It Bears Repeating

1) There is no right to immigrate.  Correlatively, no nation is under any obligation to accept immigrants.

2) Immigration must be to the benefit of the host country. Trump understands this; leftists don't. Another reason to rejoice that Trump is president.

You don't like his style? Suck it up.  He is doing good things for the country.

Diversity Visa Program? An outrage to any sane American.

David Gelernter on Trump

Via Power Line (emphasis added):

I remain absolutely a supporter and a sympathizer of Trump. And you know, no president checks every box. I think his virtues far outweigh his faults. I do wish he would take the office and the history of the office more seriously than he does . . .

Just the fact of getting elected was an extraordinary accomplishment. I mean, you could say it was the most culturally democratic moment in the history of the world. Never before has a great power spurned everything the elite — the intellectual and the social elite — knows, left and right, about who should be running the country. Never before has a great power said to hell with that. The dignity of the country is important and has a lot to do with the power of the country, but this is an emergency and we’re going to make use of the best candidate who’s out there. And the implications are enormous. The left believes that, since it refuses to report on the right, the right doesn’t really exist, that it’s just a bunch of uncollected morons with no serious thought.

We all know this. We’ve reached a point where the left’s blindness is aiding the collapse of the intellectual structure built up since the rise of Marxism . . . The left is too arrogant, too complacent, too self-satisfied to notice it or do anything about it — I hope.

This is indeed an emergency and I would go so far as to say that the so-called conservatives who refused to support Trump displayed a morally censurable degree of willful stupidity. And they are paying the price for it. The 'stock' of Bill Kristol and George Will et al. has plummeted.

More on Tribalism and the Identitarian Right

This entry continues the discussion with my Right-identitarian interlocutor.  My current position is one of rejection of both Left- and Right-identitarianism. I am open, however,  to a change of position. That is part of what makes me a philosopher as opposed to an ideologue. I wrote in my critique of Dennis Prager:

"The correct view is that racial differences are real and significant just as sexual and age differences are real and significant, but  for purposes of social harmony and political cooperation we had better not identify ourselves racially but in terms of attributes more conducive to comity." My correspondent responds:

I agree with your criticisms of Prager.  In a normal society men don't pretend that they're just human beings rather than men (who are also human beings) and women don't pretend that they're just human beings rather than women.  Rather, in a normal society the distinctive male and female abilities and interests and ways of being are accepted, and society adapts itself to these differences–these male and female 'identities'  in other words.  But then, if race is similar to sex and age in this respect, why would it be bad for people to 'identify' in terms of race along with attributes like sex and age?  Shouldn't we say instead that this is also reasonable and healthy?

In discussions like these it is always a good idea to seek (and rejoice over) points of agreement. Points of disagreement will emerge soon enough.

One thing we can agree on is that no human being can be just a human being if that implies having no sex or no race or no age or no height, etc. And so if I pretended to be a human being indeterminate with respect to one or more of the above-listed attributes, then my pretense would empty and absurd. My talk of treating people as individuals rather than as tokens of ethnic or racial types does not imply that they are bare individuals bereft of all attributes.

But there is nothing empty or absurd about prescinding from this or that characteristic in certain contexts.  Characteristics prescinded from don't matter for the purpose at hand, but they are still there. For example, age and citizenship matter when it comes to voting, but race and sex by  current law do not and ought not.  But if we don't take into consideration a person's sex when it comes to the right to vote, it does not follow that the person is sexless.  In general, if attribute A is instantiated by the members of a given population of individuals, and abstraction is made from A, it does not follow that the members of the population are indeterminate with respect to A.

So far, near-platitudes, unless my opponent questions my voting example which I fear he might. (If he does, then that discussion belongs in a separate thread.) We have yet to locate the bone of contention.

Are there "distinctive male and female abilities and interests"? I would say so, and I would add that they are not merely socially constituted.  The biology of the female plays a role in the explanation of why women are more nurturing than men, more cooperative and conciliatory, make better real estate agents, but also why they are more emotional than men and why their political judgment is not as good. (I would argue, however, that the last two points are not reasons to withhold from women full voting rights.)  So far, then, no disagreement. No disagreement with my conservative interlocutor, that is. I have already said enough to elicit howls of rage from the lunatic Left. Their howling, however, is music to my ears. Their destructive extremism only galvanizes the resoluteness of my opposition to them.

