An excellent PhD adjunct instructor in Classics at the U of Minnesota said back in the early 1980s that college teaching was turning into 'migrant labor' because one could never put together enough jobs at one institution. One would end up running all over town. — Bitter Crank

They are academic migrant workers. — Fooloso4

I assume that it was a conservative push to reduce government expenditures ...Or maybe it was born out of a basic hatred of college professors. — Bitter Crank

I think it had something to do their animosity toward higher education, and, as you say a basic hatred of college professors. The Koch brothers are fixing that. They have bought whole departments and decide who will teach in those departments. Another problem is that considerable funds go to facilities to make colleges more like country clubs.

Yes, and unfortunately, in America, people would tell those qualified people to get out there and do something (those who can do, those who can't teach). — ZhouBoTong

I wonder what they think those with a PhD in philosophy should do. Be like Socrates and harass people at the mall?

I think that if potential students and their parents are aware of the problem and make clear that they will not apply to schools with a high percentage of adjuncts things may begin to change. Grad students teaching courses is another problem, especially in the sciences when the grad student comes from another country and her command of English is poor or has a heavy, difficult to understand accent.

And you believe the American people care about the truth because...? — Benkei

Because I am not yet that cynical. Perhaps four more years of Trump and I will be.

I don't think it is because people don't care about the truth, it is rather what they believe the truth to be. But it is also about priorities. Some may not care that Trump obstructed justice or has questionable dealings with the Russians or whatever unless they think I will hurt them in some way.

I hope you caught that I was joking — ZhouBoTong

I didn't. There are some who think it is an easy way to make a living with lots of free time.

Is not good and needs fixing. — ZhouBoTong

There was at time talk of adjuncts forming a union. I don't know if that ever happened. One major problem is that they would have no power. It would be no different than declining to teach a class. In some schools full-time faculty have successfully petitioned to put limits on the number of classes an adjunct could teach. I think that is a step in the right direction but for practical purposes it simply means that the adjunct would look to pick up classes elsewhere with possible extra burden of travel.

I don't know what will bring about change but as long as there is a pool of qualified people willing to teach and an administration unwilling to hire full-time, let alone tenure track, faculty the problem will persist.

Let's try this a different way. Surely the number does not inhere in the objects we count, for they can be grouped and counted in different ways to give different numbers. So, if it is already actual, and we agree that it does not pre-exist in our minds, where is it? — Dfpolis

The number is how many of whatever it is we are counting. If I count the number of fingers on one hand and I count correctly the number is 5. That is because I actually have 5 fingers on my hand. If one of my fingers was cut off I would count 4 and that is because I actually have 4 fingers on that hand.

So, do you agree that items can be counted if and only if they are actual and distinct? — Dfpolis

As I said from the beginning, the count depends on the unit. If we cannot determine the unit we cannot determine the count. It the items to be counted are actual then their total number is also actual.

What we choose to count is up to us, how many there are of what we count is not
— Fooloso4

Think of it this way. Classical physics is deterministic. — Dfpolis

No wonder you are confused! Counting something has nothing to do with determinism.

So it is with counting. The number is predetermined, but not actual until the count is complete. — Dfpolis

I would say that the number is not determined until we count, but what we are counting, the items, as you said, are actual. It is because there is actually this item and this item that we can determine how many there are. We can call this determination the count. It we count six and we count correctly that is because there are actually six of the items to be counted.

It means that its intelligibility is actualized by someone's awareness. — Dfpolis

This is evasive. Intelligible in what way? Which is to say, as I asked, what does it mean to say the ball is known?

It has to be known as an object, as a tode ti (a this something) before it's classified. — Dfpolis

If you mean that it stands out (literally, exists) distinct from all else, that does not mean that intelligibility is a property of the object. To be is not a property of what is. To be is a necessary condition for having properties. "This" is not a property of this something. To be intelligible a thing must be distinguishable as separate from other things but to be intelligible there must also be some subject to which it is intelligible. Without subjects there is no intelligibility.

Being a baseball is intelligible, but it is the ball as a whole, not a property of the whole. — Dfpolis

What you said was:

intelligibility inheres in objects — Dfpolis

If someone from a tribe that knows nothing about baseball were to find a baseball what it it about it that would make it intelligible to the tribesman that it is a baseball? Its intelligibility as a baseball is not something that inhere in the ball. To be intelligible as a baseball one must know what baseball is.

Now that I've answered your questions, can you explain their relevance? — Dfpolis

The relevance can be seen in the what I just said. If intelligibility inheres in the object then someone would know what a baseball is even if they did not know what the game of baseball is.

That would not change how she came to the concept. It was by abstracting from her experience of counting real things -- not by mystic intuition. — Dfpolis

No, it would not necessarily be by abstracting. I gave several different things she might assume, stories she might tell herself.

