merjet

To wit: "Colorless green ideas sleep furiously" - Noam Chomsky (link)
"Colorless green" is contradictory. So try another. Short green ideas sleep furiously. 😊

I received Mr. Knapp's book,  Mathematics is About the World. It includes 'Hilbert's Game of Symbols' in the subtitle, but doesn't have much more in the body.
"At some point during my college freshman year, I realized that neither mathematicians nor philosophers of mathematics shared my perspective, offering only the alternatives of formalism (a game of symbol manipulation), Platonism (a separate world of mathematics), or, as a third, the Fregean view that mathematics is a branch of logic. I could accept none of these choices" (p. 10).
Hilbert was a Formalist.
"My specific concern will not be with counting objects, but with using numbers to measure magnitudes, such as length, weight, and speed. In this, we should not be surprised to find that our usage of numbers is indeed correct. But we will find that characterizing exactly what we are doing when we apply numbers is not as straightforward as one might have thought. Yet in laying this process bare, one creates the foundation for a similar understanding of mathematical concepts whose relationship to the world we live in may be far from obvious. It is the lack of such understanding that has led to the widespread false alternatives that mathematics is either a formal game played with symbols, a system of deduction from carefully chosen axioms such as the axioms of set theory, or an insight into a Platonic universe of mathematical concepts. On any of these views, the applicability of mathematics to reality must be viewed as a happy accident" (p. 101-2)

My second try: The suspicion, harbored by many physicists and mathematicians over the decades but rarely actively pursued, is that a description of the properties exhibited by the peculiar panoply of forces and particles of reality may be so accurately depicted by eight-dimensional numbers called “octonions.”

I’d go a little farther and modify it as 
The suspicion, harbored by many physicists and mathematicians over the decades but rarely actively pursued, is that an accurate description of the properties exhibited by the peculiar panoply of forces and particles of reality may be so easily derived springs logically    from the properties of eight-dimensional numbers called “octonions”, that one could characterize the description as springing logically from them.
... just to clarify properties of reality do not spring from numbers, although numbers can be used to refer to reality.

The Peculiar Math That Could Underlie the Laws of Nature
https://www.quantamagazine.org/the-octonion-math-that-could-underpin-physics-20180720/
 

Most of the posts I make on this thread are only links to my blog, which clearly is not part of OL, and the thread is so titled. It's up to users to decide if they want to read them or not.
If others make unwarranted assumptions about me or my blog, that's their problem, not mine.
There are plenty of posts on OL with no obvious relation to Objectivism.

You triggered my curiosity. What does "old, old" mean? Is it the same as "old-old"? I did find something on that. Here says old-old means 85 or older. Here says it's over age 75 and that I am "young-old." Here says its 85-94, and I am not even "old", but it doesn't mention "young-old". I like  "young-old." ☺️

Oh, my. The last 48 hours on this thread have been an adventure. I delayed responding to the posts StrictlyLogical made on Friday because I was hesitant about how to respond. Due to Stephen Boydstun's posts supporting me and some of our history, and StrictlyLogical's apology, my hesitation vanished.  
I reply to StrictlyLogical's Friday posts as follows. My blog isn't a "general philosophy" blog. Part of the content is philosophy, but not about philosophy in general or a wide range of philosophers. Much of the content has been about economics, finance, and technology, e.g. Marconi.
My purpose of giving links here is solely an invitation to anyone who might be interested in the content. It is not to spread or promote any philosophy as better than or against Objectivism. I will try to say a little more about the content along with the link.
Thank you, Stephen and StrictlyLogical. Thank you, dream_weaver, for moving the thread to its new forum. When I made my first post about 10 months ago, it wasn't clear to me where it fit best and I gave my okay to the moderators to move it. It just took a while. 🙂 I likely didn't choose its new forum because my blog doesn't consist of "poems, short stories, art, music, web designs, business deals, or graduations." 🙂
P.S. I will be attending OCON 2019.

I'm not so sure I've acted in my self interest raising this issue... 
Also, I have misunderstood and/or been negligent in honestly seeking the motivations of Merlin... justice demands an apology when treatment does not match desert... so Merlin I apologize for making this an issue,  I have no excuse or justification.