Does it follow that there are male and female 'identities'?  Here is where it gets tricky and sticky. 'Identity' can be used in different ways. What is meant by 'identity 'here ? A stereotype?  That is apparently what my sparring partner has in mind. I will assume that he agrees with me that stereotypes, most of them, or at least many of them, have a fundamentum in re and are true in the way that generic statements can be true.  (It is surely true, for example, that Germans are more rule-bound and respectful of authority than Italians. See this list of generic statements.) Stereotypes are not, most of them, expressions of mindless bigotry or irrational hatred of the Other. What are truly mindless and irrational are liberal denials of this plain truth.

My opponent is going to agree with me that women as a group are more nurturing, caring, cooperative, conciliatory, averse to heated disagreement, better with children, etc., than men as a group.  But that is a positive, accurate stereotype which not all women fit. Women are nurturing and Sally is a woman; it does not follow, however, that Sally is nurturing.  'Women are nurturing' is a generic statement: it cannot be replaced by a universal generalization such as 'Every woman is nurturing.' Sally is a chess-playing, nerdy engineer who works for Google, worships Ayn Rand, enjoys heated debate, and has no interest in children or in taking care of anybody. And all of this without prejudice to her being, and being essentially (as opposed to accidentally), a full-fledged biological female with the 'plumbing' and chromosomal make-up to prove it.

It may be that my opponent is conflating stereotype with identity. In one sense  of 'identity,' the identity of a thing is what it is by nature, what it is essentially. Since Sally does not fit the gender stereotype, and yet is essentially biologically female, we ought not conflate identity with stereotype. (I am assuming a distinction between sex, which is a biological reality, and gender which, while it reflects sex, is in part socially determined. Anyone who elides the distinction I would have to consider very foolish indeed.)

My claim is that there are no "male and female 'identities'."   There are male and female stereotypes and gender roles but no male and female identities. If there were a female identity or nature that included such stereotypical features as being nurturing, being conciliatory, shying away from heated argument, then every female would fit that identity; Sally does not fit the female identity; ergo, there is no female identity.

And because there is no female identity, if Sally so self-identifies, then her self-identification is a false self-identification. She falsely self-identifies if she so apperceives herself as to be nothing but an instance of that identity.  And if we deny Sally her right to be a nerdy, chess-playing, Rand-reading, non-nurturing engineer, then we reduce her to a gender stereotype in violation of her true identity as a free, self-determining person.  As an animal, Sally's biological identity or nature is essential to her; as a person, however, she is free to pursue engineering in defiance of the stereotype.

And the same goes for race. There are different races as a matter of biological-anthropological fact. (Race is not a mere social construct.) And there are different racial and ethnic stereotypes, accurate stereotypes, i.e., stereotypes with a basis in reality, some negative, some positive. But there is no white identity or black identity or Italian identity or Polish identity.  Granted, I am essentially Caucasian and essentially of Italian ancestry; no change is possible in these respects. But there is no white identity that includes stereotypical features since there is no such identity had essentially by every biological white.  Bear in mind that 'white' in this context does not refer to skin color but to race. It is a mistake to confuse race with skin color. 

So I continue to maintain my thesis that, "for purposes of social harmony and political cooperation we had better not identify ourselves racially but in terms of attributes more conducive to comity." The opponent hasn't given me any good reason to abandon this thesis. 

Is a reversion to tribalism, even if inevitable, something to be regretted, or is it healthy?

But then, in my critique of Prager, after listing some candidate attributes, I waxed pessimistic. For example, can we Americans identify for political purposes as Americans, as people  committed to the values and principles enshrined in our founding documents? Obviously not. Too many of our fellow 'citizens' have no respect for these documents. The universities of the land are lousy with such people. There are leftist knuckleheads who speak of a 'living constitution,' which, of course, is no constitution at all. And in what sense are these fellow 'citizens' fellow citizens if they don't accept our great Constitution? Think of the liberal-left liberty-haters who call for the elimination of the Second Amendment.

