do you agree that the judgement of whether or not an argument constitutes a proof is dependent on that argument being understood? — Metaphysician Undercover

It depends on what one means by 'understood'. There are proofs that I have followed step by step, and validated each step, yet I am still unable to visualise the big picture, as to why the proof works. There is a formal understanding but not an intuitive one and it is the latter that is ultimately most important to me. So I would say that there are proofs that I have verified to be valid even though I do not really understand them. But in such cases I have suffiicient understanding to recognise that my failure to fully understand the proof is a deficiency in my cognitive capabilities rather than a deficiency in the proof.

I suppose that's a 'No' then. One can judge that something is a proof without understanding it.

Perhaps a helpful parallel is a chess game. One can look at the moves in a Fischer vs Spassky game and verify that Fischer did indeed do a sequence of legal moves that resulted in Spassky being in an unwinnable position. But that is not the same as understanding the strategy by which Fischer achieved that.

Will you inform the Nobel Prize Committee? — tom

Your mistake is in mathematics, not in physics, so if you want to invoke a committee, it would be for something like the Fields medal, not the Nobel prize.

fishfry is correct

Are you going to tell me that hearing a disagreeable joke was not part of the scenario of potential victims which you had in mind? — Sapientia

I am going to tell you that any offence they took from the joke is not the harm to which the para refers. It is the subsequent loss of their job when they adopt the practice of offensive 'banter' themselves. I presume you would agree that loss of one's job is generally a greater harm than being offended by a joke. There is nothing pedantic about this. The criticism was based on a complete failure to comprehend what the paragraph said.

'Better to be Socrates dissatisfied than a pig satisfied', eh? I am more sympathetic to Bentham's view (to which I expect Mill was responding): 'Push-pin is as good as poetry' (even though personally I would prefer poetry).

You do not believe that the alleged authority is really an authority, you have no faith in that proposition, so you dismiss the endeavor as a waste of time. — Metaphysician Undercover

I do not, and would not dismiss it in that way without qualification.

I am confident that reading Aristotle would be a waste of my time. It sounds like you have found it an enriching experience, so it was not a waste of your time, nor of that of any other enthusiastic Aristotelian. If his writings on metaphysics bring joy to some people, and they do not induce them to harm others, then that is a good thing (IMHO).

I would not use the word 'ostensive' to describe learning a meaning by reading long texts. Ostension is pointing to a dog and saying 'dog', jumping and saying 'jump' or making a sad face and saying 'sad'.

But even my sort of ostension is prone to error. It's possible that I've got the wrong idea of what other people mean by 'dog' and our success in communicating about dogs thus far has been a happy coincidence of the fact that the animals we were talking about lay in the intersection between my understanding of dog and yours.

My understanding of language use is mostly WIttgensteinian, so I see my use of 'dog' or 'potential' as elements of a language game that often, but not always, works in everyday life. But it all falls apart as soon as we move away from everyday life into metaphysics.

I don't know what Aristotle would have made of Wittgenstein but my guess is that he'd have been appalled, since describing categories of objects as simply moves in a language game is like the antithesis of believing that a category has an essence.

It sounds like becoming an Aristotelian involves a process of initiation into a new language game, that involves a lot of reading. I am not inclined to do that because, while that language game may be fun (Feser certainly seems to enjoy it), it doesn't seem to lead anywhere.

As a wise member of the previous forum once said:

"Fancy piles of words cannot oblige the universe to be thus and so'

(or something like that).

I understand the point you're making with the rest of your post, but calling someone a victim because they might have heard a disagreeable joke is taking the victim card way, way too far. — Marchesk

I agree, and if you read the paragraph carefully, you'll see that that's not what it says.

Since the level-1 spheres overlap, they're all points in the beginning, and all the same point at that, else they'd not overlap.

I haven't gone through this idea carefully, but I'm moderately confident there is no 'reasonable' mathematical model in which a spatially infinite universe contains a time zero. If that's correct then there is no question of whether the universe was infinite or a single point at that time, since there is no such time.