I am saying that whatever concepts we do have are abstracted from empirical experience. — Dfpolis

I would say that since none of us are without experience we cannot say what if any concepts we would form, but that concepts are not always abstractions, the can be something we add to rather than something we take away from experience.

I think the goal of the testimony has been achieved. An educated electorate is perhaps the highest good that can be imparted by one's leaders. — Wallows

While the Republicans are anxious to declare the end of the investigation, I do not think that Mueller's testimony accomplished what needs to be done. My not rendering conclusions he left it up to Congress, but Congress is so divided along partly lines that it will not render impartial conclusions. The Democrats must do what Mueller did not. They must present the investigation's findings in a clear and persuasive manner. They may not be able to convince their colleagues to impeach but they can bring the truth to the American people.

Don't these adjuncts just have more freedom to pursue their other interests when they are paid on a 'per classes taught' basis? — ZhouBoTong

Traditionally, adjuncts were experts working in other fields who brought their knowledge to the classroom. Since there is now a shortage of academic jobs and there are several financial advantages to the university, adjuncts are taking the place of full time instructors. They would prefer a full-time position but they are few and far between. The workload carried by an adjunct may the about the same as a full-time faculty member, but since adjuncts are so poorly paid and there are no healthcare and other benefits they must either work full time doing something else or work at multiple schools with a workload that far exceeds full time faculty, and still make only a small fraction of full-timers. They rarely have the time or energy to pursue other interests.

I have gotten the feel from both of you that you may be agreeable to American libertarianism? — ZhouBoTong

If you are referring to me then no I am not a libertarian. In my opinion libertarians cannot see passed their own self-interests narrowly and myopically construed. While I certainly favor individual rights I do not accept the notion of social atomism. Due consideration should be given to the public good and the good of the whole not just the protection of individual rights.

There are two potentials here. One is our potential to be informed, which belongs to us. The other is the set's potential to have its cardinality known, which belongs to what is countable, and is the basis in realty for the proper number to assign to the set. — Dfpolis

Both are dependent on us to determine, that is, to know or be informed of the number. In neither case is the number a potential number except with regard to our potential to know it.

I beg to differ. The items can be counted if and only if they are actual distinct items. — Dfpolis

I am not going to get into methods of counting bacteria.

How many there are of whatever it is we choose to count is independent of us.
— Fooloso4

This is self-contradictory. If the number is "How many there are of whatever it is we choose to count," it is not independent of us. — Dfpolis

What we choose to count is up to us, how many there are of what we count is not.

Necessarily, whatever is actually done can be done. If the ball is known, necessarily it can be known, and so is intelligible. As it can be known whether or not it is actually known, intelligibility inheres in objects. So, why do you say it is not a "property"? — Dfpolis

You ignore a great number of questions. What does it mean to say the ball is known? When someone identifies an object as a ball is the ball known? If they cannot tell you whether the material is rubber or synthetic is the ball known? If they do not know the molecular or subatomic make-up is the ball known? If they know it is a baseball is being a baseball an intelligible property of the object? If some other ball is used to play baseball is being a baseball an intelligible property of the object? If the ball is used as a doorstop does someone who only knows it as it is used for this purpose know that it is a ball? A baseball? If they saw someone hitting it with a stick wouldn't they wonder why he was hitting the doorstop with a stick? Perhaps they might think that he does not know what a door stop is.

And abstract arithmetic concepts from that experience. You let a child count four oranges, four pennies, etc., and she abstracts the concept <four>.. — Dfpolis

She might be a platonist and assume that <four> must still exist even when the oranges are eaten and the pennies spent. Or she might assume that <four> vanishes with the oranges and pennies. She might assume that there is only <four> when there are this many objects, even if they are not oranges and pennies. The "experience" of abstract arithmetic concepts may only come as the result of being taught to think of numbers in a certain way.

If numbers were objects in nature, you would be right, But they aren't objects in nature, they are the result of counting sets we chose to define. Why count only the fruit in this bowl instead of some other set we define? — Dfpolis

We might say, for example, that the number of bacteria in a petri dish is potentially thousands or tens of thousands. Whether one is platonist or not, however, in such a case the number refers to the objects being counted. At any given moment that number is an actual number, even if we do not know what that number is. Here potential means we do not know what the actual number is.

What you said was:

Quantity in nature is countable or measurable -- potential not actual numbers. "There are seven pieces of fruit in the bowl" is true, if on counting the pieces of fruit, we come to seven and no more. — Dfpolis

The number of bacteria in the petri dish or fruit in the bowl or whatever it is that we are counting cannot be counted if that number is not an actual number of items.

That makes the numbers partly dependent on us and partly dependent on the objects counted. So, numbers do not actually exist until we define what we're going to count and count it. — Dfpolis

What is dependent on us is what we choose to count. How many there are of whatever it is we choose to count is independent of us. Here we are not talking about the concept of number but how many of something.

