49
个编辑
更改
→逻辑和语义
==Logic and semantics==
==Logic and semantics==
===经典问题（Classic puzzles）===
====反事实的问题（The problem of counterfactuals）====
According to the material conditional analysis, a natural language conditional, a statement of the form ‘if P then Q’, is true whenever its antecedent, P, is false. Since counterfactual conditionals are those whose antecedents are false, this analysis would wrongly predict that all counterfactuals are vacuously true. Goodman illustrates this point using the following pair in a context where it is understood that the piece of butter under discussion had not been heated.
根据实质条件的分析，自然语言条件句即“如果p，那么q（if P then Q）”的陈述，只要其前件p为假就是真。由于反事实条件句是那些前置假设的条件句，这种分析会错误地预测所有反事实条件句都是虚假的。Goodman在理解到正在讨论的那块黄油没有被加热的情况下，用下面的一对例子来说明这一点。
If that piece of butter had been heated to 150º, it would have melted.
If that piece of butter had been heated to 150º, it would have melted.
如果那块黄油被加热到150度，它就不会融化。
如果那块黄油被加热到150度，它就不会融化。
More generally, such examples show that counterfactuals are not truth-functional. In other words, knowing whether the antecedent and consequent are actually true is not sufficient to determine whether the counterfactual itself is true.
More generally, such examples show that counterfactuals are not truth-functional. In other words, knowing whether the antecedent and consequent are actually true is not sufficient to determine whether the counterfactual itself is true.
更一般地说，这些例子表明反事实不具备真理功能。换句话说，知道前件和结果是否为真并不足以确定反事实本身是否为真。
====上下文依赖和含糊不清（Context dependence and vagueness）====
====The problem of counterfactuals====
Counterfactuals are ''context dependent'' and ''[[vague]]''. For example, either of the following statements can be reasonably held true, though not at the same time:<ref>{{Cite journal |last=Lewis |first=David |date=1979 |title=Counterfactual dependence and time's arrow |journal=Noûs |volume=13 |issue=4 |pages=455–476 |doi=10.2307/2215339 |jstor=2215339 |quote=Counterfactuals are infected with vagueness, as everyone agrees.|url=http://pdfs.semanticscholar.org/b736/55909cf4d6a54cd36c4ed449afbe71f3c44b.pdf }}</ref>
反事实是依赖于上下文且含糊不清的。例如，以下任一陈述都可以合理地成立，但不能同时成立：
If Caesar had been in command in Korea, he would have used the atom bomb.
If Caesar had been in command in Korea, he would have used the atom bomb.
# 如果凯撒（Caesar）当时在朝鲜指挥，他会使用原子弹。
If Caesar had been in command in Korea, he would have used catapults.
If Caesar had been in command in Korea, he would have used catapults.
# 如果凯撒在朝鲜指挥，他会使用弹弓。
====非单调性（Non-monotonicity）====
Counterfactuals are ''non-monotonic'' in the sense that their truth values can be changed by adding extra material to their antecedents. This fact is illustrated by ''[[Jordan Howard Sobel|Sobel sequences]]'' such as the following:<ref name="jstor.org"/><ref>{{cite journal |last1=Lewis |first1=David |date=1973 |title= Counterfactuals and Comparative Possibility |journal=Journal of Philosophical Logic |volume=2 |issue=4 |doi=10.2307/2215339|jstor=2215339 }}</ref><ref>{{cite book |last=Lewis |first=David |date=1973 |title= Counterfactuals |location=Cambridge, MA |publisher=Harvard University Press|isbn= 9780631224952}}</ref>
反事实是非单调的，因为它们的真值可以通过在其前件中添加额外的信息而改变。这一事实可以通过 Sobel 序列得到说明，例如：
If Hannah had drunk coffee, she would be happy.
If Hannah had drunk coffee, she would be happy.
If Hannah had drunk coffee and the coffee had gasoline in it, she would be sad.
If Hannah had drunk coffee and the coffee had gasoline in it, she would be sad.