We can create a model in which the spacetime contains all times after time zero but does not contain time zero itself. The earlier the time (The smaller its time coordinate), the greater the universe density becomes, so that it increases without limit as t approaches zero. If the universe is spatially infinite now, it will be spatially infinite at all those times too, no matter how small t is.

When I say 'no reasonable model' I mean that a model that included time zero would have to be discontinuous in most significant respects at that time, in which case there's really no point in including time zero in the model since it would have no causal connection with the rest of the spacetime.

These problems do not arise with a spatially finite universe.

In practice, we don't need to worry about a time zero for either a spatially finite or a spatially infinite universe, because the General Theory of Relativity, which is used to do the backwards projection, loses validity as the scale becomes very small, and we have no theory to replace it. We can't use quantum mechanics because it ignores gravitational effects and in a very dense universe those cannot be ignored.

TJO the human reaction to dramatic landscapes - which we distinguish from beautiful, peaceful ones - is generally filed under the category of the 'Sublime'. There has been much written about this in aesthetics. It is contrasted with beauty, because the sublime is associated with things that can be frightening - eg dark, craggy, dangerous looking mountains or ferocious seas.

One of the most influential writings on this was by Edmund Burke. I haven't read it, but there is an episode of the Partially Examined Life podcast where they discuss it here.

Sublimity and its partly opposite twin Beauty were much discussed in the 18th century. I'm pretty sure Kant wrote about it in his Critique of Judgement. Turner's oil paintings of stormy seas are a classic instance of trying to capture the sublime. But of course nothing can reproduce the full feeling of being physically in the landscape.

When I saw the title of your thread, for some reason, my mind turned to the fantasy landscapes painted by Roger Dean in the seventies, appearing in some cases as cover designs for albums of the band Yes, but also being popular as posters on the walls of teenagers and college students. They are not real landscapes, but I do wonder whether they appealed because they catered to people's fascination with the strange, the awe-inspiring and the unknown.

What does a spiritual disposition entail for you?

A fuzzy, shifting melange of Vedanta, Buddhism and pan-psychism. I try to meditate but am hopeless at it. I am better at chanting, which I find quite helpful. I also sing in more than one choir, which I find spiritual in a way that is probably only comprehensible to people that have experienced singing in an enthusiastic choir.

Love without condition, "love, no matter what", in theory, is very romantic.
....
How this severity of the cost of Unconditional Love can obtain without a spiritual context is completely lost on me.

I didn't mean Eros. Erotic love is absolutely rife with conditions. I think the most common manifestation of something approaching unconditional love is that of a parent for a child (not all parents though). And yes, it can be brutal, especially when the child chooses a path that is self-destructive, or becomes hostile to the parent.

Well I think I have a spiritual disposition (although there are some on here who believe I am an unreconstructed reductionist, despite my protests to the contrary), so it's hard for me to comment on what it would be like for someone without one. But I don't see why a non-spiritual person couldn't subscribe to the 'love is unconditional' notion. Isn't it part of the notion of agape that it involves an unconditional concern for the welfare of the other?

and a little Eckhart

Tolle, or Meister?

So what's the point of doing good on earth if we all are saved without even needing to try and live moral lives?

Because most of us care about others. Morality has nothing to do with 'earning salvation' unless one belongs to a handful of particular religions.

The set of possible outcomes from an infinite sequence of coin tosses is uncountable. It has a natural one-to-one correspondence with the real numbers in the interval [0,1], via their binary representation, where a Head (Tail) on the n-th toss is interpreted as a 1 (0) in the n-th position after the dot (comma for Europeans). An infinite sequence of pure Heads (Tails) maps to 1 (0) - the upper (lower) bound of the interval.

I think that mathematically, a coin cannot come up tails forever. There cannot not be a dup Earth given infinite space. The probability of that is 0.000... which is zero.

In an infinite sample space, Probability zero is not the same as Impossible. The term 'almost surely' was invented to cover exactly this case. It is applied to an event that is in the sample space (ie 'possible') but has zero probability.

