him an institutionalist. Unlike Trump, he is a man who highly values norms, running on "restoring normalcy" as his 2020 pitch. The idea of running without the full support of your party is certainly breaking one of those norms and sure he may continue to soldier on as the donor network and congressional support dries up, but that is not easy for someone who's been a lifelong Dem. Trump certainly would since he never was a traditional politician, but as much as he tries to imitate him would Biden? — Mr Bee

Biden campaigned on normalcy, then ran as a corrupt leftist authoritarian. Lot of people see that.

If the lord almighty visited Biden and Trump the same day that would be the greatest day in American history where we're saved from this nightmare of an election. — Mr Bee

I'm kind of enjoying it. Just want to see the Dems get their comeuppance.

You hardly see because it's a feature not a bug. But some things that have me grimace in distaste are the ability of US Presidents to:

Rule by executive order (which have included travel bans, torture (Bush's classified "directive"), immigration, listening in on all data (for "security" EO 12333), healthcare reform and environmental policies).
Veto legislation.
Deploy troops in foreign territory without congressional authority (because technically it isn't a war)

Yes, this is absolutely authoritarian from the view of a European democracy. Unitary executive theory would take this even further. — Benkei

Ok. You started out saying that Republicans are authoritarians. Then you reverted to Trump alone, and only because of the American Reichstag fire that Democrats seized upon to go on yet another of their post-2016 Trump hysterias.

And now you make a very different point. You say that the American executive, as defined by the US Constitution, is inherently authoritarian.

Now this of course is an interesting theses that we could discuss in a forum on political philosophy. Perhaps in a different thread. Quite a bit has been thought and written about the subject since we yanks tossed King George's tea into Boston harbor.

But we are in the thread on the US election. Two men are vying to be president, unitary or not, morally-defined presidency or not.

So I think you've undermined your own point. Although in the end, you came to a very interesting subject. In theory the three branches of the US government are co-equal. But in recent decades the president has become way too powerful. I tend to agree with you. But that's not what we were talking about. It's not even what you were talking about. You wanted to bash Republicans, or Trump; and in the end, it's the role of executive power in theory and practice under the US Constitution.

I sure as hell opposed Bush's torture. And I equally strongly opposed Obama's coming into office and, by not holding the Bush administration accountable for their many abuses, institutionalizing the torture.

That was, by the way, yet another of my many data points along the way to being a disaffected liberal Democrat. Bush was a criminal when he tortured people. But Obama was worse, because when he chose (for good political reasons) not to hold Bush accountable, he turned the US into a torture regime.

I agree with you about all your particulars. The Constitution does not allow the president to start wars without a declaration of war from Congress. But the last time the president got a Congressional declaration was in World War II. Every single war since then has been illegal. I'm quite unhappy about that. But it's a bipartisan affair, hardly limited to one party.

And in our lifetimes, what president started no new wars? It was Trump. A point totally lost on the "Orange Hitler" brigade. I just don't know what happened to my former fellow liberals. Trump's victory over Saint Hillary drove them quite insane. They now love the national secuity state, the wars, the CIA, the NSA, the FBI, the lying, the spying. Back in the day they opposed all that. I still do.

This is exactly the problem, failing to distinguish between "same as" and "equal to". — Metaphysician Undercover

It's not a problem to me. I suspect, but have no supporting evidence, that it's not a problem even for most philosophers. It's a problem for you, and I hope you can get it resolved so that it no longer troubles you.

Because you do not believe that there is a distinction to be made here, — Metaphysician Undercover

They're two phrases or words for the same thing. I concede that you have some deep or perhaps pseudo-deep reason to make a distinction, but you haven't explained it to my satisfaction.

you will not notice the effects of such a failure, and you will insist that it doesn't bear on anything you care about. — Metaphysician Undercover

Is it your contention that if I understood this failure, I would suddenly arise and go over to the math department at the nearest university and give them a piece of my mind? Or renounce my heresy, do penance, confess to a priest? Or what, exactly, would you like me to do?

Insisting that it doesn't bear on anything you care about will allow you to be mislead, even tricked by intentional deception (as you were by the sophist's employment of "identity of indiscernibles"), and you may never ever even notice it. — Metaphysician Undercover

You're cracking me up. I find your prose very funny tonight. You are going on about this but making no point at all.

Here is a simple example of where the difference bears in a substantial way, though I am sure there are more complex examples. In quantum physics, — Metaphysician Undercover

AHA!!!!!!! After berating me about the playground, and getting me to stop using real-life examples, you whip out an example from physics. But physics is not math.

Now explain this to me ONCE AND FOR ALL. Are we talking about pure math and set theory? Or are we talking about the physical world of time, space, energy, quantum fields, and bowling balls falling towards earth?

You can not have it both ways.

a quantum of energy is emitted as a photon, and an equal quantum may be detected as a photon. Since these two quanta of energy are equal, they are said to be "the same" photon. That is the mathematician's use of "same", equal quanta implies one quantum, a photon. By the law of identity "same" implies temporal continuity, such that the photon exists, with that identity, for the entire period between emission and detection. Equivocation between these two senses of "same" inclines some people to believe that the photon exists, as the same "particle" for the entire period of time between emission and detection. However, the electromagnetic energy is observed to exist as waves in the meantime. — Metaphysician Undercover

The physics complaint department is across the street. I'm the math complaint department. In math, "equals" and "the same" and "is identical to" are synonymous. I can't help you with your complaints about physics.