The intelligibility of an object simply means that we are able to understand it in some way. That is not an aspect of the object.
— Fooloso4

So, being rubber or spherical are not aspects of a rubber ball? — Dfpolis

Rubber and spherical are properties of the object. Intelligibility is not a property.

Just because we can fix on the ball's matter or the form does not mean that the ball's intelligible properties depend on us (unless we're the ones defining the object). — Dfpolis

The intelligible properties are those properties we understand, rubber and spherical. Intelligibility is not another property that is intelligible.

What depends on us is which notes of intelligibility we choose to fix upon. — Dfpolis

What depends on us is the ability to understand, to make the object intelligible to us.

What we experience is not an assumption. It is data. — Dfpolis

We are talking about what a number is, the concept or ontology of numbers. That is not an experience or data. We do not experience numbers, we experience objects of a certain if indeterminate amount.

Right. I never said that variables and determinate numbers were the same. — Dfpolis

You were responding to the following:

In the briefest terms, the arithmos is always a definite number of definite things,a collection of countable units, whereas in modern math a number, '4' for example, is itself an object. With the move to symbols, 'x' does not signify anything but itself. — Fooloso4

The point was the one you now acknowledge. Klein's insight is into the radical shift in mathematics from numbers to symbols. Although we treat them as interchangeable when we assign value to the variable, numbers and symbols are not interchangeable. We do not assign values to numbers, we must assign value to variables. Numbers are determinate. Symbols are indeterminate. 3+2=5 is true. a+b=5 may be true or false. 3+2=5 is not dependent on us. a+b=5 is dependent on the values we assign to a and b.

Yes, the cardinality of the fruit in the bowl is seven whether we count or not. — Dfpolis

My issue is with what you call "potential numbers". The number of pieces of fruit in the bowl or the number of seeds in the pieces of fruit in the bowl in never a potential but an actual number. We may have the potential to determine that number but that does not make it a "potential number".

It is not trivial that the intelligibility of an object does not constitute an actual concept. A state's potential for a seven count does not exclude is simultaneous potential for other counts when conceived in other ways. So, it is not trivial that states require further (mental) determination to be assigned actual numbers. — Dfpolis

This is really convoluted and seems to be contradictory. The intelligibility of an object simply means that we are able to understand it in some way. That is not an aspect of the object. The way in which something is understood is not an aspect of the object but rather of our ability to see it or understand it in different ways. If a state requires mental determination then that determination is not an aspect of the object but rather something we say or know or understand or have determined about the object.

Exactly, and so one that requires justification. — Dfpolis

No inquiry is free of assumptions. The ontology of mathematical objects is an open question. It is not that different theories of mathematical objects are without justification it is that there is no universal agreement regarding their justification.

It lacks determinant reference, but it has a reference type. That type may be a numerical value or something else that can be represented by the formalism. — Dfpolis

Which means that it differs fundamentally from a number, which is always has a determine value.

...to which end, Trump is about to sign off on the all-time record for Government deficits..... — Wayfarer

Once upon a time, long, long ago, before Trump that was supposed to have mattered to Republicans, although the truth is that the Democratic administrations have done much better at lowering the deficit. In any case, I don't think it has ever been much of a concern for the Evangelicals, since for them small government means staying out of their business, the business of religion.

I can’ t fathom how any self-described Christian could approve of Trump if they know anything about him.
— Wayfarer

Might have something to do with ushering in the End of Time. — Amity

I agree. To fill it out a bit. Based on Revelations a "new Jerusalem" is one of the signs of the Apocalypse according to Evangelicals. One of Trump's promises was to make Jerusalem the capital of Israel.

A few other points:

Trump is a man and even if he is, as some believe, sent by God, he is a man and has human foibles, he sins and is deserving of forgiveness no matter of how many pussies he grabs and how many women he cheats on his wives with.

He claims to be anti-abortion and has promised to overturn Roe, packing the courts with anti-abortion judges.

Evangelicals favor small government and the dismantling of the administrative state because they see the government as a threat to freedom, specifically religious freedom, and more specifically their religious freedom. Trump has positioned himself as a champion of religious freedom, even if they see through his phony religious piety.

Many of these students are ill-prepared for higher education but there is a persistent push to get students to attend college. Higher education has adopted a business model sometime in the seventies and since the bottom line is now the most important thing, a major concern is retention. It is couched in terms of the interest of the students but it is really all about not having empty seats. "The customer is always right" is their unspoken motto.This has contributed to grade inflation. Instructors bear the brunt of the blame from both students and administration if students fail or get poor grades. Students expect to get A's of B's for doing minimal work of poor quality. There is an enormous sense of entitlement.

Some years back I read something by a professor whose evaluations by students were always low. The most common complaint was that he was too demanding. And so he decided to treat the class as if it were kindergarten. He even brought cookies for snack time. He praised them for whatever they said or did. He made sure all assignments were easy and if they could not handle even that he still graded them as if they were the exceptional students they thought they were. He quickly became teacher of the year.