With the usual binomial model of fair coin tossing, the event of an infinite sequence of heads is one that 'almost surely' will not occur, which is not the same as saying it cannot occur.

We can be tempted to apply this to an infinite universe and say it will Almost Surely contain duplicate Earths. To do that we need to first assume and specify a probability distribution for the configuration of mass-energy across the universe. I imagine that can be done, but it's too long to get into in this post.

I can think of two different uses of 'fact'. In both cases its use is to make an important distinction, but they are different distinctions.

case 1: Fact vs Opinion
When we say something is a fact with this intent, we are asserting that it is an objective feature of the world, not a subjective matter of opinion. In everyday life this distinction generally works well, and Fact is taken to mean 'a proposition to which almost any [say 99% of...] mature, sane, reasonably intelligent person observing this phenomenon would assent'.

When we try to carry that notion into philosophy we immediately run into trouble, because of dream hypotheses and uncertainty about the existence or meaning of a mind-independent world.

case 2: Fact vs Deduction
Here we take facts as readily observable propositions, and we distinguish those from a deduction made from those facts. For instance, it was a fact that Doctor Watson had a limp and a sun tan (I'm not sure of the 'military bearing' though - that sounds a bit subjective to me), but it was a deduction that he had recently been in Afghanistan.

Love is unconditional. A loving parent gives their child what is necessary for their flourishing, without conditions. If God is Love, and Salvation is a flourishing state, she will give it to every one of her children, without imposing conditions.

An easier response is to note that it is your friend that is making the positive claim, so the onus is on him to prove it. There is no obligation on you to provide any evidence to the contrary. You just need to challenge him by saying 'that doesn't sound very plausible to me. What argument do you have to support your claim?'

FWIW, the claim sounds implausible to me.

This doesn't save you in any way. — Agustino

Goodness me, do I need saving? From what? My original sin perhaps? Oh dear. Or am I to be punished by a posse of Aristotelians, for having the unmitigated temerity to decline to adopt their worldview?

I'm afraid I don't understand the assertions and questions in your post. Perhaps they mean something to Aristotelians.

This seems to contradict what you were saying earlier, that reasoning requires exact, objective definitions. — Metaphysician Undercover

What is required is that any defined terms used in the proof have exact, objective definitions. However it is not mandatory to use any defined terms. One can write a proof without any defined terms, in which case no definitions are needed.

There can be a grey area in that axioms that refer to a particular item in the Domain of Discourse may in some circumstances be considered as in a sense constituting a 'definition' of that item. For instance, the axioms that refer to the item '0' in Peano Arithmetic might be interpreted as constituting a definition of '0'. But there are various complexities about that, which I think it would not be fruitful to delve into now, as I don't think they relate to the topic under discussion.

So it appears to be as I stated, you would produce your definitions according to what is useful to prove your point. — Metaphysician Undercover

A definition can't enable or disable the proof of a point of any interest, as any proof that uses the defined term can be converted to one that doesn't by simply replacing every instance of the defined term by that which it is defined to mean.

For instance, if I have a proof about bachelors, and I have defined bachelor to mean 'Live, adult, male human that has never married', I can change the proof to one that does not use the defined term, simply by replacing the term by those italicised words, wherever it occurs.

The purpose of a definition is to enable one to write shorter, more intuitive proofs. Semantically, introducing or removing a definition cannot change the provability of anything.

A useful definition is one that shortens a proof or attempted proof in a way that makes it easier to find a way through the logical maze.

I believe that it is very important to argue over definitions. — Metaphysician Undercover

Maybe that's another key A vs non-A difference. My non-A position is that there's no such thing as a correct or incorrect definition. For a non-A the worth of a definition is determined solely by its usefulness and clarity.

I'd be interested to hear what other Aristotelians think about the importance of arguing over definitions.

You simply redefine "proof" in such a way that the A's proof does not qualify as proof under you restrictive definition of proof. — Metaphysician Undercover

That difference in standard of proof is part of the divide. It appears that the As and non-As differ in that respect. There's no point in arguing over definitions. I expect we can at least agree on the following statements.

