Logicians From The United States

"[P]rior to Newton, Galileo sought to specify the "intertial" motion of terrestrial objects—...the motion they would display if subject to no forces—and he concluded that such motion would be uniform circular motion. He arrived at this conclusion from his experimental work with inclined planes."

"I have never bumped into Tim Maudlin, but I have felt his gravitational tug. A Reddit discussion... called Maudlin "probably the most influential person in philosophy of physics." Someone chimed in that Maudlin... is "without a doubt an intellectual beast." Maudlin impresses even... Jim Holt... When I asked Holt "What’s your utopia?," he replied "arguing eternally about gauge theory" with Maudlin and a few other pals. ...Maudlin's ..."The Defeat of Reason"... ends by suggesting that we "shorten the dignified designation Homo sapiens to the pithier and more accurate Homo sap." Ouch."

"[N]o consensus... exists among physicists about how to understand quantum theory. There... is no precise, exact physical theory... Instead there is raging controversy. ...How can the manifest and overwhelming success ...be reconciled with complete uncertainty about what the theory claims about the nature of matter?"

"The Theory of Relativity is presented, first and foremost, as a theory of the geometry of space-time. Special Relativity is explained in enough detail to solve specific problems about the behavior of clocks and rigid objects in a relativistic world. General Relativity is presented less rigorously. My aim... make the conceptual foundations of these theories absolutely clear..."

"[M]ost clear philosophical ideas can be presented intuitively, shorn of the manifold qualifications, appendices and terminological innovations that grow like weeds in academic soil."

"The presentation of Bell's inequality needs no more than some algebra... Understanding Relativity also requires no more than algebraic manipulation... but would tax the patience of the average reader. So I have tried to present Relativity pictorially..."

"At its most fundamental level, physics tells us about what there is, about the categories of being. And modern physics tells us that what there is ain't nothing like what we thought there is."

"Quantum theory... formalism... uses no more than linear algebra and vector spaces. ...A particularly nice and accessible presentation of the requisite mathematics can be found in 's Quantum Mechanics and Experience (1992, Ch. 2)."

"Relativity is commonly taken to prohibit anything from traveling faster than light. ...[H]ow can the particles continue to display the... correlations..? The two pillars of modern physics seem to contradict one other."

"Perhaps the most vexing question confronting any study of Bell's inequality, and the experimental observation of violations of that... would never have been discovered if not for the existence of quantum formalism. On the other hand, the inequality... is derived without any mention of quantum theory and the violations are matters of plain experimental fact. So the explication and analysis of the importance of Bell's work can in principle proceed without mentioning quantum mechanics at all. Should an account of Bell's inequality emphasize its historical roots... or... sever those ties in the interest of clarity? ...I chose the second option ...the interpretation of quantum theory is troublesome enough ...to overshadow and confuse the relatively straightforward proof on non-locality."

"I have often felt that whatever is of value in this book could be found in Bell's "The Theory of Local Beables" (1987, Ch. 7)... this book will have served a great purpose if it does no more than encourage people to read Bell with the care and attention that he deserves."

"Fundamental conceptual changes occur, but they are always modifications of a previously existing structure. ...[T]actical adjustments are made in order to render the whole consistent. The ad hoc nature of this procedure may leave us with lingering doubts as to whether the whole really is consistent."

"Maudlin's book is likely to upset many physicists and metaphysicians, but in a positive, thought provoking way. Moreover, its plain presentation style makes it a good introductory book for students and non-specialists. In short, it is highly recommended for anybody interested in quantum theory, and especially in what "happens in between.""

"[S]pace and time... do not appear to our senses: they have no color or flavor or sound or smell or tangible shape. ...[They] seem rather to have is a geometrical structure."

"Non-locality appears at exactly the point where the "measurement problem" which infects standard quantum theory is resolved."

"Starting from what we understand and seeing clearly its inadequacies can provide a path to conceptual progress."

"[P]roblems about the fundamental consistency of our two fundamental physical theories may appear. ...It arises from the remarkable results derived by John Stewart Bell in 1964 ...[C]ertain pairs of particles that are governed by quantum laws... appear to remain "connected" or "in communication" no matter how distantly separated... [T]he connection exists even when the observations carried out occupy positions... which cannot be connected by light rays. The particles communicate faster than light."

"If one resolves the measurement problem by postulating additional variables beside the wave function, it is the dynamics of these variables which manifests the non-locality and which resists a fully Relativistic formulation."

"If one resolves the measurement problem by allowing a real physical process of wave collapse, it is the collapse dynamics which manifests the non-locality, and which resists the fully Relativistic formulation."

"To argue that people need faith is to abandon hope, and to condescend and accuse the faithful of being incapable of understanding the importance of reason and rationality. There are better and worse ways to come to terms with death, to find strength during times of crisis, to make meaning and purpose in our lives, to interpret our sense of awe and wonder, and to contribute to human well-being— and the faithful are completely capable of understanding and achieving this."

"A criticism of an idea is not the same as a criticism of a person. [...] Ideas don't deserve dignity; people deserve dignity."