More and more classes are now being taught by adjuncts. As full time faculty retire or move on they are not replaced by tenure track instructors. Adjuncts are often as qualified as tenured faculty but are paid very poorly and must teach multiple courses at several schools and take other jobs on top of that if they are to live above the poverty level. The are academic migrant workers. No contracts and no benefits.This is not an exaggeration. No matter how qualified they cannot keep up with the amount of classes they teach. It is one of higher educations dirty little secrets.

My comment is directly on point, and does not attack a straw man, but premise ii. — Dfpolis

2+2=4 is not a "Platonic relationship". That 2+2=4 is true, according to mathematical platonism is due to the nature of numbers. The relationship is made possible by their nature. The relationship itself is not another platonic object.

Quantity in nature is countable or measurable -- potential not actual numbers. "There are seven pieces of fruit in the bowl" is true, if on counting the pieces of fruit, we come to seven and no more. — Dfpolis

The number of pieces of fruit in the bowl is undetermined until counted. This does not mean that the number of pieces is a potential number. It is an actual number that before we count we might say it could be six or seven or eight. There are actually seven pieces whether we count them or miscount them. They do not become seven by counting them. We are able to count seven because there are actually seven pieces of fruit in the bowl.

I'm saying that every note of intelligibility is an aspect of the object known. — Dfpolis

So, an aspect of something known is that it is knowable. Aside from being tautological and trivially true it raises questions that go beyond the current topic and so I will leave it there.

Do you mean different concepts that were in prior use?
— Fooloso4

No, I mean that concepts don't change. — Dfpolis

The question was about your wording. Whether the 'not' in "not in prior use" was a typo.

This is an interpretive, not a mathematical, claim. — Dfpolis

Of course it is interpretative! What is at issue is the concept of number. That is an interpretive question.

No, "x" does not mean the letter "x." It has reference beyond itself. — Dfpolis

It does not have any reference until it is assigned one. That is the point. It is a variable that can stand for any unknown. In this sense it is different from both "4" as how many or "4" as an object.

[Added trivia note: I read somewhere that Descartes' publisher used x because he was low on letters an x was not frequently used in French. Whether that is true or not I did not verify.]

It may mean an unknown we seek to determine, a variable we can instantiate as we will, or possibly other things ... — Dfpolis

Right.

but it never signifies itself — Dfpolis

It is because it is indeterminate that it does not signify something other than itself, which is to say, unlike a number it has no signification until or unless assigned one. It could stand for any number or no number at all.

I personally don't believe that a God played any role in the apparition of life on earth or in evolution (I am saying this because maybe my post suggested otherwise). — Patulia

I took your statements to be about Darwin and evolution, not your own beliefs on the matter.

I respect those who believe that everything happened according to God's plan — Patulia

I have always found this claim to be problematic. It may be for some a source of comfort, but since things happen as they do there is no way to know whether they happen according to plan since whatever happens can be said to happen according to plan but just as well can be said to happen without a plan or at least in the case of human actions contrary to God's will.

Darwin was a believer and, after reading his books and notes, one could come to the conclusion that Darwin actually believed there was a God behind the whole evolution process. — Patulia

The Origin of Species says nothing about the origin of life. This is an important point that is often overlooked. Whatever his beliefs in God may have been, it is quite clear that he did not describe God as playing any role in speciation. And, as you say, the science of evolution has evolved since Darwin.

Fooloso4 The old jokes are still the best ones, eh? — Pattern-chaser

I have become one.

Since the topic of this thread is Trump I will refrain from saying more about Warren.

I am going to leave it there. This thread is not the place to discuss economic realities.

As others have said, education in the US varies widely, both in an between public and private schools. I cannot speak of elsewhere.

A few observations:

The idea of individuality is of central importance, thus there not much emphasis on conformity, except perhaps with such things as school uniforms. Individuality of thought and action plays well, within certain bounds.

I do not know if things have changed recently but last I checked those receiving degrees in education were in general at or near the bottom of their class.

Parents tend to take the side of their children when it comes to discipline problems and will blame the teacher if the student is failing.

Some years back I did some reading on the philosophy of education and it was a dismal affair. Schools would change their approach to education often and sometimes radically based on questionable theories of education and research that seemed to be designed to confirm whatever assumptions it intended to prove.

Someone earlier - was it you? - mentioned that for whatever reason the average American credits and/or discredits the current president - at that time - for the economy - at that time. Well, this sort of thinking has all sorts of problems inherent to it... — creativesoul

Yes, there is are all sorts of problems inherent to it, but it is a common belief.

There is no measure of what ought be done. — creativesoul

This is something the Federal Reserve is dealing with now. The economy is not behaving according to the common assumption that when employment is high it creates inflation. Contrary to standard practice rather than raise interest rates Powell is lowering them. His idea is to respond quickly to what is occurring at the moment rather than based on predictions of what will happen. Since no one really knows the consequence of whatever action is taken it is hard to say whether his strategy is sound. There are always unintended consequences and unforeseen factors. Quick corrections might be the way to go. But the US is just one player in the global economy. It is not really in control of what happens to the US economy.

