Wikipedia:Reference desk/Archives/Humanities/2008 December 25

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December 25

Subject area: philosophy, reasoning, logic. "in the limit where x goes to y"

I'm wondering if there is theoretical/philosophical understanding/definition of forming a logical argument in which something is logically deduced using a construct like "While most of the time A is equal to B, in the limit as (some feature) x (of A and of B) goes to a value (some limiting value/instance) y, A is not equal to B, so it can not be said absolutely that A is equal to B." If so, what would I look under? I've spent hours searching the web, but only find examples of authors using the construct, and nothing really about the syllogistic aspects of the construct.

In fact the case I'm trying to understand a little better is slightly more complicated than the case outlined above. The real problem is closer to: If A is a necessary condition for C, and B is a necessary condition for C, (and assume (A and B) are sufficient for C), where A is a 'driving force,' and where B is 'means' that requires A to produce C, it is known that in the limit as A goes to 0, C cannot result, so it can not be said that B causes C. These kinds of arguments seem to made without invoking any formality. They're "intuitively obvious." But not everyone understands what is trying to be accomplished by trying to use the construct/logic, and I don't know anywhere on the web where I can send someone for a better understanding. blackcloak (talk) 05:53, 25 December 2008 (UTC)

As you posed it, it appears to me in somehow too a large generality to fit into a precise category. What is x and what kind of dependence from x have you in mind? An example could help. I assume here you mean x is a time, but I would also distinguish whether "most of the time" just means "a period of time" or "all values y<x". In the first case I'd say that a bifurcation has occurred. It means here that the evolution of A in time, although possibly very regular, is not determined just by x and its states in the past. The second case means discontinuity (of either A or B or both) at the time x, for continuous dependence is what allows you to extend the equality also at the time $x$. --PMajer (talk) 15:43, 25 December 2008 (UTC)

I am indeed trying to find out something about the formalism of logical argument. It is a general subject, but someone must have tried to develop a set of "rules" to avoid obvious pitfalls. While the actual problem involves "invisible" quantities, let me present a simple physical close equivalent. Consider the elementary problem of an ideal spring (no loss of energy) attached to a mass on one end and a force being applied to the other end of the spring (let the mass be on a frictionless table). A force is applied and the mass moves (the result). So what caused the mass to move? My A is the force. My B is the spring. My C is the observation that the mass moves. Some say that B causes C. I argue (after stating that both A and B are necessary conditions, and taken together are a sufficient condition) that because in the limit as A goes to 0, C does not happen. Therefore B is not a sufficient condition for C, so it is improper to say that B causes C. Now I understand that there are a whole lot of issues around the use terms that have unequal "value." I don't want to get back a list of all the errors I've made in formulating a particular problem. My question has to do with a formal process of correctly formulating cause/effect arguments with the "in the limit" construct. Perhaps all I'm looking for is a tutorial on formal ways of stating cause and effect problems. Maybe it's just a matter of finding a description of how to impose strict constraints on what can be identified as a cause and what can be identified as a result. blackcloak (talk) 21:13, 25 December 2008 (UTC)

I'm not clear on what you mean by "in the limit", but you may be interested in the article on probabilistic causation on the Stanford Encyclopedia of Philosophy website, [1]. It's been emotional (talk) 16:52, 27 December 2008 (UTC)

I'm not interested in probabilistic forms, so the article did not really help. But, it is by far the best article I've seen on the general subject of cause and effect arguments. It has the level of rigor I'm looking for. Thanks. "In the limit" arguments are made all the time when trying to answer general questions about the result that will occur when something is allowed to happen (a cause)- such as changing the temperature of something. There is usually an implied assumption of linearity (actually, monotonicity) (the effect gets "worse" as the magnitude of the cause continues to change in the initial direction). There may also be an implied assumption that something highly non-linear (e.g. some kind of runaway event) does not happen. If you need a simpler example than the one above, just ask and I'll provide one. blackcloak (talk) 05:09, 28 December 2008 (UTC)

On what basis is the potential unfairness of Social Security defended?

While Social Security is portrayed as an 'insurance' program, some people believe the program is effectively regressive, especially at lower earnings levels.

Although the payout formula is nominally progressive, payouts for low earners are effectively much less so, and possibly regressive. due to shorter lifespans and lower marriage rates among low earners. For example, some have noted that black men as a group get an especially poor deal from Social Security, since their life expectancy is (or was, at the time such claims originated) only months beyond the age at which they can start collecting full retirement benefits; not to mention their low marriage rates which result in relatively fewer qualified widow(er)s and children to collect survivor benefits.