"Give faith-based justifications no countenance. [...] Let the utterer know that faith is not an acceptable basis from which to draw a conclusion that can be relied upon."

"The thrust of our message must be that there are things we don't know and it's okay not to know— even in death. Not claiming to know something you don't know isn't a character flaw, it is a virtue."

"I'm worried about 33 trillion in debt. [...] I'm worried about the fact that one third of the taxes collected last year went to pay the interest on the debt. I'm worried that nobody really gives a hoot about it. I'm worried about the national divorce talk. I'm worried about wide-scale ideological capture of our institutions, particularly legacy media and legacy institutions. I'm worried about the geopolitical situation. [...] I'm worried about the Israeli Palestinian problem [...]. I'm worried about Chinese militarization of Taiwan, the semiconductor industry. I'm not worried about rogue [artificial intelligence] [...], but I'm worried that we have lost an understanding of what makes America great. [...] I'm worried that we have forgotten why freedom matters, why it's important, that's what I'm worried about. And unless we start to care about those things then we can't reconstruct reason; we can't reconstruct a civil society."

"Faith taints or at worst removes our curiosity about the world, what we should value, and what type of life we should lead. [...] Faith immutably alters the starting conditions for inquiry by uprooting a hunger to know and sowing a warrantless confidence."

"Inquiry and wonder must replace dogmatism and certainty. The long-term goal is to create conditions that turn the dispositions of inquiring and wondering into culturally trumpeted values."

"Don't complain, apologize, or mumble in the defense of reason. [...] Tell people exactly what you think and why you think it."

"[About what to do to counter hypocrisy in academia:] The first order of business, if a stream is being polluted, you have to stop the pollution at the source. The wrong way to think about it is 'Let's clean up the stream.' The right way to think about it is 'Let's stop polluting the stream.' You have to stop donating to your alma mater. First order of business. [...] This should be the easiest ask on planet Earth. [...] Give it to anybody, but don't give it to university. Because when you give it to your university, you're supporting an indoctrination mill, you're supporting an institution whose very values are antithetical to Western liberal democracy, so you have to stop."

"[About homelessness:] Some people on the far left don't want that problem solved because they look at the manifestation of homelessness as indicative of a problem with the system. And as long as we can keep homelessness there, we can see that the system is corrupt and then we can incentivize people to rip down the system because we want social justice. [...] We want to remediate these larger economic problems that we know the source of these are the capitalist structure."

"Most basic elements of civil discussion, especially over matters of substantive disagreement, come down to a single theme: making the other person in a conversation a partner, not an adversary. To accomplish this, you need to understand what you want from the conversation, make charitable assumptions about others' intentions, listen, and seek back-and-forth interaction (as opposed to delivering a message)."

"Peter Boghossian's techniques of friendly persuasion are not mine, and maybe I'd be more effective if they were. They are undoubtedly very persuasive — and very much needed."

"When your conversation partner is getting angry, the single best thing you can do in most circumstances is to stop whatever else you're doing and listen. It's very difficult to remain angry with someone who is patiently and earnestly listening, and if you break the cycle of frustrating dialogue early by switching to listening and learning, you can halt a great deal of your partner's mounting anger before it starts."

"Seemingly impossible conversations typically have one thing in common: they're about moral beliefs rooted in one's sense of identity, but they play out on the level of facts (or assertions, name-calling, grandstanding, threats, etc.). [...] The most difficult conversations, then, masquerade as discussions about something other than morality, but they are actually about what qualities, beliefs, attitudes, and behaviors individuals believe make them good people or bad people and why it is important to hold the right views among those."

"Know when to walk away, even when the conversation is going well. Putting pressure on your partner to continue a discussion beyond their comfort level shuts down listening, encourages defensiveness, and turns the conversation into a frustrated rehearsal of why one of you is correct and the other dense."

"What it means to hold a belief based on evidence is, by definition, that one is open to the possibility that evidence might be discovered that would change one's mind. If no evidence would change one's mind, then one is not forming one's beliefs on the basis of evidence."

"The most difficult thing to accept for people who work hard at forming their beliefs on the basis of evidence is that not everyone forms their beliefs in that way. [...] Many people believe what and how they do precisely because they do not formulate their beliefs on the basis of evidence-- not because they're lacking evidence."

"Here's a heresy: "How do you know that?" is a powerful question for helping people think, but it's not the best question. The best question is, "How could that belief be wrong?""

"Notices: Can you tell me your memories of Julia Robinson, what she was like as a person? Davis: Very nice, very straightforward. Broad in her interests, mathematical and otherwise. And great power—there is no question in my mind that she was a much more powerful mathematician than I. We worked together on a problem on which we didn’t get anywhere. We were trying to prove the unsolvability of the decision problem for word equations. It turned out that we wouldn’t have been able to do that because the problem is solvable. Makanin solved it positively."

"In Julia Robinson we find a mathematician who was a heroine in her own time and a role model for all time. It is a story of childhood, illness, love, marriage, disappointment, obsession, and triumph."