I appreciate all the links Merlin makes to his blog entries. They are informative, and convenient for me to go to from here. I don't get to follow up with comments usually, because I'm on other things for in-depth assimilation in these years of my life. Merlin's professional background and continuing study of economics and of philosophy are a lucky stream into this site. I'm delighted to see that such an old, old man is still learning. I remember 25 years ago when he and I together studied philosopher after philosopher concerning theory of truth. I'll try to link to some of his essays on that and on other subjects naturally of interest to learners who have an interest in the span of topics Rand undertook. 
I had not heard of this book and social theory of Walzer's until Merlin conveyed notes on it to us in this modern medium. Makes me kind of feel like being back with Merlin in hours after our business jobs, plodding our way through Spinoza. (I'm not kidding; to us that is interesting and very worthwhile.) I see that Merlin has summarized Waltzer through chapter 2 and that there are several chapters more he might think to convey notes on to folks here who might well be interested in modern theories of justice. Perhaps he will have some evaluations and Rand-comparisons at the end.
Good research and thinking from Merlin in these finished products:
Imagination and Cognition
Theories of Truth I II III 
On Probability
Pursuing Similarity
Perhaps some participants here would like to talk to Merlin right here in this thread about some things he wrote on these topics. 
~~~~~~~~~~~~~~~~
PS - I first met Merlin, as I recall, listening to tape lectures being played at Northwestern in 1977. That was The Philosophy of Objectivism which had been recorded the year before in New York. (It was by Leonard Peikoff, and Ayn Rand participated, a fine experience.) It's quite possible one could get acquainted with this learned guy by attending OCON 2019. He and wife reside in that vicinity, and I know he attended OCON last year.

A possible world makes sense if and only if it refers to a future state of the one real world. Other ways I've seen it used are gibberish.

Jordan Peterson interviewed Objectivist philosopher Stephen Hicks almost two years ago. In March he did so again.
Links: video of first interview    audio of second interview
They are long, about 1.5 hours each.

The typical advice from financial advisers to clients is to put their money into an index fund, getting a combination of: low commissions and lowered temptation to try an beat the market. In general, this is still good advice. but... 
... it is based on a key assumption that the future U.S. performance will be pretty much like the past.  Stocks can be hurt by inflation, but their prices inflate too. And, couple that to an unwritten assumption that statist governments have an incentive to subsidize the most common vehicle of investment. 

A true hyper-inflation type scenario is different. But, since such  situation has not really occurred in U.S. history, a financial adviser will never advise you to plan for it; not qua financial adviser. A few economists might be willing to predict hyper-inflation in the U.S., but they're basing their advice on a theory that has not been borne out for a century. 
One can compare the DOW vs. Gold, but looking at the DOW "priced in gold", how many ounces of gold would it take to buy the DOW. 

Source: https://www.macrotrends.net/1378/dow-to-gold-ratio-100-year-historical-chart
A big problem with this raw chart is that the price of gold was fixed in the U.S. from the great depression all the way to Nixon. So, the relatively bad performance of the DOW during the 1970s was gold shooting up in price from many years of pent up legal binding.
Given that legal context, one really ought to look at post-1980 data. Which gives us this portion:

Since 1980, the only time when one could have bought gold and still be better off than the Dow today was the years between 2000 and 2008. Notice that this is pre-Great recession, pre-housing-crisis, not post. Why? because the factor at play was the DOW rather than gold. It was the DOW that was shooting up. 

Since 2009, the DOW has shot up again, far beyond its previous highs. Since about 2012, the price of gold has not followed. Consequently, the DOW has risen significantly in gold terms. if you think the DOW is in a new bubble, then that might be an even better (as in history-based) reason to buy gold than a hyper-inflation scenario. 

However, betting against the stock market averages is something that a typical financial adviser will not recommend because it is usually a way to under-perform.

My personal view on gold is that if I own it, it will likely under-perform the stock-market over most multi-decade periods. Personally, I don't see a complete break down of the U.S. system during my lifetime. I'm also aware that in a complete breakdown, either the government or some thug is likely to take my gold from me, and to prevent that it may become necessary to hide it and not actually use it... making its value theoretical. But, as I said, I don't expect anything even close to this scenario in my lifetime.
 I think gold is a decent multi-generation asset, if you want to buy some to leave to your grand children. Even here, buying something like a rental property is likely to have better returns, because it is a true investment.

Finally, if you do buy gold, beware of the scammers out there. Companies that hype the coming inflation etc. are dicey. Many of them  try to convince their customers to buy coins that are not near 100% gold. So, if you do buy physical gold, stick with regular U.S. Gold eagles and the like.
 
 

The linked page has a Libraries button. When I clicked it, the title wasn't auto-fed to the new page. However, entering the title and clicking Find a Library gives search results as a list of titles. Clicking on a title there may help in locating a copy of the book in a library not too far away.