As a lifetime low earner, I consider my likelihood of surviving to full retirement age dubious. What do advocates of the program say to people like me? It has got to suck to pay in for decades and live on the economic margin and then die with an effective total loss of your 'contributions.' —Preceding unsigned comment added by Boomerpdx (talk • contribs) 06:09, 25 December 2008 (UTC)

Suppose you are 18 in 2008 and get a job earning $20,000 a year. Suppose also that you get a cost of living increase (3%) every year and retire at 66. According to the Social Security Administration's calculations, your monthly SS retirement benefit will be $5,152. Sounds like a lot, *but* if the government had not taken out social security taxes from your paycheck and instead allowed you to invest the money yourself (let's assume you put the money in bonds -- pretty safe -- yielding 7% interest), by the time you retired, your private retirement account would pay you $6,370 per month. That's more than 20% better than SS. It gets worse: As you say, when you die, you lose SS but you would not lose a private retirement account (it goes to your heirs). That makes the private retirement account worth about 140% more than SS. Not done yet: Repeated economic studies indicate that the half of the SS tax paid by employers really comes out of the employee's pay (the employer just reduces the amount he pays the worker by the amount of SS tax the employer has to pay). That means that, if SS tax were eliminated, workers wages would rise by around 7% *in addition* to the 7% workers would no longer have to pay to SS. That makes a private retirement account -- even for lower income workers -- worth around 400% what SS is worth. Wikiant (talk) 16:19, 25 December 2008 (UTC)

Of course, there's also the (likely) possibility that Social Security won't exist when your hypothetical wage-earner gets to retirement--the entire system is predicated on low life expectancy and a continually growing workforce, neither of which is currently true. The chance that Social Security could fail or be scaled back raises the 400% expected value of individual retirement accounts even higher (depending on how likely this failure/reduction is within the wage-earner's lifespan). Theoretically if the government actually invested the contributions as described above there would be sufficient funding, but relying on politicians to set aside money for retirement is like relying on foxes to guard the chicken coop. I certainly don't expect to recover one cent I've 'invested' in Social Security, which makes the 14% 'tax' ageist in addition to racist and sexist. —Preceding unsigned comment added by 76.11.230.33 (talk) 16:58, 25 December 2008 (UTC)

If you do the math, you'll find that social security is an expected net negative for everyone except the *extremely* low income people (i.e., annual income circa $15,000). So, from the start, one can deem it unfair in that the system forces almost everyone to invest in a sub-optimal retirement fund. Social security is also (de facto) discriminatory by race. Because blacks have a lesser expected life span, and because social security benefits cease upon death (unlike private retirement accounts that become the property of the heirs on the death of the retiree), social security ends up transferring wealth from blacks to whites (and, similarly, from men to women). Wikiant (talk) 12:02, 25 December 2008 (UTC)

"Very low income" people (defined as those below 30% of median income) might have an expected net positive return, but people in this group typically have shorter-than-median lifespans, hence the concerns of total loss and negative return. Nominally progressive payouts are of no value to those who die prematurely. —Preceding unsigned comment added by Boomerpdx (talk • contribs) 06:10, 26 December 2008 (UTC)

Another regressive aspect is that poorer people tend to start working at an earlier age. —Tamfang (talk) 19:47, 27 December 2008 (UTC)

Social security also pays out disability income which often far exceeds the amount the person ever paid in. Some of the 3,700 folks who started collecting the first Old Age Insurance payments in February 1940 really made out like bandits, since they had paid in for the minimum period and collected for decades. Ida Fuller only paid in $24.75, but lived to be 100 and collected $22,888. If the program were ever phased out, the truly unfortunate would be those millions who paid in all their working life and did not get a meaningful payout. "Privitizing" by allowing younger workers to invest in private investment accounts rather than their input going to pay out the benefits for the retired, would be such a phaseout. At present, it keeps 40% of Americans over 65 out of poverty. But over the lifetime of the program, the age to collect has been lowered and the payments have been increased, since giving away more money is popular in election years. Edison (talk) 20:22, 25 December 2008 (UTC)

Pulleys first used in the British Isles

When did the concept of complex pulleys begin to become popular in the British Isles? Tiailds (talk) 07:45, 25 December 2008 (UTC)

Not sure how you want to define "popular" here. We know that the Greeks and Romans used block and tackle systems on winch cranes and treadmill cranes - see the History of cranes section in our crane (machine) article. So complex pulleys were certainly used in Roman Britain. I don't know whether this technology was widely known in pre-Roman Britain. Gandalf61 (talk) 11:27, 26 December 2008 (UTC)

Some theories of the building of Stonehenge rely on this technology. Xn4 (talk) 10:47, 31 December 2008 (UTC)

Atheism in American politics

Double-whammy.