The standards of measurement for success/good are suspect to say the least. — creativesoul

Elizabeth Warren's concerns with income inequality is not egalitarian ideology or anti-capitalism. She thinks that based on past history when there is great disparity between rich and poor the result will be depression. Right now that disparity is greater than it was before the Great Depression. She has a pretty good record on things like this. But again, the economy right now is defying predictions.

No reason at all. We're all gonna die. Etc. — bongo fury

Being smothered to death by a blanket though does not seem like a good way to go.

Let's compromise: snooty joke. — bongo fury

Sure, why not.

Fair, if snooty, point. — bongo fury

I prefer the term arch. It was a joke.

If my last post above is in any way to blame for your sense — bongo fury

Don't take it personally. I won't name names or initials.

Aw shucks.

There's a C S Lewis book called God in the Dock. It's a collection of essays, but the meaning of the title is that it implies a "God on Trial", based on an analogy made by Lewis suggesting that modern human beings, rather than seeing themselves as standing before God in judgement, prefer to place God on trial while acting as his judge. Which is exactly what I think the OP does. It my view, it's related to the (false) modern, anthropological conception of deity, which sees God as a kind of super-manager or ultimately responsible agent, in the same way as a CEO or executive is responsible. — Wayfarer

This is a big part of what the story of Job is about. It is by no means a modern conception of deity.

See also Elie Wiesel's discussions and play about putting God on trial while he was in Auschwitz.

18.

Furthermore, the living substance is the being that is in truth subject, or, what amounts to the same thing, it is in truth actual only insofar as it is the movement of self-positing, or, that it is the mediation of itself and its becoming-other-to-itself.

In #17 he said:

... substantiality comprises within itself the universal, or, it comprises not only the immediacy of knowing but also the immediacy of being, or, immediacy for knowing.

How are we to reconcile these statements? Is it immediacy or mediation?

#17 begins as a view from the end or completion, a view which Hegel says:

... must be justified by the exposition of the system itself ...

Hegel identified two modes of this exposition. Both are the consequence of thinking identity without difference. These should not be thought of as simply abstract logical consequences but as having occurred within the history of philosophy, the logic of the development of spirit.

In the first it is the identity of thinking with itself - universality, simplicity, undifferentiated, unmoved substantiality.

In the second the identify of thinking and being as immediacy - inert simplicity, actuality itself in a fully non-actual mode.

In #18 he shifts from lifeless categories to living substance, the being that is in truth subject. In its immediacy it is both the knower and what is known (#17). But in is in truth only insofar as it
is the movement of self-positing. The term comes from Fichte:

Fichte is suggesting that the self, which he typically refers to as "the I," is not a static thing with fixed properties, but rather a self-producing process. Yet if it is a self-producing process, then it also seems that it must be free, since in some as yet unspecified fashion it owes its existence to nothing but itself. https://www.iep.utm.edu/fichtejg/

Hegel adds that it is the mediation of itself and its becoming-other-to-itself. As self-determining it is other than itself in that it is not yet what it determines itself to be.

As subject, it is pure, simple negativity, and,as a result, it is the estrangement of what is simple, or, it is the doubling which posits oppositions and which is again the negation of this indifferent diversity and its opposition.

Self-positing is negative in that it is a rejection of what it is in order to become what it will be.

That is, it is only this self-restoring sameness, the reflective turn into itself in its otherness.

The movement is within the subject, a turning from within itself away from and back to itself. In its otherness it is still its sameness. That is, it is never wholly other.

The true is not an original unity as such, or, not an immediate unity as such. It is the coming-to-be of itself, the circle that presupposes its end as its goal and has its end for its beginning, and which is actual only through this accomplishment and its end.

The subject here is not the individual or only the individual but mankind.

I think our poor little three year old has suffocated under her blanket. It seems that no one has been paying attention to her.

I myself like to use a kind of falsification method... not sure how to describe that in English, an "Ausschlussverfahren"? As in, I see what ideas, associations and hypotheses I can come up with myself, and then check if they hold up under scrutiny: Test them against the text itself, and with external sources, shave them with Occams razor and see what remains. — WerMaat

I do something similar. I start with what I think he is saying and then go back to the text to see how well that squares with what it says. It may seem as though I am on the right track but then I ask myself how this or that statement fits in. Without forcing it I see if I can make it fit and whether this helps make sense of the larger context or if I need to change how I initially understood it. This process continues as I read. Sometimes what I thought fit together must be torn apart and rebuilt if I cannot get what I am now reading to fit. Maybe what I had put together is not right and maybe what I am now trying to put together is not right and sometimes neither is right and the whole thing needs to be revised. But it may be that there are pieces that come later, and so, everything remains tentative.