If Hannah had drunk coffee and the coffee had gasoline in it and Hannah was a gasoline-drinking robot, she would be happy.
If Hannah had drunk coffee and the coffee had gasoline in it and Hannah was a gasoline-drinking robot, she would be happy.
# 如果汉娜喝了咖啡，她会很高兴。
# 如果汉娜喝了咖啡，而且咖啡里有汽油，她会很伤心。
# 如果汉娜喝了咖啡，咖啡里有汽油，而汉娜是一个喝汽油的机器人，她会很高兴。
# If Hannah had drunk coffee, she would be happy.
# If Hannah had drunk coffee and the coffee had gasoline in it, she would be sad.
# If Hannah had drunk coffee and the coffee had gasoline in it and Hannah was a gasoline-drinking robot, she would be happy.
One way of formalizing this fact is to say that the principle of ''Antecedent Strengthening'' should '''not''' hold for any connective > intended as a formalization of natural language conditionals.
One way of formalizing this fact is to say that the principle of ''Antecedent Strengthening'' should '''not''' hold for any connective > intended as a formalization of natural language conditionals.
对此事实进行形式化的一种方法是说，''前件增强（Antecedent Strengthening）''原则不适用于任何旨在作为自然语言条件句形式化的连接词>。
* '''Antecedent Strengthening''': <math> P > Q \models (P \land R) > Q </math>
* '''Antecedent Strengthening''': <math> P > Q \models (P \land R) > Q </math>
* '''前件增强''': <math> P > Q \models (P \land R) > Q </math>
===考虑可能存在的世界Possible worlds accounts===
=== Possible worlds accounts ===
The most common logical accounts of counterfactuals are couched in the [[possible world semantics]]. Broadly speaking, these approaches have in common that they treat a counterfactual ''A'' > ''B'' as true if ''B'' holds across some set of possible worlds where A is true. They vary mainly in how they identify the set of relevant A-worlds.
The most common logical accounts of counterfactuals are couched in the [[possible world semantics]]. Broadly speaking, these approaches have in common that they treat a counterfactual ''A'' > ''B'' as true if ''B'' holds across some set of possible worlds where A is true. They vary mainly in how they identify the set of relevant A-worlds.
反事实的最常见的逻辑解释是可能世界语义学。一般来说，这些方法的共同点是，如果B在A成立的某些可能世界中成立，那么它们就认为反事实 A > B为真。它们的主要区别在于如何确定相关A世界集的方式。
David Lewis's variably strict conditional is considered the classic analysis within philosophy. The closely related premise semantics proposed by Angelika Kratzer is often taken as the standard within linguistics. However, there are numerous possible worlds approaches on the market, including dynamic variants of the strict conditional analysis originally dismissed by Lewis.
大卫·刘易斯（David Lewis）严格可变的条件被认为是哲学中的经典分析。安吉利卡·克拉策（Angelika Kratzer）提出的紧密相关的前提语义常常被视为语言学中的标准。然而，市场上有许多可能世界的方法，包括最初被Lewis摒弃的严格条件分析的动态变体。
====严格的条件Strict conditional====
====Strict conditional====
The [[strict conditional]] analysis treats natural language counterfactuals as being equivalent to the [[modal logic]] formula <math>\Box(P \rightarrow Q)</math>. In this formula, <math>\Box</math> expresses necessity and <math>\rightarrow</math> is understood as [[material conditional|material implication]]. This approach was first proposed in 1912 by [[C.I. Lewis]] as part of his [[Axiomatic system|axiomatic approach]] to modal logic.<ref name="Counterfactuals"/> In modern [[relational semantics]], this means that the strict conditional is true at ''w'' iff the corresponding material conditional is true throughout the worlds accessible from ''w''. More formally:
The [[strict conditional]] analysis treats natural language counterfactuals as being equivalent to the [[modal logic]] formula <math>\Box(P \rightarrow Q)</math>. In this formula, <math>\Box</math> expresses necessity and <math>\rightarrow</math> is understood as [[material conditional|material implication]]. This approach was first proposed in 1912 by [[C.I. Lewis]] as part of his [[Axiomatic system|axiomatic approach]] to modal logic.<ref name="Counterfactuals"/> In modern [[relational semantics]], this means that the strict conditional is true at ''w'' iff the corresponding material conditional is true throughout the worlds accessible from ''w''. More formally:
