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Luca Incurvati’s Conceptions of Set, 12

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We turn then to Chapter 6 of Luca’s book, ‘The Stratified Conception’. This chapter starts with a brief discussion of Russell’s aborted ‘zigzag’ theory, which tries to modify naive comprehension by requiring that it applies only to sufficiently “simple” properties (or rather, simple propositional functions). It seems that Russell thought of the required simplicity as being reflected in a certain syntactic simplicity in expressions for the relevant properties. But he never arrived at a settled view about how this could be spelt out. It is only later that we get a developed set theory which depends on the comprehension principle being constrained by a syntactic condition. In Quine’s NF, the objects which satisfy a predicate A form a set just when A is stratifiable — when we can assign indices to its (bound) variables so that the resulting A* would be a correctly formed wff of simple type theory. And so the rest of Chapter 6 largely concerns NF. Luca also touches on NFU, the version of Quine’s theory which allows urelemente. And — though this is a matter of emphasis — I’m was a bit surprised that the main focus here isn’t more consistently on this version. At the beginning of the book, Luca seems to hold that the most natural form of a set theory should allow for individuals: thus he describes the iterative conception (for example) as being of a universe which starts with individuals, and then builds up a hierarchy of sets from them. And if, when considering its technical development, we then concentrate on an iterative set theory without individuals, that’s because of easy equi-consistency results: adding urelements to ZFC’s theory of pure sets doesn’t change the scene in a deep way, so for many purposes it just doesn’t matter whether we discuss ZFC or ZFCU. But, famously, it isn’t like this with NF vs NFU. The consistency status of NF is still moot (Randall Holmes claims a proof, but its degree of opacity remains extremely high), and NF is. . .

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News source: Logic Matters

Ask Yourself This Question Every Day

Jim Kwik is the type of person I typically would steer away from. He appears to have created an industry around, well, himself. As a self-styled learning expert, he focuses on self-helpish type activities such as speed reading, memorization techniques, and enhancing “brain performance.” He sells t-shirts that sport fake college logos and has photos of himself with famous people on his web page. Not exactly my jam. In fact, I like to read slowly for pleasure and couldn’t care less about hanging around with people that are known for being well known. But I listened to an interview with him on a podcast and he does have some damn good ideas.

One of those ideas is a method for helping focus the mind on things that prevent us from moving forward on goals we want to accomplish. We all have those things that we work at for months or years that never seem to move forward. While we typically tend to think about our goals in terms of the specifics about what we want to accomplish, we may not spend the time thinking about why we haven’t been able to accomplish them — at least not in a clear way that can help us move forward.

Kwik’s idea is that there probably is an overarching psychological block that not only is impacting your ability to reach your goals but affecting all other parts of your life and health. So he suggests that we spend time thinking about that one question that will isolate that issue and we should ask ourselves that question every day perhaps multiple times a day when we noticed that we can’t make progress on something. The essence of the question as I’m framing it is this:

What is the one thing that dominates my mind when I need to act?

The question should be framed as “Why do I . . .?” or “Why am I . . .?” or “Why don’t I . . .” The idea is that you frame the question broadly to isolate a mindset and not specifically to get at why you didn’t do this or that one thing.

I did this little experiment and it was very enlightening. The question I came up with is “Why do I fear so much?” Now that’s not a very well-worded question. Asking “Why am I afraid?” is better grammatically. But I want to use the term “fear” because it captures more of the emotional state I believe I’m feeling in a variety of situations. As I thought about it, I realized that I tend not to do a whole host of things because I have fear of the outcome. I fear I’ll fail. I fear I won’t be liked. I fear I’ll offend someone. I fear the outcome won’t be what I want. I fear the future.

I was raised in a fairly toxic home environment where absolute authority, whether it be parental or divine, was the reason most things should be done. Duty and obedience where the operating model for behavior. And fear was the mechanism of obedience. If you don’t do X, bad things will happen. So I learned day in and day out that I must follow the rules or be punished or get a verbal undressing or upset a parent (or God). Fear became my default emotional state. That became a dominate “meta-narrative” that has been a part of me my entire adult life.