"So I end with a dark thought: in the end tribalism wins."

Again I wonder why this is a dark thought.  You seem to be considering the possibility that identities like 'citizen' or 'American' are too weak to form the basis for a healthy society.  But suppose that's true.  Then it's _good_ that people will eventually reject these identities in favor of some 'tribal' identity which could serve as a better basis for society–something that is more "conducive to comity".  Suppose it's not true, and identities like 'citizen' are enough.  Then it seems to me that people should be able to get along and share a society simply on the basis of being 'citizens' or 'Americans' while at the same time having distinct racial or tribal identities, just as they can share a society and get along despite having distinct identities based on sex and age.

Amazingly, my opponent thinks that tribalism is good and that tribal identification can unify us. I can't see that this makes any sense at all. So here we find a bone of serious contention!  If we can no longer identify as citizens or Americans, it does not follow that tribal self-identification with the resultant Balkanization would be good.

I am saying that we conservatives, through inattention and inaction, have allowed things to get to the point where identities like 'citizen' and 'American' can no longer form the basis of a healthy society and polity.   We are now in a very bad state of affairs. But tribalism makes things worse.  The reversion to tribalism may be inevitable, but as I see it, it can't be good.  Tribalism can't be the basis of comity or social harmony precisely because different tribes with different values and interests oppose one another.  Furthermore, when we think and act tribally we fail to see important individual differences.  Clearly, there are important differences between Clarence Thomas and Trayvon Martin, Jason Riley and Ta-Nehisi Coates, Walter E. Williams and Michael Brown. Coates is a despicable racist fool and an enemy, but I would love to have Riley and Williams and Thomas as next-door neighbors. No social harmony is likely to ensue if we lump all these blacks together as members of the opposing tribe.  It is of course different in war. But we want to avoid war. Don't we?

I am saying that, as a matter of contingent fact, we are no longer united under an umbrella of shared values and principles, and that tribal identification will only make it worse.  If, on the other hand, we were united under that 'umbrella,' then of course there would be no problem.  We would be united publicly, and privately people could do their tribal thing.

Of course, there is a crucial disanalogy:  Human nature is such that differences of sex and age occur naturally and inevitably within a given human community, since these are part of the basic structure of the extended family.  By contrast, differences of race and ethnicity do not occur within the natural human community.  On the contrary, since the natural community is based on the family and extended family, that kind of community eliminates racial or ethnic differences–any natural community ends up being a single racial-ethnic community. 

So it's doubtful that racial difference and racial identity can be accepted as part of the normal structure of society in the way that these others already are.  To the extent that racial and ethnic differences exist within a society, that society must be somewhat artificial; it must be made up of sub-cultures that have a stronger claim on the natural loyalties and identities of its members.  Racial-ethnic differences are a primordial sign of Otherness, of Not Belonging–of potential danger and competition rather than safety and co-operation.  We can try to pretend otherwise, but this is contrary to our own instincts, and it probably won't work in the long run.  But, again, is this dark?   

Well, intermarriage among different European ethnicities has worked hasn't it?  

My opponent seems to be suggesting that racial/ethnic uniformity is essential for a well-functioning society.  I don't buy it.  Suppose blacks had never been brought as slaves to North America. The other racial and ethnic groups get along tolerably well. But the key is assimilation and commitment to a set of values and principles that transcend blood.  Unfortunately, the Melting Pot is a thing of the past never to return. Leftists have destroyed it by exploiting racial tensions to forward their agenda.  And of course we no longer agree on values and principles.

Horribile dictu, leftist filth are now attacking free speech!

Is invocation of Blut und Boden dark? I would say so.  For one thing, blood ties and racial purity do not insure comity. I have more in common with Korean and Turkish philosophers than with anyone in my family. Consanguinity is no guarantee of spiritual affinity, and  spiritual affinity can exist without consanguinity.  We are told that "To the extent that racial and ethnic differences exist within a society, that society must be somewhat artificial; it must be made up of sub-cultures that have a stronger claim on the natural loyalties and identities of its members."