And you see, having BERATED ME ABOUT THE PLAYGROUND, you now give me yet another physical example. But I have already agreed not to use physical analogies or examples anymore, because physical things are different than abstract things.

So your physics example has no bearing on mathematics. In any event, photons are just excitations in the electromagnetic field. It's far from clear what a "thing" or "object" is in physics these days.

This produces significant theoretical problems. Some claim a contradictory wave/particle duality theory, in which the energy travels as both waves and as particles at the same time. Furthermore, since the photon of energy emitted is assumed to be "the same photon" as the photon detected, and it's path cannot be determined, it is claimed to have multiple paths all at the same time. All of this sort of problem is due to equivocation of "same". The mathematical "same", an equal quantum of energy is emitted and detected, is confused with "same" by the law of identity, to conclude that a distinct quantum (particle) of energy, known as the photon, has continuous existence between the time of emission and the time of detection. — Metaphysician Undercover

You rejected my playground story and now you're resorting to examples in physics. Please stay on topic, You are wasting your keystrokes talking about the wrong thing.

Photons are not sets. I have no idea what physicists mean by "same," "equal," or "identical." I doubt they do either, they don't bother themselves with philosophy these days.

You say that this issue doesn't bear on anything you know or care about, — Metaphysician Undercover

When I'm talking about the foundations of math, of course. When I arrive home in the evening, it makes quite a big difference to me if I return to the same residence or just one that's "equal" to it in value.

You are quite the sophist tonight yourself.

but until you recognize and understand the issue you'll never know how it bears. Furthermore, I saw how the head sophist, persuaded you to see a mathematical axiom differently, through reference to the identity of indiscernible, so I know that it really does bear on things that you care about. — Metaphysician Undercover

You haven't said a single thing of substance. You've given an example from physics when the subject is math. You've said nothing. As Truman Capote once said of a book he didn't like, "That's not writing. That's typing."

What is said about a thing is distinct from the thing itself. Contradiction is not in the thing itself, it is in what is said about the thing. To say that a thing has contradictory orderings is contradiction. The contradiction "is distinctly and noticeably separate from the [thing] it applies to". — Metaphysician Undercover

Well that certainly clears things up.

You are in denial, just like the sophist. "Equal" means to have the same value within a system of valuation, "same" means identical, not different. Notice that "equal" is a qualified sense of "same" the "same value", meaning identical value, whereas "same" refers to identity itself without such qualification. Two distinct things are said to be equal, being judged according to a specified value system. Two distinct things are not the same. Please tell me that you understand this difference. — Metaphysician Undercover

In physics? In playgrounds? Could be, for all I know, to the extent that your word salad communicated anything at all. In math? No. You don't understand how math works, and you continually demostrate that.

This is colloquial vernacular insufficient for logical rigour. The proper classification is like this. The abstraction "number" is more general, and the abstraction "5" is more specific, just like "animal" is more general, and "human being" is more specific, or "colour" is general and "red" specific. Neither is a "particular instance". — Metaphysician Undercover

When it comes to colors, or colours if you prefer, I admit I'm on shaky ground. I don't know if if philosophers consider red an instance of color, though I think it is.

But when it comes to math. I am sure. The set of real numbers is most definitely a particular set in the universe of sets, and is an instance of the general concept of set, or the universe or sets, or the category of sets,

One might however say that there is a particular instance of the abstraction "5", and the abstraction "number", in your mind, and another particular instance in my mind. But that would be an ontological stance which would be denying common Platonism. Platonists would say that what I just called particular instances, are really just parts of one unified concept "5". — Metaphysician Undercover

You finally said something interesting. Is the 5 in your mind the same as the 5 in my mind? I think so, but I might be hard pressed to rigorously argue the point.

So what do you say? Are the 5 in your mind and the 5 in my mind the same? Identical? Equal? Curious to know. You did interest me with this example.

Fishfry, do you not understand what "instance" means? Here, from OED, "an example or illustration of". How do you think that a specific colour, red, is an example or illustration of the concept of colour? Red cannot exemplify "colour", because all the other colours are absent from it. That's why we go from the more general to the more specific in the act of explaining. Referring to the more specific abstraction, "red" is an instance of "specifying", it is not an instance of "colour". — Metaphysician Undercover

Is an apple an instance of fruit? Apples don't have a peelable yellow skin. 'Splain me this point. By this logic, nothing could ever be a specific instance of anything, since specific things always differ in some particulars from other things in the same class.

How do you propose that this indicates that equal implies "same as"? — Metaphysician Undercover

Equal is the thing being formally defined or referenced from logic. "Same as" is a colloquial usage with no formal definition.

I cannot follow your association. What the head sophist calls "identity theory" is simply an axiom of identity which is inconsistent with the law of identity. The sophist dictates that "=" means identical to, and this is the first principle of the sophistry referred to as "identity theory". — Metaphysician Undercover

You demean only yourself and nobody else to continually refer to another member of this forum by a pejorative.