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God desires that we make our own choices and then we are shown that reality is still constructed in such a way that all this freedom and these choices intersect to serve his timing.


What are good introductory books for logic (classical and intuitionistic)? For category theory? Do you know any similar representation of paraconsistent logic?


For category theory, I like Spivak's books.

For logic, it really depends of what you are searching for, for classical logic you can read the the classics, for example Russell and Tarski.

For constructive logic I cannot think of a good introduction (besides mine ;) ), I personally picked it up from books about category theory and computer science.


I think the general program of categorical logic, the work of Lambek and Scott, and J. Bell on topos theory and local set theory really make clear the relationship between category theory and logic, as well as lambda calculus.

A topos is essentially a cartesian closed category with a subject classifier. In Set this is the two element set of 1/0 which is a Boolean algebra and thus the internal logic of the category Set is classical.

In general though the subobject classifier is a heyting algebra which expresses the semantics of intuitionistic logic.

There is also a very good, but introductory, book by Goldblatt on Topoi that covers this logical aspect

So in terms of logics the category of Sets is the exception.

By internal logic I mean that for every topos one builds up a theory using it's objects and function between them. An equivalence theorem (see J. Bell) states that a given topos is essentially equal to the category generated by this internal theory.

This program began with Lawvere who noticed that conjunction and implication were really adjoints, the same one as between the product and hom functors in a cartesian closed category.


At first sight, this looks like an absolutely great resource for a friendly introduction to this stuff. Thanks HN (and author).


Btw, the Catholic Church is not against birth control because it wants to fill up the planet with people.

The Church is obliged to teach that sex is supposed to be about a man and a woman taking part in God's ecstatic act of creation, a selfless act of love. Sex without being open to life is porn: without the act of self giving and preparedness to receive children, you are left with a corrupted, self-directed form of pleasure.

This is why the Church is not against quite effective natural methods like NFP, because in this method it's the people who change their own behaviour, based on a natural cycle. It's quite effective but does not close fertility in a mechanical way.

Second, if people were really listening to Jesus Christ and the Church, much more people would hear a calling to lead a consecrated life, as a priest or a monk or a nun.


> Sex without being open to life is porn: without the act of self giving and preparedness to receive children, you are left with a corrupted, self-directed form of pleasure.

Nope. I've had 3 kids. I have emotionally and rationally concluded that having another child is inappropriate; it is a form of excess and inbalance. So, I want to have sex for love now. Really, you are going to tell me that, by stopping at 3, I am going against the will of god?

Also, what's up with believing in a God-man that supposedly rules over 100 billion galaxies and yet is so damn petty about human sex lives and other foolishness? I'm all good with the importance of spiritual fulfilment, an underlying faith in an ineffable oneness of the cosmos, and even in the notion that belief in the eternal Logos gives eternal life (i.e., if i believe that my self is vastly bigger than my bodily identity, then "I" don't die with our body). It's comforting and rational.

But damn. Belief in a petty, spiteful God-man? How can people perpetuate such an idea? Just to scare children?


> But damn. Belief in a petty, spiteful God-man? How can people perpetuate such an idea? Just to scare children?

this is something i've always found hilarious. he's all-powerful, all-knowing, all-seeing. he created us, and now demands our love, adoration, and is jealous. is he lonely? is there nothing else to do in this universe except be concerned with how we live our lives? punish us with plagues? he gave us free will to then judge us in the end based on how restrained we were in exercising it?

it's silliness.


It's capriciousness. The god of the bible has all the psychological characteristics of man. The slogan is "God made man in His image." But the foundational documents show it is, yet again, another man-made deity. One of thousands man has created and disposed of.

Job is the best book though. God and Satan make a bet...


Religion has always been and will always be a very effective way to control the masses. It is much cheaper and easier than armies and bombs.

Can you get large groups of people to do stupid stuff like don't have sex before marriage, don't swear etc, by any method? The only way, is religion. We can read religious texts and take some good things from them, but following everything a religion (any religion) says blindly is just dumb. Most the time, religious texts are interpreted for convenience and petty agenda anyway, not necessarily for truth.