Each part must be understood in its details and taken together all the parts should form a whole with those parts serving their function within the whole. The parts themselves can form wholes in the same way that a hand is a whole but a part of a larger whole. The process of reading is both analytic and synthetic, breaking things down and putting them together.

I noticed that often when I appeal to common sense, people will want some background reference, or statistical or other evidence to support an opinion. — god must be atheist

There is a difference between an opinion and an informed opinion. Common sense is not sufficient when what you are offering an opinion about is something that involves matters of fact. If your opinion is an informed opinion then you need to say what it is that informs that opinion. An example, let's say you are arguing about vaccines. Common sense is that we should not inject harmful substances into the body, but that does not tell us whether the substances in vaccines are harmful or whether the benefits outweigh the risks.

I also noticed that when I make an opinion, and state it as a claim, on the works of some classic philosopher, then people will ask me "where did he state that / can you quote an exact page number and book where he said that, so I can look it up, etc. — god must be atheist

There are several reasons why one should cite the source. So that others can read what the author actually said. To determine whether what you said accurately represented the author's words. To see the context, which is important to understanding the meaning of what is said.

Case in point I talked about Wittgenstein on July 20 and 21, 2019 — god must be atheist

Case in point, without providing information on where you said this we cannot read what was said or evaluate it without access to content and context.

At this point I don't know if this demanding nature of other users of the forum is genuine, and they really need me to back up my opinion with quotes, statistics and other hard evidence, or else they are using this tool as a tactic to discredit my opinions. — god must be atheist

I cannot speak for everyone but there are some of us here who do not think that is is being demanding but rather is just standard practice in philosophical discussion that makes reference to philosophers or deals with matters of fact.

... I'll ask them to please forego the demand for evidence, and accept my argument on the strength of my reasoning. — god must be atheist

The strength of your reasoning is directly tied to the evidence on which it is based. Or, if your claim is that in any particular case or in all cases there is no need for evidence then you must be able to explain why evidence is not needed.

If your position is that it is just your opinion then why should anyone take it seriously? Is it your opinion that a philosophy forum exists simply to allow you to inform us of your opinions?

[Added]: Out of curiosity I tracked down the posts where you talked about Wittgenstein. You presented your opinion:

In my opinion Witty lacked the insight of accepting the status quo of language.

but qualifying it by saying it is your opinion does not mean that it is correct. It is completely at odds with what Wittgenstein was showing in the Investigations. There is a reading group in the forum on Wittgenstein's PI. Meaning as use it discussed at length and citations are given. He repeatedly points to the "status quo of language" as fundamental to most of our language games. If you opinion is at odds with what is said in the text then it is up to you to show that your opinion should be taken seriously by appeal preferably to the text or to the secondary literature. Note that this is how the reading group functions. It has nothing to do with a tactic to discredit your opinions.

It is common wisdom that the better the economy the better the incumbent president's chances of being re-elected. There are worrisome signs that Trump's trade war with China pose an increasing threat to the health of the economy. In today's NYT:

Chinese direct investment in the U.S. fell to $5.4 billion in 2018 from $46.5 billion in 2016, a drop of 88 percent, according to data from Rhodium Group.

In addition, China is the largest importer of US goods. It is also the largest creditor.

Like it or not the two countries' economies are tied to each other and Trump's attempt to hurt China hurt the US. To be fair, it is not just the trade wars. Concern over security is also a factor. And this has global repercussions that may further hurt the US economy.

Timing is everything. Even if the dire predictions turn out to be true if they are not apparent to the average voter before the election Trump will be ahead of the curve, and if he looses the Democrats will be blamed for the downturn.

The context was that of showing the consequence of the questionable claim that 2 + 2 = 4 exists in a Platonic realm. It was not me stating my own position. — Dfpolis

I do not wish to defend mathematical Platonism, but I think you misrepresent the position. The problem stems, at least in part, from jumping from Aristotle's criticism of Plato's Forms to mathematical platonism.

From the IEP article on Mathematical Platonism:

Formulated succinctly, Frege’s argument for arithmetic-object platonism proceeds as follows:

i. Singular terms referring to natural numbers appear in true simple statements.

ii. It is possible for simple statements with singular terms as components to be true only if the objects to which those singular terms refer exist.

Therefore,

iii. the natural numbers exist.

iv. If the natural numbers exist, they are abstract objects that are independent of all rational activities.

Therefore,

v. the natural numbers are existent abstract objects that are independent of all rational activities, that is, arithmetic-object platonism is true.

Your example of counting fruit is a straw man.

And, yes, abstraction does not create content, it actualizes intelligibility already present in reality. — Dfpolis

This strikes me as a form of Platonism, as if intelligibility is something somehow present in but other than the objects of inquiry.