A good review of the book is here.
 

“If p, then q” is taken in logic texts to be identically equivalent to “Not (p and not-q).” “Not (there is a naturally evolved bird with talons, and it is not a bird of prey)” is identically equivalent to “If there is a naturally evolved bird with talons, then it is a bird of prey.” It seems that we know up front that this “identically equivalent” relation holds however much our knowledge of birds increases; it cannot be found false. Whether there are presently unknown conditions under which this particular “If p, then q” can be found false is open, though until specific prima facie plausible conditions of that sort are proposed (at least in a sketchy way), that open possibility is a vacuous possibility, a degenerate, impotent sort of possibility, whether the if-then concerns nature or mathematics. The nature of birds is a matter of identity, but it seems a wider sort of identity than that in the “identically equivalent” relation. And the latter would seem to be something one learns about later than the former, although maybe the latter is already present in a precursor way in prelinguistic action schemata (eg. there’s more than one way to get attention, more than one form under the schema get attention).
In his book How We Know, Harry Binswanger takes syllogistic inference to be a case in which what is already implicit in the premises is drawn out and made explicit in the conclusion. That is a common perspective on deductive inference. The syllogism is a form of “If p, then q” in which p is a conjunction of two propositions: “If r and s, then q.” For r and s to be true and to bear implicit truths, of course, r and s both have to express awareness of facts (254–55). This viewpoint is smooth with the views of Rand that logic is a form of identification and that existence is identity.
In his book Objectivism: The Philosophy of Ayn Rand, Leonard Peikoff remarked: “The method of logic . . . does reflect the nature and needs of consciousness. It also reflects the other factor essential to a proper method: the facts of external reality. The principle which logic provides to guide man’s mental steps is the fundamental law of reality” (120–21). There are no contradictory facts in reality, I should add, to be thought in conjunction if thought is aimed at fact. To put forth without evidence or design for evidence the thesis that there are naturally evolved birds with talons that are not birds of prey contradicts evident facts without resolving the purported contradiction with other (not-adduced) evident facts. I suggest that denials of modus ponens should be understood as that sort of denial under the basic conception of logic in Objectivism. Logical validities are never independent of all facts of reality.
Some excerpts from Nathaniel Branden’s lectures The Basic Principles of Objectivism: “Logic is the tool of reason. Logic is based on facts, on the fact that that which is, is; but it is not a science of facts. It is a science of method (75).” “One proves a proposition by demonstrating that it is logically necessitated, that its denial would contradict facts already known to exist. . . . . “Until one has grasped that A is A, and that contradictions cannot exist, there can be neither proof nor the concept of ‘proof’. . . . “The Law of Identity is a genetic root of the concept of ‘proof’. . . . (73, transcription in The Vision of Ayn Rand)

A possible world makes sense if and only if it refers to a future state of the one real world. Other ways I've seen it used are gibberish.

Infinity contra-Cantor #1

Infinity contra-Cantor #2

Approaching Infinity

I didn't see a forum where I thought this post fits well. If the moderators want to move it to another forum , that's okay. Anyway, I've been posting to this blog for a while, and believe some would find an interest in a couple recent ones.
LeBron, Trump, Altruism

Marconi #6   This is one of a series of 11 that I wrote while reading a biography of Guglielmo Marconi, the inventor of wireless technology and often credited with inventing the radio. The post refers to John Galt.
 
 

I didn't see a forum where I thought this post fits well. If the moderators want to move it to another forum , that's okay. Anyway, I've been posting to this blog for a while, and believe some would find an interest in a couple recent ones.
LeBron, Trump, Altruism

Marconi #6   This is one of a series of 11 that I wrote while reading a biography of Guglielmo Marconi, the inventor of wireless technology and often credited with inventing the radio. The post refers to John Galt.
 
 

The first sentence of the second paragraph in the opening post expresses a centuries old view about universals. Wikipedia's summary of the problem of universals is here. It refers to conceptualism, for which Wikipedia has a link to another summary. It arose later and now is generally considered a major alternative to realism and nominalism. 
The quote in the opening post is from Objectivism and the Corruption of Rationality. On Amazon there are several reviews, most of which are 1-star or 5-stars. One of the 1-star reviews is by me. If you haven't already read the book, maybe the reviews will help you to decide whether or not the book is worth reading.

.
A Rejection of Egoism —Excerpts from this linked article:
The first strand in Rand’s move from agent egoism to beneficiary egoism was the thesis that if one does not hold one's own life as the motive and goal of one’s actions (at least indirectly), one is acting in a self-destructive way. The second strand, wound together with the first, is that if one does not hold one’s life as the motive and goal of one’s actions, one is acting in a disintegrated way, and integrated life is better life.
. . .
The third strand in the cord by which Rand ties beneficiary egoism to agency egoism is the stress she lays on the self-sufficiency of organisms in general and individual humans in particular.