严格条件分析将自然语言反事实视为等同于模态逻辑公式<math>\Box(P \rightarrow Q)</math>。在这个公式中， <math>\Box</math>表示必要性，<math>\rightarrow</math>被理解为实质条件。这种方法最早是在1912年由C.I. Lewis提出的，作为他对模态逻辑的公理化方法的一部分。
* Given a model <math>M = \langle W,R,V \rangle</math>, we have that <math> M,w \models \Box(P \rightarrow Q) </math> iff <math>M, v \models P \rightarrow Q </math> for all <math>v</math> such that <math>Rwv</math>
* Given a model <math>M = \langle W,R,V \rangle</math>, we have that <math> M,w \models \Box(P \rightarrow Q) </math> iff <math>M, v \models P \rightarrow Q </math> for all <math>v</math> such that <math>Rwv</math>
* 给定一个模型 <math>M = \langle W,R,V \rangle</math>, 对于所有 <math>v</math> 使得 <math>Rwv</math>， 当且仅当<math>M, v \models P \rightarrow Q </math> ，我们有 <math> M,w \models \Box(P \rightarrow Q) </math>。
Unlike the material conditional, the strict conditional is not vacuously true when its antecedent is false. To see why, observe that both <math>P</math> and <math>\Box(P \rightarrow Q)</math> will be false at <math>w</math> if there is some accessible world <math>v</math> where <math>P</math> is true and <math>Q</math> is not. The strict conditional is also context-dependent, at least when given a relational semantics (or something similar). In the relational framework, accessibility relations are parameters of evaluation which encode the range of possibilities which are treated as "live" in the context. Since the truth of a strict conditional can depend on the accessibility relation used to evaluate it, this feature of the strict conditional can be used to capture context-dependence.
与实质条件不同，严格条件在其前件为假时严格为真。要知道为什么，请观察，如果有一些可能世界math>v</math>，其中<math>P</math>为真，<math>Q</math>为假，那么<math>P</math>和 <math>\Box(P \rightarrow Q)</math>在<math>w</math>处都为假。严格条件也是依赖于上下文的，至少在给定关系语义（或类似的东西）时是如此。在关系框架中，可及性关系是评价的参数，它编码了在上下文中被视为 "活 "的可能性范围。由于严格条件的真实性可能取决于用来评价它的可及性关系，所以严格条件的这一特征可以用来捕捉上下文的依赖性。
The strict conditional analysis encounters many known problems, notably monotonicity. In the classical relational framework, when using a standard notion of entailment, the strict conditional is monotonic, i.e. it validates ''Antecedent Strengthening''. To see why, observe that if <math>P \rightarrow Q</math> holds at every world accessible from <math>w</math>, the monotonicity of the material conditional guarantees that <math>P \land R \rightarrow Q</math> will be too. Thus, we will have that <math> \Box(P \rightarrow Q) \models \Box(P \land R \rightarrow Q) </math>.
严格条件分析遇到了许多已知的问题，特别是单调性。在经典的关系框架中，当使用标准的蕴涵概念时，严格条件是单调的，也就是说，它验证了''前件增强''。要知道为什么，观察一下，如果<math>P \rightarrow Q</math>在每个来自<math>w</math>的世界上成立。那么物质条件的单调性保证了 <math>P \land R \rightarrow Q</math> 也将是如此。因此，我们将有<math> \Box(P \rightarrow Q) \models \Box(P \land R \rightarrow Q) </math>。
This fact led to widespread abandonment of the strict conditional, in particular in favor of Lewis's [[counterfactual conditional#Variably strict conditional|variably strict analysis]]. However, subsequent work has revived the strict conditional analysis by appealing to context sensitivity. This approach was pioneered by Warmbrōd (1981), who argued that ''Sobel sequences'' don't demand a ''non-monotonic'' logic, but in fact can rather be explained by speakers switching to more permissive accessibility relations as the sequence proceeds. In his system, a counterfactual like "If Hannah had drunk coffee, she would be happy" would normally be evaluated using a model where Hannah's coffee is gasoline-free in all accessible worlds. If this same model were used to evaluate a subsequent utterance of "If Hannah had drunk coffee and the coffee had gasoline in it...", this second conditional would come out as trivially true, since there are no accessible worlds where its antecedent holds. Warmbrōd's idea was that speakers will switch to a model with a more permissive accessibility relation in order to avoid this triviality.