1. What sacred text would an atheist use in inaugurations?

2. What officially atheist politicians have there been in the US federal or state government, who were known publicly to be atheists at the time they held the position? I have a friend who believes there are none. This is outrageously impossible considering the number of politicians who have passed through positions over the years.

99.245.92.47 (talk) 12:06, 25 December 2008 (UTC)

Easy answer to 1: surely nothing. The Constitution says virtually nothing about presidential inaugurations — Calvin Coolidge swore the constitutionally-required oath of office in front of his father, a local official in Vermont, and that by itself was sufficient for him taking office. I'm sure that federal law discusses inaugurations, but I don't think that there is anything that is required, except the oath of office — and surely there's nothing requiring a religious text, for such would blatantly violate the First Amendment. Therefore, the only way you could answer the first question except by saying "He/she wouldn't use one" would be to ask the atheist.

On your second question, I can't tell you for sure, but I'd actually not be surprised if your friend were correct. The USA is much more religious overall than many other developed countries, and I've heard it said that avowed atheism would be a major political liability, as large numbers of religious people would be opposed to an avowed atheist for that reason alone. Look at the place religion plays in American politics, how politicians (especially presidents and presidential candidates) speak of their religion. I remember during the troubles of the Clinton era, how many conservative Christians saw Clinton's religious activities as highly hypocritical (Clinton's admitted actions that were the basis of the Lewinsky scandal really don't accord with the Bible), and thus opposed him for religious reasons. If Clinton's actions received so much flak for religious reasons from those who believed that he wasn't truly a Christian (although never questioning that he was somewhat religious), imagine how much religious opposition any atheist would receive! All this is not to say "no atheist has ever held major elected office", but it's highly unlikely that one has held office who was known publicly to be an atheist at the time s/he held the position. Nyttend (talk) 13:24, 25 December 2008 (UTC)

List of atheists (politics and law) has a couple of American governors, but no recent ones... Adam Bishop (talk) 14:06, 25 December 2008 (UTC)

That’s got to be one of the best sourced lists we have! --S.dedalus (talk) 21:30, 25 December 2008 (UTC)

I wonder how many are there in this list...--PMajer (talk) 14:59, 25 December 2008 (UTC)

Pete Stark, California congressman, atheist. --jpgordon^∇∆∇∆ 16:37, 25 December 2008 (UTC)

I thought my logic was good...apparently the evidence demonstrates that it wasn't good enough. Thanks for coming up with concrete examples! Nyttend (talk) 17:33, 25 December 2008 (UTC)

At least as far as the popes, I can assure you none. How could someone become pope if they disavowed God? Unlike many liberal Protestant churches, the Catholic Church has never been open to having prominent leaders who challenge its core doctrines, and everybody was professedly Christian during times when the Papacy was being fought over for political reasons. Nyttend (talk) 17:35, 25 December 2008 (UTC)

Well, no Pope was openly atheist, of course, but as to the inner religious feelings of a Pope, as well as the feelings of any other politician, we may well doubt whether there is any correspondence with what he declares. Note that I say this with the greatest admiration for the men of the Church, beginning with a genius like St.Paul who had the idea of starting the enterprise. They lasted 2000 years, so they know what they do... You ask: How could an atheist become Pope? If I knew the answer, for sure I would try to become Pope myself!--PMajer (talk) 21:11, 25 December 2008 (UTC)

I agree that both politicians and popes can and do sometimes believe otherwise than they openly state (I seriously doubt the faith of the popes of the Pornocracy), but the IP's original question regarded those who are openly atheists: that's why I said "(dis)avowed". Nyttend (talk) 00:13, 26 December 2008 (UTC)

I'm an atheist American, though not eligible for the presidency (for two different reasons, in addition to being non-religious!), but I shall answer anyway: I would place my hand on an original copy of the Constitution of the United States of America, which in my view should be the only sacred document for an incoming president. --Sean 00:19, 26 December 2008 (UTC)

Good job Sean; until reading your answer, I thought the IP meant "which sacred text would be read at the ceremony"? It's important to remember (as you plainly do; I'm not criticising you) that placing one's hand on a Bible is only tradition, and "so help me God", always spoken at the end of the oath, is not required by the Constitution. Nyttend (talk) 02:47, 26 December 2008 (UTC)

