A Counterexample to Horseshoe Analysis of Indicatives

The horseshoe analysis identifies indicatives as having the same semantic content with material conditionals. But is that right? Look at the following conditional:

C: "If I ate one and only one egg this morning, I ate two eggs this morning."

C is obviously false, actually necessarily false. But suppose I did not eat any egg this morning. Then, given the horseshoe analysis, C is true because it has a false antecedent and false consequent. So the horseshoe analysis is committed to treating something necessarily false as true. This I take to be evidence against the horseshoe analysis.

Of course, a horseshoe analysis may retort to my example this way. Since I know that I didn't eat any egg this morning and indicative conditionals do not tolerate known-to-be false antecedents, C is inappropriate. But this reply may commit the horseshoe analysts to much bigger problems, I reckon.

Tricky conditionals

First, to get started, do you think the following two conditionals are contrapositives to each other?

(1) If he made a mistake, then it was not a big one.
(2) If he made a big mistake, then he did not make any mistake.

These two have been used by some as evidence that indicative conditionals in real life do not abide by the inference of contraposition. What do you think?

There is a huge number of tricky conditionals, couples or singles. Here is a really interesting and really tricky one:

(R): If Reagen was a KGB, no one would ever know it.

You can opt to replace the "know' in the consequent with anything you like, "believe", "find out", "think of", etc. (I actually can't think of more that makes sense.)

This conditional is intended by some as evidence against the Ramsey test. But, alas, as I see people do such things, I am wondering inside of me whether they are sincerely naive or they are sophisticated animals intending to make the water ever blurrier. The operator of the consequent--"no one would ever know"--is a modal operator! It's as much a modal operator as devices like "Shakespeare believed", "Necessarily it is the case that", "It is morally obligatory that", etc. (Don't get me wrong. This time I do have a lot of backups reserved in my mind. Sorry, a bit overly alert to etcs.) Should we not separate out modal operators when we are analyzing truth conditions of a logical connective like "if"? We did so when we defined truth-functional connectives like "or", "only if", "and", etc. (I am silent this time.)

Conditional decision theory versus Causal decision theory

I've been trying to understand Creation by building models for it. These models center around the process of divine deliberation (maybe not in the usual sense of 'process'). How does God deliberate on which world to create? The guiding idea is that there is a number of possible creative acts God can take each of which will lead to the actualization of one particular world. The deliberation ends when God decides to choose a particular creative act which will lead to the actualization of one certain world. After this decision being made, God starts performing the chosen creative act and "Boom!" Creation begins.

But how exactly should we understand the relation between creative acts and the worlds they are connected with. In the above passage, I used the phrase 'lead to'. It is ambiguous. Most obviously, there is a causal relation between divine creative acts and the worlds they are connected with. But there are also conditional relations between creative acts and the actualization of the worlds they are connected with. I say 'conditional relations' because there are different kinds of conditionals. When God deliberates over the decision about which world to actualize, He may balance the alternative creative acts in terms of their causal relations to the actualization of worlds, or in terms of their conditional relations to the actualization of worlds. And these two ways of balancing creative acts may lead to different results, even when we assume that God holds the same preference scale about all the worlds. So an important issue here is which decision theory should we take God to be using (a bit of over-theorizing, isn't it?)--the conditional decision theory or the causal decision theory?

I start with the conditional decision theory. So given this picture, God balances and compares the possible creative acts in terms of the benefits from the actualization of worlds that are conditional over their performance. But what kind of conditional relation is involved here? Strict? Material? Indicative? Or subjunctive? These are the major conditionals I have in mind. And these are the ones I will explore for the potential of being used in modeling deliberation.

After exploring the conditional decision theory, I will start looking at its alternative--the causal decision theory.

First test of Intro to Logic

We had our first test this past Friday. The average score is around 81. Among the seventeen taking the test, eight people surpass 90; five are below 60. The rest are in between. I'm not sure what I should do to those who failed the test. Should I give them a chance to make up their low scores? Another puzzle for a new teacher.