Reminds me of https://www.youtube.com/watch?v=8r-e2NDSTuE


We have evolved to remove God from religion but we still blindly follow pop-cultural leaders, politicians, appointed experts. Controlling people with mass media is easier than organized religion.


You're not going against the will of God by stopping at 3. Or by not having children at all.

But if you give contraception a fixed place in your life, to have sex which is fundamentally closed to children, then you have introduced a contradiction into your body and into your life.

And yes, He rules over 100 billion galaxies (more if we live in a multiverse) and cares about such things. If you think this is petty or spiteful, then you think too little of your sexuality and of yourself. These 100 billion galaxies were required for you to exist as a human being, called to (try) living a life that prepares you for Heaven.


> If you think this is petty or spiteful, then you think too little of your sexuality and of yourself.

No, i just expect more from the unifying principal of the universe. And so should anyone who wants real faith and not myths and fairytales.


No direct cable between US and Russia... e.g. linking up the Bering Strait. Anybody know the reason for this?


There’s not a lot of content to be exchanged between Siberia and Alaska. And running long stretches of fiber over land is actually more costly and subject to failure than under the sea, so going from Moscow -> Vladivostok (or something) over land, then going subsea, and then Alaska -> West-coast US over land, is not really beneficial.


Few people live there. Coincidentally that's why there's no bridge up there, either.


Cold war?


And that solution comes in many, many shades of gray. Picking the right shade is less obvious.


Not just incomplete but badly translated. Such as the warning against "vain repetition" in prayer in KJV Mt 6:7, targeting ancient Christian prayer practices like e.g. petition prayers and the Rosary (which are in direct continuation of old Jewish litanies, such as Psalm 136, and sanctioned by Heaven itself: "Sanctus Sanctus Sanctus"). "Battalogein" should refer to "babbling": using lots of grand words to impress God and other people, as opposed to the simple but dignified petition of a humble soul.


Working with coinduction. So that’s not a good definition :-)


Yes it's on a website on fashion, not a site focused on Christian spirituality :-)

In the text of the interview, it doesn't say "broke away from the Catholic Church" but "from the Catholic rule". Which is also a confusing phrasing in itself and probably the source of the error found in the abstract.


They would have said that they returned to the Rule of St. Benedict in its full rigor, no?


I personally find it highly likely that the decision mechanism emerges from physical computation in the brain.

However, when we talk about decision mechanisms, we inevitably introduce the question of whether this decision mechanism can work better or worse.

“Free will” may be seen as a computational notion of “health” for this decision mechanism, similar to how we use the term health for our physical bodies. A free will is a healthy will, in the sense that our decision mechanism is not broken by e.g. drugs, electrodes or mental illness.

Second, many people, myself included, hold the assumption that the ordering between options A and B is not purely subjective. If there exists an ordering of options which is objective and external to the agent of choice, then the choices that are actually made can be compared to that external ordering. Free will in this sense denotes the observation that our choices may reflect an ordering which is significantly different from the ordering imposed by reality. This is not a scientific claim and cannot be disproven scientifically. Holding this assumption is in fact a choice.


I personally find it highly likely that the decision mechanism emerges from physical computation in the brain.

I think it's more likely that the decision mechanism emerges from a race condition between multiple competing signals. We choose the one that arrives first, even if it takes time to be consciously aware of the choice.


> A free will is a healthy will, in the sense that our decision mechanism is not broken by e.g. drugs, electrodes or mental illness.

Isn't the drug example a contradiction? If my brain was healthy ("free") when I decided to take drugs, why would the resulting drugged state be less "free"? After all, it was my "free" choice to take the drugs and alter my mental state.

Edit: Also the definition of "mental illness" is somewhat nebulous and not historically fixed. Homosexuality was at one point called a mental illness.


Consider hypnotics used during light medical procedures to keep you awake but compliant. From a state of more freedom you can freely choose to enter a state of arguably less freedom. Why would this be a contradiction?

> Edit: Also the definition of "mental illness" is somewhat nebulous and not historically fixed. Homosexuality was at one point called a mental illness.

Yep, insights and definitions of illness will keep changing. But while insights in the details of e.g. psychosis may vary, few would deny a correlation with chemical issues.


Excellent to note that it is in fact not a scientific question. You know your epistemology:)


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