Over the past few days, as I’ve focused on things I need or want to do but don’t do them, I’ve begun to notice that my stomach tightens up on regular basis when I think about relationships, or about a task I have to do at work, or about writing, or about what book to read. I’ve noticed that when I have to make certain decisions, I hesitate and spend way too much time thinking through all the options. I notice that I’ll hesitate to reach out to a friend or fail to send an email I need to send or don’t make a purchase I thought I had decided to make. As I’ve started noticing these things, I ask myself the question and have realized that fear is at the root of all it.

I’ve also noticed that when I attempt to answer the question, the answers aren’t really substantial. The thing I fear really isn’t worth worrying about. So what if I get rejected? So what if I don’t get the best price? Who cares if that person gets upset because I asked them to do something? Of course I want to be genuine and kind in my interactions. I want to do some research to find a good price. I need to make sure I’m doing the things that let me sleep well at night before I act. But once I’ve done those things, don’t fear the outcome. The answer to the question of why I fear typically doesn’t have a good answer and so I shouldn’t fear.

I’ve tried to embrace the Socratic Method in my intellectual life and ask more questions and make fewer statements. Kwik’s suggestion is to make yourself both Socrates and Glaucon, both the questioner and the one who provides the reply.

What is your one question?

The Powers Metaphysic

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2020.05.12 : View this Review Online | View Recent NDPR Reviews Neil E. Williams, The Powers Metaphysic, Oxford University Press, 2019, 256pp., $70.00 (hbk), ISBN 9780198833574. Reviewed by Anna Marmodoro, Durham University What does Neil E. Williams' new book add to the on-going (and fast-going!) development of metaphysics of powers, on which so much has been written already? Among the most novel and attractive features of Williams' work is its earnest engagement in the project of understanding what the opponents -- the neo-Humeans -- hold. Rarely do those who are in one camp invest effort in giving a fair presentation of opposing camps; whilst Williams devotes two of his ten chapters to clarify what is at stake in the debate between 'friends' and 'enemies' of powers in terms of their respective worldviews. Further, and in the same vein, Williams devotes a chapter to discussing the most well-known objections to powers, the virtus dormitiva objection. Even... Read More

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News source: Notre Dame Philosophical Reviews // News

Guest post: Thomas Forster on Conceptions of Set and motivating NF

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The next chapter of Conceptions of Set discusses set theories like NF that modify naive comprehension by imposing a stratification condition. My friend Thomas Forster, NF-iste extraordinaire, has been looking at some of Luca’s book too, and dropped me this note, which I thought it would be good to share here. The usual on dit about stratification is that it has no semantics. This is the kind of thing people go around saying. And, as Luca points out, it simply isn’t true. There is this theorem of mine (building on work of Petry and Henson) that says that the stratifiable formulae are precisely those that are invariant under Rieger-Bernays permutations. I’m pretty sure that Dana Scott knew this result ages ago but didn’t feel the need to write it out. Henson must have known it too. I wrote it up and published it because it seemed to me that it mattered and that it should be brought out into the open. And that the on dit needed to be knocked on the head. Here is another way of making the same point. There is the di Giorgi picture of (structures for the language of) set theory. A structure for the language of set theory is a set equipped with an injection into its power set (after all, a structure for the language of set theory is a set with an extensional relation on it, and an extensional relation on X is an injection from X into its power set [see my Logic, Induction and Sets, esp. §8.1]). We can think of this picture as each member of the set “coding” a subset of the set. Now Cantor’s theorem tells us that no such injection can be surjective. So some subsets must be left uncoded. So, in constructing a structure for the language of set theory, one has two steps to take. (i) One decides which sets are to be left out, and then (ii) one decides which surviving sets are to be coded by which elements. Natural question Q: which sentences have their truth-values already determined by stage (i)? That is, what sentences have the feature that their truth-values are. . .

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News source: Logic Matters

Finding Pleasure in Addiction

I heard a quote a couple of days ago that has stuck in my head and incessantly keeps repeating in my mind. It is this simple phrase:

Addiction is a progressive narrowing of the things that bring you pleasure.