"And I continued to struggle with the Tenth Problem. In 1961 Martin Davis, Hilary Putnam, and I published a joint paper, "The undecidability of exponential diophantine equations," which used ideas from the papers Martin and I had presented at the International Congress along with various new results. The paper contains what is sometimes referred to as the Robinson hypothesis (or, as Martin calls it, "J.R.") to the effect that if there were some diophantine relation that grew faster than an exponential but not too terribly fast—less than some function could be expressed in exponentials—then we would be able to define exponentiation. It would follow from the definition that exponential diophantine equations would be equivalent to diophantine equations and that, therefore, the solution to Hilbert's tenth problem would be negative. At the time many people told Martin that this approach was misguided, to say the least. They were more polite to me."

"In this paper, we shall show the validity of an iterative procedure suggested by George W. Brown ... This method corresponds to each player choosing in turn the best pure strategy against the accumulated mixed strategy of his opponent up to then."

"We say a mathematical theory is decidable if there is an effective method of determining the validity of each statement of the theory. If there is no such method, the theory is undecidable. It is clear that if there is a mechanical way of transforming each statement of an undecidable theory into an equivalent statement of another theory, the second theory is also undecidable. This principle, together with the fact that the arithmetic of natural numbers is undecidable, enables us to solve the decision problem for fields of finite degree over the rationals."

"A partially computable function may be thought of as one for which we possess an algorithm which enables us to compute its value for elements of its domain, but which will have us computing forever in attempting to obtain a functional value for an element not in its domain, without ever assuring us that no value is forthcoming. In other words, when an answer is forthcoming, the algorithm provides it; when no answer is forthcoming, the algorithm has one spend an infinite amount of time in a vain search for an answer."

"Nonstandard analysis is a technique rather a subject. Aside from theorems that tell us that nonstandard notions are equivalent to corresponding standard notions, all the results we obtain can be proved by standard methods. Therefore, the subject can only be claimed to be of importance insofar as it leads to simpler, more accessible expositions, or (more important) to mathematical discoveries."

"Takeuti has studied models of axiomatic set theory in which the “truth values” are elements of a complete Boolean algebra of projections on closed subspaces of a Hilbert space, and has found that the real numbers of such a model can be taken to be self-adjoint operators which can be resolved in terms of projections belonging to the Boolean algebra. It is suggested that this is the mathematical source of the replacement of real quantities by operators in quantizing a classical description, and that quantum theory involves a relativity principle with Takeuti's Boolean algebras serving as reference “frames.”"

"The analysis of algorithmic process that emerged from the work of Gödel, Church, Turing, and Post has been of great importance not only for theoretical investigations but also for practice, by providing an expansive framework for computer science. The discussion of computation-like processes that transcend the limits imposed by the Church–Turing thesis can likewise be framed either in terms of theory or of practice."

"Davis became one of the earliest computer programmers when he began programming on the ORDVAC computer at the University of Illinois in the early 1950s. His book Computability and Unsolvability ... first appeared in 1958 and has become a classic in theoretical computer science."

"My sense, in bringing to art the double criteria of meaning and embodiment, is to bring to art a connection with cognizance: to what is possible and, to the faithful, to the actual. Gregory the Great spoke of the carved capitals in the Romanesque basilica as the Bible of the Illiterate: they show what the Bible tells us took place. They tell the uneducated what they are supposed to know. That is, they tell them what they are to believe as true. Beauty has nothing to do with it, though the capable carver presents the Queen of Sheba as the great beauty she was. It is possible that she looked that way. But it can be art without being beautiful at all. Beauty was an eighteenth century value."

"It struck me only recently that nineteenth century painters must have believed that visual truth was defined by photography, however alien to human vision what the camera reproduced often was. A good example of this would have been Eadweard Muybridge’s photographs of horses in motion. Painters decided that Muybridge’s images showed what horses really look like when they run, and in effect copied Muybridge’s photographs in their paintings of horses, even though that is not at all the way we see horses when they run. We really don’t see animals move the way Muybridge shows them moving, or else there would have been no need for the photographs in the first place: Muybridge hit upon his awkward but seemingly authoritative experiments that were really designed to answer such questions as whether all four of a horse’s hooves ever touch the ground at the same time—in other words, phenomena the human eye could not perceive."

"The great thing about the sixties was the dawning recognition that anything could be a work of art, which was something evident in all the main movements of the time—in Pop art, Minimalism, Fluxus, Conceptual art, and so on. What accounted for the difference? The big mantra in the art world was Frank Stella’s sullen “What you see is what you see.” But there was not a lot of difference between what you see when you see a Brillo Box by Warhol and the Brillo boxes designed by James Harvey for the Brillo people to use for moving their products about. So: why weren’t they artworks if Andy’s Factory-produced boxes were? I have answered this in my first chapter, so what I want to do now instead is to marvel at the way in which the camera helped give form to the philosophical question that had been kicking around for a few millennia, “What is art?,” and to explain why the photography-painting paragone had to be the last paragone. By the time Duchamp and Warhol had left the scene, everything in the concept of art had been changed. We had entered the second phase in the history of art, broadly considered."