This question prompted me to research my own state constitution. The Preamble to the North Carolina State Constitution starts with "We, the people of the State of North Carolina, grateful to Almighty God, the Sovereign Ruler of Nations, for the preservation of the American Union and the existence of our civil, political and religious liberties..." Wait a minute. Grateful to God... for the preservation of... religious liberties. What bible were they reading? I don't remember the bible presenting God as being very accepting of differing views. Oh, wait a minute! Preservation of one particular group's religious liberties! Hmm... this isn't looking good. Let's see what else the state constitution has to say. ARTICLE I (DECLARATION OF RIGHTS) Sec. 19. (Law of the land; equal protection of the laws) states, in part, "No person shall be denied the equal protection of the laws; nor shall any person be subjected to discrimination by the State because of race, color, religion, or national origin." Okay, no person shall be subjected to discrimination by the state because of religion. Well, then, what am I to make of article VI? ARTICLE VI (SUFFRAGE AND ELIGIBILITY TO OFFICE) Sec. 8. (Disqualifications for office) states, in part, "The following persons shall be disqualified for office: First, any person who shall deny the being of Almighty God." It seems that the state constitution ensures equal protection and non-discrimination by the state, unless you're an atheist or belong to a religion that does not recognize the Christian God. I wonder if anyone who has attained public office in North Carolina has ever tried to challenge that? 152.16.16.75 (talk) 11:18, 26 December 2008 (UTC)

As a fellow Tarheel, I encourage you to unbunch your panties! States can put whatever backward-ass stuff they want in their laws and constitutions, but the US Constitution is the supreme law of the land, so this kind of stuff doesn't even pass the sniff test. See No religious test clause and Torcaso v. Watkins. --Sean 15:37, 26 December 2008 (UTC)

I guess the humorous, tongue-in-cheek nature of my previous comment was lost on Sean. 152.16.59.190 (talk) 23:17, 26 December 2008 (UTC)

When was Jesus born?

Jesus wasn't born on Dec 25th right? Or even in December for that matter. Do we know when he was really born? ScienceApe (talk) 16:01, 25 December 2008 (UTC)

We don't know; the Bible gives no real indication. There's only one exception: I've heard it said that the idea of shepherds watching their flocks by night in the fields would be impossible in the winter, however, so anytime in December would be impossible. I've never seen a scientific study done on when ancient Jewish shepherds would be out in the fields with their flocks, but the idea sounds reasonable enough to me that I believe that Jesus was born in the spring, summer, or autumn. Nyttend (talk) 17:32, 25 December 2008 (UTC)

He was born in Bethlehem right? Does it get cold there in December? ScienceApe (talk) 21:48, 25 December 2008 (UTC)

So I've heard. Interesting, googling bethlehem december weather yields nearly 1.5 million hits, so you're not the only one asking this question. This church website quotes various authorities, including an Israeli meteorologist, to state that the area frosts overnight in December; assuming that they understood reliable sources properly, there's good reason to believe that the weather would be too cold. This website proposes the end of September; I don't have time to read it, so I don't know why they advocate it. Have fun reading the explanation if you feel like it. Nyttend (talk) 00:19, 26 December 2008 (UTC)

Please see [2] for an explanation of some of the historical difficulties. These difficulties are simplified where there is no belief in the birth or the person, of course. In short, believe what you will; we do not know. ៛ Bielle (talk) 20:10, 25 December 2008 (UTC)

No one knows the time of year for sure, but its fairly certain he was born in 4 BC.--GreenSpigot (talk) 02:02, 26 December 2008 (UTC)

Also Shepherds watching their flocks and wise men is probably also bullshit used to garnish the story.--GreenSpigot (talk) 02:17, 26 December 2008 (UTC)

Depends which gospel you read. Matthew says he was born in the reign of Herod the Great, who died in 4 BC. Luke says he was born at the time of the census when Quirinius was governor of Syria, and that was in AD 6. The two gospel accounts of the Nativity are very different in a number of ways. Just about all they agree on is that he was born in Bethlehem in Judea, the son of Mary and supposed son of Joseph, and grew up in Nazareth in Galilee. --Nicknack009 (talk) 01:53, 31 December 2008 (UTC)

There's also the Star of Bethlehem, which has proven rich fodder for many scientific types who equate it to a comet, supernova, conjunction of planets or what have you, and have tried dating his birth from that perspective. There's no consensus on the exact date, and there likely never will be. -- JackofOz (talk) 22:38, 29 December 2008 (UTC)