. . .
In the Strand One section, I interpreted Rand as holding to an egoism in which some right actions are not directly for the actor’s sake, only indirectly so. Directly, they could be for the sake of one not oneself, nonetheless count as egoistic. By this interpretation, Rand’s type of ethical egoism would fall outside Kraut’s exceptionally restrictive definition. “Egoism holds that there is only one person whose good should be the direct object of one’s actions: oneself” (WGW 39).
My interpretation of Rand on this point is in some tension with her text that I quoted (AS 1059–60). Further tension is added by other text of Rand’s:
“The rational man . . . . recognizes the fact that his own life is the source, not only of all his values, but of his capacity to value. Therefore, the value he grants to others is only a consequence, an extension, a secondary projection of the primary value which is himself.” (VoS 46–47) 
She goes on, in that 1963 essay, to quote Nathaniel Branden:
“The respect and good will that men of self-esteem feel towards other human beings is profoundly egoistic; they feel, in effect: ‘Other men are of value because they are of the same species as myself.’ In revering living entities, they are revering their own life. This is the psychological base of any emotion of sympathy and any feeling of ‘species solidarity’.” (VoS 47)
Rand’s contrast of secondary to primary might suggest the contrast of indirect to direct. I think, considering the layout of the psychology to which Rand points, that suggestion should be rejected.
 
Rand in Full —Excerpts from this linked article:
Catherine Halsey learns to greatly curtail her personal desires and to devote her efforts to helping others. This she does because she wants to do what is right and because she accepts the idea that selfishness is evil (ET XIII 384). 
Catherine also accepts the idea, advocated by Toohey (ET XI 342), that selfishness leads to unhappiness. I have been unable to recall or locate any major thinker who advocated this proposition, but it will follow from the premises that happiness requires morality and that selfishness is immoral.
Catherine’s success at unselfishness makes her unhappy and resentful. She speaks with her Uncle Ellsworth about it. She acknowledges that he is much brighter than she and that “‘it’s a very big subject, good and evil’” (ET XIII 384). Rand then uses their dialogue to argue the incoherence and pointlessness of absolute unselfishness. Rand’s lead into her case for the goodness of pure selfishness consists of the sensibleness and pleasure of having personal desires (together with having one’s own thoughts and choices) and guiding one’s own actions. (ET XIII 384; GW II 454). We have seen this way of entering the case for egoism before, in the development of Andrei after he meets Kira.
After her deep conversation with Uncle Ellsworth, Catherine gets together with Peter Keating. He is feeling dirty because of his testimony against Roark at the court case over the Stoddard Temple. Peter and Catherine reaffirm their love, which is a first-hand personal preference satisfying their own identities. They kiss. “Then he did not think of the Stoddard Temple any longer, and she did not think of good and evil. They did not need to; they felt too clean” (ET XIII 391). This suggests that at least one reason the concept of good and evil is needed is the human potential for betraying egoistic innocence.
. . .
I should pause over the necessity of intended self-benefit for correct values. Not all of one’s potential selves are worth benefitting. Among those who are, Rand maintains that only potential selves whose every value is intended to benefit themselves hold entirely correct values. “Concern with his own interests is the essence of a moral existence, and . . . man must be the beneficiary of his own moral actions. / The actor must always be the beneficiary of his action” (VS ix–x; also OE 46–47).
One is a beneficiary in ways other than by one’s resulting positive feelings, because one is a self that is not only feelings. Man’s self is “‘that entity that is his consciousness. To think, to feel, to judge, to act are functions of the ego’” (HR XVIII 737). It is the self—one’s soul—that has thoughts, meaning, will, values, desires, and feeling (GW II 454).
Roark loves the buildings he designs not only because of the positive responses they elicit in him. Dagny loves diesel-electric locomotives and the minds that create them not only because of the positive responses they elicit in her. It is not plausible that when she finds that man at the end of the rails, the one for whom she has longed since her youth, she will love him only because of the positive responses he evokes in her.
There is, however, a thread of subjectivity in Rand’s conception of value and love and normative selfishness that is puckering up the fabric. In my judgment, that thread is unnecessary and should be removed. Speaking metaphorically, the solemnity of looking at the sky does not come only from the uplift of one’s head (HR V 598). In extreme desire for another person, the other does not recede in importance compared to the desire (GW IX 539). A rational desire to help someone in need is animated not only by “your own selfish pleasure in the value of his person and struggle” (AS 1060, emphasis added). Rather, it is enough for rational egoism that, by design, no actions be contrary self-benefit (of a self worth benefitting). The requirement that all actions should intend primarily self-benefit should be dropped. In this way, one can love persons simply for the particular ends-in-themselves that they are.
~~~~~~~~~~~~~~~~
Those linked articles (and those excerpts just shown) are old one's of mine (2010). I've still some settling out to do, particularly on what are the most liberal restrictions on what could still be called ethical egoism, consistent with the long history and varieties of it in ethical theory.