This begs the question by assuming what I argued against, namely, that there are ethnic and racial identities. Beside, the emphasis on narrow natural loyalties works against social harmony. That's the mentality of mafiosi. Social harmony requires a commitment to higher loyalties.  John Gotti's children should have 'ratted out' their father.  The Unabomber's brother was right to turn him in. He was acting under the inspiration of a higher loyalty.

Multi-culturalists and Leftists would say it's 'dark' to imagine shutting down mass immigration of Muslims into Europe–because for them, the attempt to force incompatible cultures together into some kind of incoherent mess seems good!  But a conservative doesn't want to force people to live in weird new ways that (we think) go against human nature, so a conservative doesn't think it's 'dark' to imagine Muslims in Muslim lands, Christians in Christian lands, etc.  Feminists think it's 'dark' to imagine a world where most women are focused on having kids and staying home to care for them, because they think the ideal is to have women be just like men in all respects; but a conservative thinks it's better to let the sexes live in ways they find natural,  and so doesn't think this scenario is 'dark'.  Of course, excessive tribalism is possible (and 'dark') but why not allow for some degree of tribalism?  A sound conservative position, I think, is that society must provide people with healthy ways of expressing their instincts rather than forcing us to suppress them.  Telling people they have to think of themselves as just 'citizens' or 'humans' is telling them to suppress some very powerful instincts.  So (I think) conservatives should regard this as an oppressive and unhealthy policy.

We agree that allowing mass immigration of Muslims into Western lands is suicidal.  This is because they don't, as a group, share our superior Western values and because they want to replace them with unenlightened Sharia-type values. It is not because of their being Turks or Arabs or whatever. (The few that do share our values can be allowed to immigrate.) And of course there is nothing 'dark' about traditional Muslims staying in their lands.

Nor is there anything 'dark' about women devoting themselves to the noble and difficult task of being good mothers and homemakers.  The feminists who attack motherhood have a lot to answer for.

What I see as 'dark' is the racial self-identification on the identitarian Right. It amounts the deliberate erasure of one's unique personhood in favor of being an interchangeable token of an ethnic or racial type. (This has some connection to the Marxist notion of man as Gattungswesen, but I am not in a position to explain it clearly.)  How can my identity reside in an attribute shared with billions of others?

My identity is what make me be me and no one else. It is therefore impossible to locate one's identity in being an interchangeable token of a  racial type. For every token of a type, qua token of a type, is the same as every other one.  

There is also a slippery slope consideration. If you identify as white, then why not as Southern white, and if Southern white, why not rural Southern white, and so on until you identify as a Hatfield or a McCoy?  

Furthermore, race is part of my animality. So if I identity racially, then I identify myself as a particular instance of a particular race of animals. But I am more than an animal, and my true self cannot be located in my animality.

But now we move into metaphysics. This is unavoidable in a thorough discussion. But this entry is already too long. Tomorrow's another day.

False Expectation

He who expects all of life to be both wise and philosophical is neither.

……………..

Modeled on Giacomo Leopardi (1798-1837):

Nessun maggior segno d'essere poco filosofo e poco savio, che volere savia e filosofica tutta la vita.

There's no greater sign of being a poor philosopher and wise man than wanting all of life to be wise and philosophical.

(Giacomo Leopardi, Pensieri, tr. W. S. Di Piero, Baton Rouge: Lousiana State University Press, 1981, p. 69) Do you see how the translation imports an ambiguity that is not present in the Italian original?

Happy Halloween!

Hillary-Ditch-the-witchThe more I know about Hillary, the gladder I am that Trump sent her packing. The cartoon appeared before the election, but proved to be prophetic. What is truly scary is that if she had won, all her recently-revealed greed-driven dirty dealings would never have come to light.