A dip into astrology

金牛－射手
金牛座：射手座配对指数：　　友情：★★★★　　爱情：★★★　　婚姻：★★　　亲情：★★★
谈情必读：
　　如果你们选择要在一起，首先一定要非常了解对方，因为大有可能你们是由友情转化成爱情，在一起前你们并没有看清楚是否是自己所要的。金牛座不要以为和射手座的人一起挺开心的，他教你好多好玩的事便就是爱情。　　本质上你们两个是相反的人，一个内向一个外向，一个实际一个虚浮，一个动一个静，射手座不爱留在家，金牛座就家庭至上。两人差得这么远，勉强对方做自己那一套，大家都只会不开心。明白这点之后，再认真想清楚是否要在一起？决定了吗？决定了就别再后悔了，加油！
金牛决不会改变他们缓慢而稳定的步伐，因此如果这两个星座的人在一起时，只有射手座有时会停一会儿。
　　由于射手座的标志是半人半马怪，所以他们之间的关系总是令人愉快的。几乎每位射手座人都渴望得到与旅行有关的职业，而且他们中的大多数都以这种或那种方式得到了。当射手座人用他们马的部分，或他们的标志马尾巴来扮演小丑或快乐的达观者时，金牛觉得他们特别有意思。金牛座人对射手座人的滑稽剧大叫，挑他们说话的毛病，取笑他们的蹄子。
　　但当射手座人的身躯出现时，金牛座人会感到困惑和生气。当金牛座人看到射手座人作为一个严肃的理想主义都出现，或审判室、教室、电视屏幕、政治讲坛上激烈辩论时，他们就不知道是欢呼好还是害怕好了。
　　此刻木星的献身精神会使射手座对现有的权力机构展开激烈斗争，这将会使较为保守的金牛座感到不安，并使他们在惊讶中一边后退，一边问自己：“这个像喝醉了的梦游人一样走来走去、朝着社会坚实稳固的风车冲刺的怪东西是谁啊？”一匹笨拙但有时又是优雅的赛马可能是相当可爱的，并能银铃般的笑声，但是一个威胁要揭露令人舒适的日常惯例中的问题的理想主义者却完全是危险的。金牛座想不出怎样才能合情合理地同一个被比赛刺激得非常鲁莽的射手打交道(但愿他输了，因为如果你赢了，他将给你更多的关切——但射手很幸运，他们几乎总是赢家)。
　　每一位射手(包括外向的和内向的)从骨子里就是一位眼睛发光尾巴浓密的乐观主义者，他们由衷地相信一切事情都有好的结果，如果不这样，他们就会流下大滴感人的眼泪——在金牛看来，这种乐观使他(或她)对生活的期望值过高了。
　　金牛则是眼睛清澈，尾巴平滑的悲观主义者，他们从不期望一切事情都会有好的结局——因此当他们在洗衣房丢了双袜子时，他们就会不断设想出种种消极的可能性。射手不愿意与情绪眼泪或许是非常充沛的，但当永存的木星彩虹将光辉撒在他们肩头并用希望的色彩照耀他们时，他们的眼泪很快就会止住。
　　这就是6—8日宫型，它强调贡献、健康和一切神秘感。因为对金牛来说，射手代表“别人的钱”(这种关系与日宫其他星座间的关系都不样)。射手可能成为金牛筹集资金来实现他们目标的人，因为金牛代表工作、责任、奉献的占星术第6宫，所以金牛与射手常常在某些共同的事业中合作，这事业把木星的推销和游说能力与金牛建立稳固基础的能力结合起来(这一点在射手的期望没有实现尤为重要)。金牛欣赏射手所描绘的令人振奋的图景，但当射手的绘画笔法对讲求实际的金牛来讲过于明快、色调过于绚丽夺目时，金牛就会感到人安并持怀疑态度了。
　　射手座人到处飘游，经常犯错误和摔跟头，但他们不愿意因纯粹、十足的运气而跌跤，正像他们不愿倒栽葱地摔进打开的阴沟一样。他们跌跤是由于他们出色的自信、勇气和乐观——他们摔进阴沟则是由于被挡住了视线。当你盯着天空，射出希望之箭，却不看看你跳到什么地方时，你掉进沟里的可能性自然就增大了。
　　金牛经常盯着地面，因此他们能帮助射手发现打开的阴沟和其他等着他们跌人的陷阱。他们俩可以在股票市场或任何种类的赌博冒险中结成一个战无不胜的组合。如果他们的太阳——月亮和谐的方面，那么他们很快可以成为百万富翁。事实上，他们在完成任何包括钱(不论是他们自己的或是别人的)的任务时，不管是出售水果和蔬菜，还是销售外国的运动卡，他们都将合作得很好。你可以在任何地方，从电影制作到饲养赛马，从报界到教堂发现这种合作(大部分金牛在宗教信仰上相当教条，通常他们恪守童年时的宗教，而所有射手都有强烈的——尽管有时是纠缠不清的——宗教特色)。
　　金牛一般都和家庭保持密切联系。金牛会为他(或她)所爱的人作出许多牺牲，会为他们顶住一大堆麻烦。射手也乐于从一定距离之外向他们的亲戚伸出援助之手，或说些让人高兴的话，典型的射手和他们的家庭成员在经济上互不依靠。射手对整个人类的善良比对关注血缘关系更感兴趣。马就是这样的，对吧？对，而且半人半马的射手也是如此。
　　这两种人都能一眼就认出一个伪君子或骗子，他们也都有愿意为了挽回面子或仅仅为了礼貌撒谎。金牛通常会坚定而清晰地讲出他们所见的真相。然而如果他们认为这样作确实会伤害某个人的话，他们就会闭口不语(如果这件事并不急迫)，而不会惹出不必要的麻烦。射手却不会这样勉强自己。所有的射手都有某种诚实——令人难受的诚实。真相有时会伤害人，但射手在义愤填膺时，不愿意了解这点。希望他们抑制他们那木星的正直是没用的，但他们或许会稍稍改变一点儿。