1. The OP would be considered by an A to be a proof.
2. The OP would not be considered by a non-A to be a proof.

From a quantum mechanical viewpoint, nothing always happens. The most we can say is that the probability of it not happening is negligible. But we can still work with that.

Is the following a fair rendition of your concept of 'is directed towards'.

We say that an object of category C1 (e.g. a match) is 'directed towards' phenomena of category C2 (e.g. ignition) if there exists a set of conditions S that include at least one condition relating to an object of class C1, such that our current scientific theories predict that, whenever conditions S are satisfied, an event of class C2 will occur with probability p, where p is very close to 1 [we would need to specify an exact value to complete the definition. Let's say 0.99999].

Why will it occur if certain conditions are met? — Agustino

There will be a straightforward explanation involving physics and chemistry and the interactions of particles of certain types. I'm afraid this is getting beyond my area of expertise. I haven't done any Chemistry since high school.

What I do know is that, if one is not an A, there is no need to use the concept of being 'directed towards' in the explanation, which is just as well, because I don't know what that concept means.

I was asking why does it always and consistently catch fire in that particular set of circumstances? — Agustino

Every particular set of circumstances happens only once. Each match strike is different. There is no 'always and consistently' to explain. For a particular strike, current scientific theories predict that, If certain conditions are met, ignition will almost certainly occur.

I'm still not seeing the A-connection.

I don't understand the relevance to A vs non-A. An explanation for the match lighting up is that heat arises from friction between the match and the match box. The friction is particularly high because of the roughened match tip and matchbox side. The match is coated with material that has a combustion point lower than the temp generated by the friction, so the material ignites. None of this requires adopting an A worldview.

Plus, being a pedant (sorry) I'd probably correct the child's use of 'always' and point out that sometimes it doesn't catch fire, and there can be various reasons why that happens (e.g. strike speed too slow, combustible material layer too thin, matchbox side worn smooth).

The Aristotelian notions are signposts which signal to some relevant aspects of reality. — Agustino

It goes straight back to the A vs non-A divide. The As believe that reality has those aspects and that they have objective meanings, and the non-As do not. The As have no proof of their view, and the non-As have no proof of theirs. It comes down to core beliefs. They seem to be what Alvin Plantinga calls 'properly basic beliefs'. One either believes them or one doesn't. There are no arguments for or against them.

This thread has petered out. It became apparent - after a long discussion - that if one accepts the Aristotelean view of the world, in which notions like 'potential, 'essence' and 'directed' are believed to have meanings beyond their everyday pragmatic meanings, then the OP argument has some bite, and if one doesn't, then it has none.

I like to learn wherever I can from discussions, and the lesson from this one has been that the gulf between Aristoteleans and non-Aristoteleans is immense. I am starting to think that it is bigger than that between theists and anti-theists.

But, no one wants to understand all that.

Well, not no-one. There are plenty of people that are concerned about that - you and me for a start, and probably other contributors to this thread. It's just that they don't get heard above the shrill, vengeful shouting of the 'law and order' zealots.

Such is the sad state of public discourse on important issues like this. If it's any consolation (probably not) I don't know that there was ever a time in the past either when governments were prepared to take on the difficult, real solutions, rather than the popular, ineffective, cruel ones.

The government where you are is democratically elected, yes? — Sapientia

I got the impression that Agustino lived in the US, in which case the answer to that question is 'Not really' (ref state governments disenfranchising the poor with 'voter fraud prevention' measures, elections being held on work days with no time off to vote, minimising voting places in poor neighbourhoods, gerrymandering, enormous financial domination of campaigns by the rich, collusion with foreign governments by candidates).

If you want to use the word 'proof' in that bizarre way, then go ahead. There's no point in discussing it further.

Yes, unless one finds the statement meaningless, which covers the second statement.

What, exactly, is the negation of the following statement?

'The process is functioning to do things'

It is not what you wrote.

Similarly, your alternate version of the third statement is not its negation.

So, the process of homeostasis attempts to not do things, works indeterminately, in order to not maintain the internal regulation of its temperature and fluid balance. — Marty

No. None of those statements follow from what I wrote.