The Scariest Passage in the Critique of Pure Reason

With Halloween upon us, it is appropriate that I should present to my esteemed readers for their delectation if not horror the scariest passage in Kant's magnum opus:

Unconditioned necessity, which we so indispensably require as the last bearer of all things, is for human reason the veritable abyss. . . . We cannot put aside, and  yet also cannot endure the thought, that a being, which we represent to ourselves as supreme among all possible beings, should, as it were, say to itself: 'I am from eternity to eternity, and outside of me there is nothing save what is through my will, but whence then am I? (A613 B641)

Interpretation later.

‘Liberals,’ Conservatives and Stereotypes

Yesterday I said that an infallible mark of a 'liberal' or 'progressive' is a refusal to distinguish legal and illegal immigration. Another infallible mark is the refusal of 'liberals' or so-called 'progressives' to admit that there is truth in some stereotypes, that some of them have a basis in reality, and are not the product of mindless bigotry.  We conservatives, however, being fundamentally sane, admit the obvious: there are accurate stereotypes and inaccurate stereotypes. An example of an inaccurate stereotype is the black watermelon stereotype according to which black folk are disproportionately fond of watermelon.  Examples of accurate stereotypes below.

It occurs to me that our 'liberal' pals can be taxed with swallowing a negative, inaccurate meta-stereotype: they falsely think that all stereotypes are inaccurate and of course 'racist'! What bigots these 'liberals' be!

Lee Jussim gets to the heart of the matter with the following quiz. I got every answer right. See how you do. Answers below the fold.

1. Which group is most likely to commit murder?
A. Men
B. Women

2. Older people are generally more __________ and less __________ than adolescents. 
A. Conscientious; open to new experiences 
B. Neurotic; agreeable 

3. In which ethnic/racial group in the US are you likely to find the highest proportion of people who supported Democratic presidential candidates in 2008 and 2012?
A. Whites 
B. African Americans

4. People in the US strongly identifying themselves as ___________ are most likely to attend church on Sunday.
A. Conservative
B. Liberal

5. On 24 December 2004, a father and his three kids wandered around New York City around 7pm, looking for a restaurant, but found most places closed or closing. At the same time, his wife performed a slew of chores around the house. This family is most likely:
A. Catholic
B. Baptist
C. Jewish
D. Pagan/Animist

 

Continue reading “‘Liberals,’ Conservatives and Stereotypes”

October Ends . . .

. . .  and we say farewell once again to Jack Kerouac, cat man and mama's boy, as he prepares to "leave all San Francisco behind and go back home across autumn America" proving once again to his romantic predecessor Thomas Wolfe that one can go back home again where

it'll all be like it was in the beginning — Simple golden eternity blessing all . . . My mother'll be waiting for me glad — the corner of the yard where Tyke is buried will be a new and fragrant shrine making my home more homelike somehow — On soft Spring nights I'll stand in the yard under the stars — Something good will come out of all things yet — And it will be golden and eternal just like that – There's no need to say another word. (Big Sur, 1962, last lines, last page.)

It's a good last word: something good will come of it all: of all of the wandering, all of the searching, all of the pain, and misery, and drunken folly, and lonely nights, and broken dreams.  The vanity will give way to vision.  The beat will taste beatitude.  The road will end and the restless will rest.

On the Reference of Proper Names

London Ed writes and I respond in blue:

Still thinking about how to frame the main argument, so please help me out here. 

               There is a woman called ‘Clinton’. Clinton is a politician. 

I claim there is a semantic connection between the name ‘Clinton’ that is used in the second sentence, but mentioned in the first sentence. It is this connection which licenses the inference to ‘some woman is a politician’.  My central claim is that this exhausts the semantics of the proper name. The function of the name is simply to connect the second sentence to the first.

 My question is, what arguments best support my claim. Some ideas.

(1) It’s just obvious that ‘Clinton’ refers back to the first sentence. The meaning of the two sentences is unchanged whether we write ‘he’ or ‘the man’. But since ‘he’ is just a pronoun, whose only function is to back-refer, it follows that ‘Clinton’ here is no primary reference.

BV: Your second example, then, is this:

There is a man named 'Clinton.' He is a politician.