这一事实导致了对严格条件的广泛放弃，特别是支持刘易斯的可变严格分析。然而，随后的工作通过对语境敏感性的诉求恢复了严格条件分析。这种方法是由Warmbrōd（1981）开创的，他认为''Sobel序列'' 并不要求非单调逻辑，而事实上，随着序列的进行，说话人可以切换到更宽松的可及性关系来解释。在他的系统中，像“如果Hannah喝了咖啡，她会很高兴”这样的反事实，通常会用Hannah的咖啡在所有可及世界中不含汽油的模型进行评价。如果这个模型被用来评估随后的“如果汉娜喝了咖啡，而咖啡里有汽油……”的话语，这个第二个条件就会被认为是微不足道的真实，因为没有任何可访问的世界的前件是成立的。Warmbrōd的想法是，说话人将转向一个具有更宽松的可及性关系的模型，以避免这种琐碎性。
Subsequent work by Kai von Fintel (2001), Thony Gillies (2007), and Malte Willer (2019) has formalized this idea in the framework of [[dynamic semantics]], and given a number of linguistic arguments in favor. One argument is that conditional antecedents license [[Polarity item#Determination of licensing contexts|negative polarity items]], which are thought to be licensed only by monotonic operators.
Subsequent work by Kai von Fintel (2001), Thony Gillies (2007), and Malte Willer (2019) has formalized this idea in the framework of [[dynamic semantics]], and given a number of linguistic arguments in favor. One argument is that conditional antecedents license [[Polarity item#Determination of licensing contexts|negative polarity items]], which are thought to be licensed only by monotonic operators.
Ginsberg (1986) has proposed a semantics for conditionals which assumes that the current beliefs form a set of [[propositional formula]]e, considering the maximal sets of these formulae that are consistent with ''A'', and adding ''A'' to each. The rationale is that each of these maximal sets represents a possible state of belief in which ''A'' is true that is as similar as possible to the original one. The conditional statement ''A'' > ''B'' therefore holds if and only if ''B'' is true in all such sets.<ref name="rev. no. 03011">{{Citation |title=Review of the paper: M. L. Ginsberg, "Counterfactuals," Artificial Intelligence 30 (1986), pp. 35–79 |url=https://zbmath.org/?q=an:0655.03011&format=complete |work=Zentralblatt für Mathematik |pages=13–14 |year=1989 |publisher=FIZ Karlsruhe – Leibniz Institute for Information Infrastructure GmbH |zbl=0655.03011}}.</ref>
Ginsberg (1986) has proposed a semantics for conditionals which assumes that the current beliefs form a set of [[propositional formula]]e, considering the maximal sets of these formulae that are consistent with ''A'', and adding ''A'' to each. The rationale is that each of these maximal sets represents a possible state of belief in which ''A'' is true that is as similar as possible to the original one. The conditional statement ''A'' > ''B'' therefore holds if and only if ''B'' is true in all such sets.<ref name="rev. no. 03011">{{Citation |title=Review of the paper: M. L. Ginsberg, "Counterfactuals," Artificial Intelligence 30 (1986), pp. 35–79 |url=https://zbmath.org/?q=an:0655.03011&format=complete |work=Zentralblatt für Mathematik |pages=13–14 |year=1989 |publisher=FIZ Karlsruhe – Leibniz Institute for Information Infrastructure GmbH |zbl=0655.03011}}.</ref>
== The grammar of counterfactuality ==
== The grammar of counterfactuality ==