　　射手跳来跳去，实实在在地对待生活和人们，他们播撒快活，有时他们也会发怒，但一般情况下他们是和蔼而有耐心的。然而不幸的是，当冲动的射手长时间面对和蔼和耐心时，却往往会发怒了。有时对射手来说，死板而谨慎的金牛简直慢慢像群蜗牛。
　　然而，如果这两个星座的人决意参加一场赌博，并把金牛的聪明、常识与射手的运气和逻辑结合在一起，他们就太有可能赚大钱了。赚钱的消息会响亮而清晰地传到他们耳中。金牛会把钱存入银行，射手会让钱继续生钱。
　　金牛座(女)——射手座(男)
　　他在那儿，快活地跳上跳下，像个典型的木星橡皮球，想着他将对交一位美妙的新朋友。而且既然她是一位女士，那么，谁知道呢？也许随之而来的是妙不可言的做爱，或基至更好些，也许是陪伴终生的纯精神友情。既然射手如此喜欢事情的真相，现在就是他应该在胆面对真相的时候了。如果她是位金牛座姑娘，那么她心里既不想成为他的朋友，又不想成为随便性生活的伙伴。她在心中为自己设计了另外的角色。
　　看到这种局面的射手可能会装出很吃惊的样子，而且对自己嘟囔：“这是什么意思？”她是什么意思，这局面是什么意思？这这意思是结婚，就是如此，他不应该这么惊讶。作为一位因自己的诚实而感到自豪的射手座男士，面对风流韵事可以非常灵活。他可能认为在这场他叫作“现在恋爱，然后分手”的游戏中，他永远能赢，但如果他的对手是金牛座的，那他最好是准备输——既输了游戏，也失去她。
　　金牛座女人有极为充分的理由与射手座男人恋爱。他是个理想主义者，一个在她情绪低落时的快活伴侣，一个机智的谈话对象，一个梦想家，一个达观者，一个机敏的商人——和一个需要照看的男孩子。你没指望金牛座女士能抵挡住这样一位男人的进攻。很自然的是，甚至当他直截了当地告诉她第一夜是怎么回事时，她都听不见。她的头脑在云中飘游，在他撒播的热情上漫步。射手的激情是有感染力。但有时他忘了他是火焰宫的。你知道火焰是干什么的？它会燃成大火，熊熊烈火。如果他不想被自己的火烧焦，他就必须使火冷下来——否则就会被她土地宫的气愤所埋葬。当他点燃了她的爱火，而后又不能把火熄灭时，她的愤怒就会雪崩一般落到他头上。
　　金牛座女人在恋爱时至少会满足于成为永久情妇或普通的合法妻子，尽管她并不喜欢二者中的任何一种情况，而且只能是勉强度日。她所希望的是成为射手的女眷。她并不像狮子座或白羊座姑娘那样不合逻辑地嫉妒。然而她是占有型的，这就是说她对爱的理解是排他的。这位女士永远不会接受别人的建议。一位金牛座女士若没有很好的理由不会怀疑她的男人，但她也会给他几尺绳子，让他把自己拴住。
　　事实上，这位男士能够非常忠实于他真正爱的女人。他的问题在于作了错误的选择，从而失去适宜的伴侣。首先，他的坦率和直言不讳的方式对金牛座女性来讲似乎是真诚和有益的。他的不会虚伪也有同样的效果。她不会对一个说谎者或骗子浪费一丁点时间，因此她欣赏他的诚实，直到有一天(或有一夜)，他以讨厌的明了对她说：“宝贝儿，如果我们从一开始就平等相待的话，我们就能有好多次机会出去旅游了。比如，昨天我碰见的那个老朋友，她希望我和她一道去山里度周末。你知道我是那么喜欢滑雪。在我回来之前，你能找到什么事解闷儿吗？”当射手是如此诚实时，她可能要用滑雪板敲他的头来解闷儿了。

Anne Graham Lotz

I have been fortunate enough to be in Anne Graham Lotz's audience for the last two days. She is the best orator I have seen personally in my life. My wife was with me throughout the whole process, and she left the site with a similar impression. It was a great experience for us!

A logical puzzle from the Internet

Gavagai has three boxes with fruits in his barn: one box with apples, one box with pears, and one box with both apples and pears. The boxes have labels that describe the contents, but none of these labels is on the right box.

The Question: How can Gavagai, by taking only one piece of fruit from one box, determine what each of the boxes contains?