It was stated by Dr. Andrew Huberman, a Stanford neuroscientist. It hit me between the eyes and I can’t stop thinking about it. It struck me because I’ve noticed over the past few years that I’m finding less pleasure in a variety of things that formerly may have energized me and immense pleasure in a few activities and people. The problem has become that when I’m not doing those things or with those people, I experience a sense of dread—sometimes mild, sometimes pronounced—because what I’ve come to label as the mundane simply don't do it for me anymore. In other words, I’m experiencing the narrowing that Huberman talks about.

As I’ve gotten older, I’ve noticed that I’ve also gotten more particular. I have far less tolerance for bullshit or inane conversation so the people I enjoy hanging out with has been narrowing. I can’t stand the nonsense on social media so I generally stay off of it. I find a lot of the news media manipulative, hyperbolic, and much of the time, just dishonest so I don’t read or listen to it. I pick up a popular book and find it superficial or repetitive against everything else I’ve read so I read a couple of chapters and set it down. I even find the attempts to be creative tedious because I continually remind myself how many past attempts to produce something I’m proud of have failed.

As this list gets longer over time, I find myself gravitating to the much shorter list of things I actually do enjoy. Those few friends that challenge me. Travel to places I love or have never been. That rare book that opens up dark corners in my intellectual and emotional life. In a way, I’ve become addicted to these things and that addiction has progressively narrowed my ability to find pleasure in everything else.

In a very real sense, this is a disease of getting older. When I was a young man I couldn’t figure out why a lot of older people I met seemed so grouchy and intolerant. I’m realizing that as people age (or, let’s say charitably, become more mature), many just start selectively filtering what they’ll allow in their lives and they have come to appreciate and focus on the things that bring them happiness. They’ve learned, either intentionally or subconsciously, to say no to everything else. If not managed this can turn into intolerance and rigidity. And, what the Huberman quote brought to the surface is that it can be a kind of addiction.

So perhaps the key is to learn to selectively filter but also to find small pleasures in anything you decide to spend time on and, perhaps most importantly, open yourself up to new things—create a progressive expansion of the things that might bring you pleasure. In thinking about the Huberman phrase this week, I came to appreciate the selective filtering that aging and maturity has brought. But I also realized that I’m leaving a lot on the table if I don’t allow myself to find pleasure in dozens of other ways that I may not have experienced yet.

I’ve become addicted to the things I love. But perhaps there or more addictions I haven’t yet found. Between the two is, perhaps, the sweet spot.

Victor Gorshkov (1935-2019): a life for the biosphere.

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The basic concept of the biotic regulation of Earth's temperature according to Gorshkov et al, 2002. The figure shows the potential function U(T) for the global mean surface temperature. Stable states correspond to pits, unstable states to hills. The modern value of +15°C (288 K) corresponds to an unstable state (2, thin line). Physically stable states correspond to a frozen Earth (state 1) and a red-hot Earth (state 3). We are precariously living in a shallow minimum of potential energy that defines the habitable zone for the biosphere. This state can be created and maintained only by a healthy biosphere. On May 10th, 2019, Victor Georgievic Gorshkov died at 83 in St. Petersburg, after a life dedicated to scientific research that he continued to perform up to nearly the last moment. One year later, I thought I could publish this small homage to his figure and his work. His longtime coworker and companion, Anastassia Makarieva, was also kind enough to write a summary of Gorshkov's life and work for this blog. In many ways, science follows the 20/80 rule, sometimes called the "Pareto's rule," which tells that 80% of the work is performed by just 20% of the performers. But it may well be that Pareto was an optimist if his rule is applied to science. It seems more likely that science works because, as Newton said long ago, a small number of creative "giants" emerge out of the general mediocrity. One of these creative people, a true giant of science, was Victor Gorshkov (1935-2019), researcher at the Petersburg Nuclear Physics Institute, in Russia.Understanding Gorshkov's work and ideas takes some time and patience. He was trained as a theoretical physicist and his approach was very different from the way most western scientists operate in the field of ecology. I would say that it was exactly this difference that attracted me and made me tackle the non-trivial effort to read one of two main books: Biotic Regulation of the Environment, 2000.  (see also. . .

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News source: Cassandra's Legacy

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