Thank you for your post, Stephen B. I will comment on one part of it.
I think that interpretation is consistent with most, but not all, of what Ayn Rand wrote. I think my clause "but not all" can be based on a number of things she wrote, but I will limit myself to two. One is the passage in VoS quoted in the third post of this thread. Two is from Atlas Shrugged, p. 29, as follows. Taggart Transcontinental has lost a shipping contract with Ellis Wyatt to a competitor. Dagny Taggart: "We've lost the Wyatt oil fields" (p. 16). 
Dagny Taggart: "Ellis Wyatt is not asking anybody to give him a chance. And I'm not in business to give chances. I'm running a railroad." 
James Taggart: "That's an extremely narrow view, it seems to me. I don't see why we should want to help one man instead of a whole nation."
Dagny Taggart: "I'm not interested in helping anybody. I want to make money."
How is it that Dagny is not interested in helping Ellis Wyatt? She wishes that Taggart Transcontinental still had Ellis Wyatt as a customer. If that were still the case, her making money is helping herself, and she would be helping Ellis Wyatt achieve his goals. 
Returning to your passage I quoted, I like a little different wording, indicated by brackets: "an egoism in which some right actions are not [solely] for the actor’s [benefit], only [partly] so. [Partly], they could be for the [benefit] of one not oneself, nonetheless count as egoistic."
While X can help Y when X and Y are trading partners, X rationally helping Y is not limited to trading. For example, X and Y could be co-workers for the same firm Z. X and Y each have the same goal of Z's goal/success. Similarly, in basketball player X could assist his/her teammate Y to achieve their mutual goal of their team winning the game.