And the process itself is functioning to do things, yes? — Marty

No, I would not say that.

The process doesn't work indeterminately, right? — Marty

No, I would not say that. I don't even know what it means.

Homeostasis occurs because the body needs to work out an internal regulation of its temperatures and fluid balance, right? — Marty

No, I would not say that.

Because it seems to me the body is being used as a type of organism that functions for-the-sake-of - at least in part - homeostasis. — Marty

That is your interpretation, which you are entitled to make. But I do not make that interpretation. I am content to simply describe the processes that occur within the body. If somebody asks how the body came to have those processes, it can be explained in terms of evolution, again without teleology.

It is not necessary to make a teleological interpretation in order to learn about or research homeostasis.

I'm afraid I didn't understand that post. In particular I can't parse the second sentence.

The one bit I did understand is 'what is the process describing?'. My answer to that is that the process does not describe anything, it just does things. If the body gets too hot, sweating and other temperature-lowering processes take place. If it gets too cold, shivering and other temperature-raising processes take place. Over millions of years and genetic variations, the ones that survived were those that had such features, or their precursors, in place, and that is what we see today.

I know a lot of people think that [telos] is optional, — Marty

Are you able to accept your differences with them as just a reasonable difference of opinion, or do you think they are all objectively wrong and just too stupid to realise that? If the former then I'm just one more person you can identify as someone with whom it is reasonable for both parties to differ.

I have no idea what what a nonteleological account of causation is without making your nature Humean. — Marty

I'm not sure what it means to 'make nature Humean', but I love Hume's writing as much as the Aristotelians appear to love his, so that sounds good to me.

I'm not sure what it means to say that things aren't directed, or dont have a means-end framework. — Marty

Nor am I. Nor do I know what it means to say that things 'are directed, or do have a means-end framework', unless one follows a 'God designed it that way' approach, which is not what I am sensing you are proposing.

I'm not even sure how you can talk about processes like homeostasis without then referring to, "the attempt to regulate an internal environment." — Marty

In biology, largely for historical reasons, it is common to talk about things in a teleological fashion. This is a residue of the science's history, not a logical necessity, and is a feature not shared by most other sciences. Every teleological statement can be rephrased non-teleologically if one wants to. One usually doesn't bother, for the same reason that one doesn't bother to rephrase 'sunrise' as 'earth-turn'.

I still remember thinking, in high-school chemistry classes, how weird it sounded when the teacher told us that Chlorine 'really wants to gain another electron' and Sodium 'really wants to get rid of its outer electron'. It was many years later that I finally made sense of these weird-sounding statements by figuring out the non-teleological version of them.

A non-teleological description of homeostasis is 'the body has processes that regulate its internal environment'.

I was surprised that, based on a quick scan of the wikipedia page on homeostasis, it appeared to make few if any teleological statements. But all that tells us is that the writer was likely more Humean in disposition than Aristotelean.

What I took issue with was your claim that a good argument requires clear and concise definitions, rather than demonstrating the meaning of words through examples. — Metaphysician Undercover

We resolved that already. Arguments can be proofs or dialectics. Proofs have to meet that higher standard of definition. Dialectics do not. The Aristotelian argument in the OP is a dialectic, not a proof. I thought that was all agreed. If not, which part do you disagree with?

I agree with all of your post up to the last para - quite strongly in fact. I regret the prominence of scientists like Krauss, Dawkins and Hawking who seem to have no understanding of or interest in philosophy, and I think they give science a bad name. I fondly remember Heisenberg, Einstein, Bohm and so many twentieth century scientists that were as interested in the philosophical interpretations of science as in the science itself.

I don't understand the last para though, particularly the distinction between requiring metaphysics and requiring metaphysical assumptions. Perhaps you can elaborate on that. To me they seem the same, and I think one can do science without either. I sympathise with your feeling that science without those is uninteresting, but I do not agree. I see a beauty in the patterns one finds, regardless of whether one attaches them to any metaphysical assumptions. But these are aesthetic judgements and people will vary in how they feel about that.