I am not sure how you distinguish different concepts that were not in prior use from new concepts. Perhaps examples would help. — Dfpolis

Do you mean different concepts that were in prior use? In the briefest terms, the arithmos is always a definite number of definite things,a collection of countable units, whereas in modern math a number, '4' for example, is itself an object. With the move to symbols, 'x' does not signify anything but itself.

This is a wide-ranging topic that goes far beyond the concept of number. The second part of this book review that addresses Klein will give a better sense of what is at issue as it relates to modern philosophy and science: https://ndpr.nd.edu/news/the-origin-of-the-logic-of-symbolic-mathematics-edmund-husserl-and-jacob-klein/

I think we are using "concept" in different senses. I am thinking of <number>, <line>, <irrational number> and so on when I say "concept." You seem to be thinking rules of procedure. — Dfpolis

No, I am speaking here specifically about the concept of number, that is, what a number is.

No, I don't dismiss different conceptual spaces as wrong -- they are just different ways of thinking about the same reality. — Dfpolis

What you said was:

It is an intellible whole that becomes increasingly actualized (actually known) over time. — Dfpolis

Either you think that each of these ways are retained in the development of the intelligibility of the whole or some are modified and rejected.

I see that Fooloso4 has posted already. He quotes Spinoza, "By substance, I mean that which is in itself, and is conceived through itself: in other words, that of which a conception can be formed independently of any other conception."

Our hazard here - maybe just my hazard - lies in accepting something like this from Spinoza as explanation. — tim wood

It is not a question of accepting Spinoza for an explanation of what Hegel means by substance. I introduced Spinoza because of what Hegel goes on to say about God as the one substance. Why does he introduce this here, at this point?

Were Hegel here, I'd say, "Wha-at," and ask him to go through it again. — tim wood

One thing we can do is go through it again and again and again ourselves.

My problem is that I have no idea what it means to have a single unitary conception "formed independently of any other conception. — tim wood

I do not want to get into a discussion of Spinoza but it means that there is only one substance and that it is not derived from or dependent on anything else.

I think Fooloso4 just above has got some of it, but not all. — tim wood

Hence my comment about the tentativeness of what I said. One disadvantage of the way we are proceeding is that we have not read the whole of the preface or the whole of the book.

But at the moment it seems to me Hegel is allowing himself to float a bit, no feet on the ground. — tim wood

One assumption that guides my reading of the philosophers is that when things do not make sense to me the problem is probably with me and not the text. Hegel is certainly not floating. If anything, the density and compactness of what he is saying is likely to sink us. But the sense of not having your feet on the ground is apt. He is talking about the whole from within the whole, there is no ground on which to stand.

Each field of math assumes its principles (its postulates and axioms), but that does not mean that the principles can't be investigated and justified by nonmathematically. I — Dfpolis

You are avoiding the question. Science does not simply "assume its principles". It determines them through observation, hypothesis, testing, theory, modeling, and so on.

mostly via abstraction — Dfpolis

First, someone has to do the abstracting. Second, the properties of say a triangle are not determined by abstraction.

Please read sentences in context. — Dfpolis

You mean this context?

It leaves unexplained how mathematical truths that exist only in the Platonic realm can apply to reality.

In this last point, how can the Platonic relationship 2 + 2 = 4 tell us that if we have two apples and two oranges, we have four pieces of fruit? — Dfpolis

2+2=4 does not exist only in the "Platonic realm", does not need to "apply to reality", and it is meaningless to call it a Platonic relationship. It does not apply to reality because it is counting something real.

I said most of the foundations are the result of abstraction. — Dfpolis

To say what they are the result of is not to say what they are
— Fooloso4

What they are is not my present interest. — Dfpolis

So, in a topic entitled The Foundations of Mathematics, the actual foundations of mathematics is not your present interest.

The concepts that existed before the addition of unknowns, variables, functions and distributions continue in use today. Adding new concepts does not vitiate old concepts. — Dfpolis

It is not simply adding new concepts, it is a matter of different concepts. This does not vitiate old concepts in the sense that they are wrong, but that mathematics no longer operates according to the older concepts. But this is not simply an issue of mathematics but for philosophy.

If you are interested, the following will give you some sense of what is at issue: https://www.unical.it/portale/strutture/dipartimenti_240/dsu/Klein,%20Concept%20of%20Number%20Copy.pdf

Which leads to the question of whose mathematics?
— Fooloso4

Mathematics is not personal property. — Dfpolis

It is a question of assumptions and conceptual framework. As I pointed out, there is no number 0 or 1 in Greek mathematics. You might dismiss this as simply wrong, but in doing so what you miss is the ability to understand a way of looking at the world that is not our own.

17:

I trust that everything I have said in this discussion is taken as tentative, but here it may be necessary to state it. I have worked and re-worked this, each time seeing it somewhat differently. But since, as Hegel says, we cannot see clearly what has not yet completed its development, there may be errors here that will become evident to me as we move forward.