And so 'Clinton' in the second sentence of the first example is merely a device of back reference.  Is that what you are maintaining?

We agree, of course, that 'he' is a pronoun the antecedent of which is 'Clinton.'  And so 'he' refers back to 'Clinton.'  Back reference is a word-word relation. The antecedent of a pronoun is a word, not the (extralinguistic) thing to which the word refers, assuming it refers to something.  What I deny is that 'he' in this context merely back refers.  I maintain that it also refers to Bill Clinton, a chunk of extralinguistic reality, where 'refers' picks out a word-WORLD relation.

Back reference is an intralinguistic relation; reference is an extralinguistic relation.  The reference of 'he' piggybacks on the reference of 'Clinton.' It picks up the reference of 'Clinton.'

But it is more complicated than this. For there is reference, not back reference, within a language.  For example,

" 'Red' " refers to 'red.'

There is nothing to stop us from naming words. This is a case of intralinguistic reference, not back reference.  Therefore, one cannot identify intralinguistic reference with back reference. All back reference is intralinguistic, but not all intralinguistic reference is back reference. A fortiori, one cannot identify extralinguistic reference with back reference.

It is also worth noting that 'back' in 'back reference' is an alienans adjective.

It is not clear what your thesis is. Are you an eliminativist about extralinguistic reference? That is, do you deny that proper names refer extralinguistically? Or perhaps you are an identitarian. Perhaps you hold that there is extralinguistic reference of proper names but that it reduces to back reference. (Some say that there are mental states all right, but that what they are are brain states. This is an identitarian, not an eliminativist, position. Notionally they are different even if it can be shown that identitarianism collapses of necessity into eliminativism.)

Or perhaps you maintain neither of these theses.  I'd guess you are an eliminativist from your opening statement.  I take it that you accept that there is a real world of concrete things external to language. If language 'hooks on' to these things, then presumably not via proper names. How then? Via bound variables in the Quinean way?  Or do you hold that language does not hook on to language-external things at all?

I suggest that you will never gain a hearing for your ideas unless you can answer convincingly questions such as the foregoing.

For most of us it is a datum that there is extralinguistic reference to existing concrete things in space and time.  We take it as given that in the paradigm cases reference is a word-world relation.  The theoretical problems, then, are to understand how reference is possible and how it is achieved. But you seem to be denying the datum: you seem to be denying that there is extralinguistic reference, or at least, extralinguistic reference via proper names. 

 

Which Side Are You On?

It is an appropriate question to ask in politics, though not in philosophy. Politics is warfare. If you call yourself conservative and don't support Trump, then you are helping the enemy. Which side are you on?

In philosophy we strive for objectivity. We take our time; we consider all points of view. We show respect for our interlocutors. We are civil. But one cannot be objective in a fight for one's life and way of life especially if one's way of life includes free speech, open inquiry, and resistance to the Left's totalitarian politicization and ideologization of everything, including pure mathematics! (More on this later.)  One has to secure, with blood and iron if need be, the space of objective inquiry against the ideologues who, at the present time, are chiefly leftists and Islamists, and who wittingly or unwittingly, work together. 

You don't like the vulgar Trump? Tough shit. He's all we've got. Face reality and its limitations. Don't let the best become the enemy of the good. The milque-toast McCains haven't done jack and won't do jack, except talk and obstruct. David Horowitz:

The movement galvanized by Trump can stop the progressive juggernaut and change the American future, but only if it emulates the strategy of the campaign: Be on the offense; take no prisoners; stay on the attack. To stop the Democrats and their societal transformation, Republicans must adhere to a strategy that begins with a punch in the mouth. That punch must pack an emotional wallop large enough to throw them off balance and neutralize their assaults. It must be framed as a moral indictment that stigmatizes them in the way their attacks stigmatize Republicans. It must expose them for their hypocrisy. It must hold them accountable for the divisions they sow and the suffering they cause. (Big Agenda, Humanix, 2017, p. 142)

Trump alone, an outsider who doesn't need a job, has the civil courage and is in a position to deliver the needed punches. That's why we like him. That's why we overlook his flaws. He punches back. And for other reasons given here

Infinity and Mathematics Education

Time for a re-post. This first appeared in these pages on 18 August 2010.