In my view … everything hangs on grasping and expressing the true not just as substance but just as much as subject.

It is instructive to compare this to what Spinoza says about substance.

By substance, I mean that which is in itself, and is conceived through itself: in other words, that of which a conception can be formed independently of any other conception. (Ethics , Part One, Definitions, III)

Hegel continues:

At the same time, it is to be noted that substantiality comprises within itself the universal, or, it comprises not only the immediacy of knowing but also the immediacy of being, or, immediacy for knowing.

The universal is unity of the immediacy, direct and unmediated, of knowing and being, of knowing and for knowing.

However, in part, the opposite view, which itself clings to thinking as thinking, or, which holds fast to universality, is exactly the same simplicity, or, it is itself undifferentiated, unmoved substantiality.

In what sense is this the opposite of the view Hegel presents above as his view? In Hegel’s view the universal is within substance, here thinking is itself undifferentiated, unmoved substantiality, the universal.

But, thirdly, if thinking only unifies the being of substance with itself and grasps immediacy, or intuition grasped as thinking, then there is the issue about whether this intellectual intuition does not then itself relapse into inert simplicity and thereby present actuality itself in a fully non-actual mode.

Intellectual intuition is given in its immediacy to thought by thought. It is inert simplicity because as given it does no work.

In the middle of these distinctions there is what seems to be a non-sequitur:

However much taking God to be the one substance shocked the age in which this was expressed, still that was in part because of an instinctive awareness that in such a view self-consciousness only perishes and is not preserved.

I take this is a direct reference to Spinoza’s God. Hegel thinks it shocked the age not because, as is commonly assumed, threatening the status of God as distinct and separate, but because it threatens the status of man as distinct in his self-consciousness. It is not a non-sequitur because this is precisely what is at issue - the relationship between God, man, thinking, and the whole.

First, sciences do not establish their own principles — Dfpolis

Where do you imagine these principles come from?

I did not claim that Greek math was Platonism — Dfpolis

After a full paragraph on Platonism you said:

Platonic relationship 2 + 2 = 4 — Dfpolis

This is not a "Platonic relationship", it is simple arithmos, the counting of ones or units.

I said most of the foundations are the result of abstraction. — Dfpolis

To say what they are the result of is not to say what they are. The most basic concepts of of Western mathematics underwent a fundamental change with the origin of algebra, that is when numbers were replaced by symbols. Which leads to the question of whose mathematics?

I disagree with much of the quote you gave from Maurer. — Dfpolis

Are you disagreeing with his reading of Aquinas? If so, where do the mistakes lie? Or is it that you are disagreeing with Aquinas?

Once again, the title of your topic is "The Foundations of Mathematics". Those foundations are not in modern mathematical theory or methodology. Greek mathematics is part of that foundation. Greek mathematics is not "Platonism".

To say:

... our mathematical concepts have a foundation in reality. — Dfpolis

Is like saying a building has a foundation in the ground. It says nothing about that foundation.

See Armand Maurer, The Division and Methods of the Sciences — Dfpolis

Instead, it would be more useful to direct the reader to Maurer's "Thomists and Thomas Aquinas On the Foundation of Mathematics", available free online: http://www.u.arizona.edu/~aversa/scholastic/Thomists%20and%20Thomas%20Aquinas%20on%20the%20Foundation%20of%20Mathematics.pdf

From that paper:

There are important consequences of Aquinas's placing the notions of mathematics in the second order of his quaestio disputata instead of the first. Unlike concepts on the first level, those on the second do not properly speaking exist outside the mind. Their proper subject of existence is the mind itself. They are not signs of anything in the external world. Hence mathematical terms cannot properly be predicated of anything real: there is no referent in the external world for a mathematical line, circle, or number. Finally, mathematical notions are not false; but neither are they said to be true, in that they conform to anything outside the mind. Aquinas does not suggest that they might be true in some other sense. (56)

Thank you for your comments. I have no problem with the neoplatonic One Identified as God. — Dfpolis

The title of your topic is The Foundations of Mathematics. The neoplatonic One Identified as God has nothing to do with the foundations of mathematics or anything I said. You have completely ignored the foundation of Greek mathematics which makes your pseudo-problem of counting disappear. 2 + 2 = 4 is not a "Platonic relationship", at least not for Plato or the foundation of Greek mathematics.

In the Greek arithmos a number is always a number of something. A number tells us how many ones or units. This is why Aristotle says that two is the first number. In your example of two apples and two oranges, there is no problem of determining how many as long as we know what the unit of the count is. In this case pieces of fruit. In the same way you determine that there are two apples and two oranges, you determine that there are four pieces of fruit, that is, simply by counting them. Modern number theory and set theory axioms is anachronistic.

With regard to Platonic Forms, what the One itself is remains. But the questions of the One itself and the One and the many do not concern the mathematician.

The classic modern work on this is Jacob Klein's Greek Mathematics and the Origins of Algebra.