…………………….

A reader writes,

Regarding your post about Cantor, Morris Kline, and potentially vs. actually infinite sets: I was a math major in college, so I do know a little about math (unlike philosophy where I'm a rank newbie); on the other hand, I didn't pursue math beyond my bachelor's degree so I don't claim to be an expert. However, I do know that we never used the terms "potentially infinite" vs. "actually infinite".

I am not surprised, but this indicates a problem with the way mathematics is taught: it is often taught in a manner that is both ahistorical and unphilosophical.  If one does not have at least a rough idea of the development of thought about infinity from Aristotle on, one cannot properly appreciate the seminal contribution of Georg Cantor (1845-1918), the creator of transfinite set theory.  Cantor sought to achieve an exact mathematics of the actually infinite.  But one cannot possibly understand the import of this project if one is unfamiliar with the distinction between potential and actual infinity and the controversies surrounding it. As it seems to me, a proper mathematical education at the college level must include:

1. Some serious attention to the history of the subject.

2. Some study of primary texts such as Euclid's Elements, David Hilbert's Foundations of Geometry, Richard Dedekind's Continuity and Irrational Numbers, Cantor's Contributions to the Founding of the Theory of Transfinite Numbers, etc.  Ideally, these would be studied in their original languages!

3. Some serious attention to the philosophical issues and controversies swirling around fundamental concepts such as set, limit, function, continuity, mathematical induction, etc.  Textbooks give the wrong impression: that there is more agreement than there is; that mathematical ideas spring forth ahistorically; that there is only one way of doing things (e.g., only one way of constructing the naturals from sets); that all mathematicians agree.

Not that the foregoing ought to supplant a textbook-driven approach, but that the latter ought to be supplemented by the foregoing.  I am not advocating a 'Great Books' approach to mathematical study.

Given what I know of Cantor's work, is it possible that by "potentially infinite" Kline means "countably infinite", i.e., 1 to 1 with the natural numbers?

No! 

Such sets include the whole numbers and the rational numbers, all of which are "extensible" in the sense that you can put them into a 1 to 1 correspondence with the natural numbers; and given the Nth member, you can generate the N+1st member. The size of all such sets is the transfinite number "aleph null". The set of all real numbers, which includes the rationals and the irrationals, constitute a larger infinity denoted by the transfinite number C; it cannot be put into a 1 to 1 correspondence with the natural numbers, and hence is not generable in the same way as the rational numbers. This would seem to correspond to what Kline calls "actually infinite".

It is clear that you understand some of the basic ideas of transfinite set theory, but what you don't understand is that the distinction between the countably (denumerably) infinite and the uncountably (nondenumerably) infinite falls on the side of the actual infinite.  The countably infinite has nothing to do with the potentially infinite.  I suspect that you don't know this because your teachers taught you math in an ahistorical manner out of boring textbooks with no presentation of the philosophical issues surrounding the concept of infinity.    In so doing they took a lot of the excitement and wonder out of it. 

So what did you learn?  You learned how to solve problems and pass tests.  But how much actual understanding did you come away with?

A Simple Point of Logic Journalists Ought to be Aware Of

One often encounters sentences like this one:

There are many arenas in which all ideas are not considered equal.

This example is from a recent piece in Vox. I could give further recent examples, but one is enough. To simplify, consider just the core thought:

All ideas are not considered equal.

Unfortunately it is not entirely clear what the core thought is. For the sentence is ambiguous as between 

1) No ideas are considered equal

and

2) Some ideas are not considered equal.

The thoughts (propositions) expressed are distinct since the first can be false while the second is true. Although it is fairly clear that the author intended (2), a good writer avoids ambiguous constructions unless for some reason he intends them. So don't write sentences of the form

3) All Fs are not Gs 

if you intend say something of the form

4) Some Fs are not Gs.

Write instead sentences of the form

5) Not all Fs are Gs

which, by simple quantifier negation, is equivalent to (4). 

Class dismissed.