关于三段论格的规则的性质和作用

近读两篇论及三段论格规则的论文,基本观点是:三级论总规则是三段论有效式的充分必要条件,而格的规则只是各格的必要条件,故主张废除。从理论上说,上述观点是正确的。但从运用上说,尤从初学者计,则大可不必。关键在上两文对格的规则的性质理解不确。第一格的AEE是无效的,从规则看,它有违总规则“前提中不周延的项在结论中不得周延”,犯了“大项扩大”错误;它又有违格的规则“小前提是肯定的”。不难发现,这两条规则性质相同,完全等值。后者之必要仅在“小前提是肯定”是“前提中不周延的项在结论中不得周延”规则在一格对大项的要求。同理,“大前提是全称的”规则是“中项至少周延一次”对的一格具体要求。     

周延理论难题及其解决方案

传统词项逻辑试图接纳亚里士多德逻辑不认可的负词项,但这使得传统词项逻辑成为了一个不一致的理论,原因是负词项的引入与传统的周延理论存在冲突。取消负词项的合法地位可以直接消解不一致性,但会极大缩小词项逻辑的表达与推理能力。因此,对周延理论进行怎样的修改才能使词项逻辑恢复一致并判定出全部有效三段论,是词项逻辑面临的一大难题。传统逻辑学家对该难题进行了一定的探索,但并没有产生一个公认可行的解决方案。现代逻辑学家对该难题的研究存在两种路径：一是在保留周延性传统内涵的基础上修改命题中词项周延性的四条规定,二是修改或删除周延性传统内涵以保留命题中词项周延性的四条规定。其中第二种路径可以与现代逻辑的研究成果相结合并进一步判定出接纳负词项的全部有效三段论,体现了词项逻辑中周延理论最前沿的发展趋势。解决该难题有助于完善逻辑学的理论,促进词项逻辑的进一步发展。     

漫话三段论规则

现在一般讲传统逻辑三段论的规则,第一条就是:一个三段论有且只有三个不同的概念作词项(直言命题的主谓项)。这实在不是三段论的规则,而是三段论定义的一部分.不是恰好有三个不同概念作词项的推理,就不是三段论(但不必不有效),它与三段论规则没有关系。三段论规则是三段论有效(正确)的充分必要条件.它们是: 一、中项至少周延一次.     

换质法的规则应当修订

换质法有两条规则,一曰改变判断的质,使结论与前提为不同质的判断;一曰结论谓项是前提谓项的矛盾概念。这是目前国内形式逻辑教材的普遍提法。然而笔者以为,第一条规则根本没有必要,应当取消;第二条规则不完全具备规则应有的性质,应当加以完善。     

字素-音素与词体-尾音对中国人英语语音加工的影响

研究采用命名任务,探讨了字素-音素对应规则与词体-尾音对应规则在英语假词和中高频真词读音中的作用.结果发现,中国被试同时采用字素-音素对应规则与词体-尾音对应规则命名假词和中高频真词,但是字素-音素对应规则对假词命名更重要.     

肯定判断的宾词有时周延吗?

李老师: 我是××中学的语文教师。为教好高中语文课本上的逻辑知识短文,我看了不少逻辑书。这些书讲直言判断(中学教材叫简单判断)中的名词周延问题时,都说“肯定判断的宾词不周延”。可是在概念章里讲定义的规则时,第一条又都说“定义要相应相称”。既然如此,主、宾词不就完全重合了吗?这个全称肯定判断的主词周延,宾词不也周延吗?既然“有的肯定判断的宾词周延”是真的,那么“肯定判断的宾词不周延”不就是假的了吗?除定义之外,有些释义(如,“冠就是帽子”),有的定理(如,“等腰三角形两底角相等”),也是这样,所以都可以简     

经典逻辑、自由逻辑与空词项

经典逻辑与自由逻辑都涉及空词项问题。经典逻辑对空词项采取的是一种否定的态度,它要求命题的"主词非空",在逻辑中排斥带有空词项的命题,从而导致经典逻辑与存在问题缠绕在一起。自由逻辑把空词项视为合法的逻辑词项,允许含有空词项的命题出现在逻辑系统中,并试图给包含空词项的命题以恰当的语义解释。自由逻辑对空词项的这一积极态度,带来了一系列逻辑和哲学上的好处。     

涵义语义与关于概称句推理的词项逻辑

概称句推理具有以词项为单位的特征并且词项的涵义在其中起到了重要的作用。已有的处理用A一表达式表达涵义,不够简洁和自然。亚里斯多德三段论是一种词项逻辑,但它是外延的和单调的。这两方面的情况使得有必要考虑新的词项逻辑。涵义语义的基本观点是：语词首先表达的是涵义,通过涵义的作用,语词有了指称,表达概念。概称句三段论是更为常用的推理,有两个基本形式GAG和Gaa。在涵义语义的基础上建立的系统GAG和Gaa是关于这两种推理的公理系统。     

特殊的加法

在加减乘除四则运算中加法是最简单的,其中有一条规则就是任何数加零还等于这个数,二加零还是二,无所失也无所得。可在举重比赛中,却有一套与此不同的特殊加法,任何数加零都等于零。发现这一秘密还是缘自于和朋友去观看一场举重比赛。在比赛现场,运动员馒头般鼓起的肌肉,力举千钧时的怒吼,都深深吸     

第二语言学习者形态复杂词的加工机制

大多数语言中, 形态复杂词所占的比例很高。形态复杂词形-义映射的规律性使得读者不仅能直接从心理词典中提取整词语义, 还可以利用形态规则来建构词语的语义。研究发现, 母语者可以利用形态规则来加工复杂词, 但第二语言(二语)学习者的研究结果存在较大的分歧, 且表现出和母语者不一样的结果模式。基于补充学习系统理论和情景性二语者假设, 我们尝试提出了二语形态复杂词加工机制的观点, 并据此解释研究分歧出现的原因。未来的研究需要探究词汇形态家族大小等因素对二语形态复杂词加工的影响, 以及揭示二语形态复杂词加工的神经机制。     

“中国逻辑”名称困难的辨析——“唯一的逻辑”引发的困惑与质疑

上世纪三十年代,金岳霖先生以欧洲传统演绎逻辑是唯一和普遍的逻辑学观念,对中国逻辑的研究提出了“中国逻辑”的名称能否成立的问题。否认逻辑与文化的联系,坚持逻辑的唯一性和欧洲传统演绎逻辑的唯一性与普遍性,这些是提出“中国逻辑”名称困难的依据。上述观点将会面对由逻辑学研究对象、逻辑学学科性质以及逻辑史所展示的事实所引发的诸多困惑与质疑。逻辑学的研究对象是逻辑思维。逻辑思维不是单纯的自然现象,而是属于人的精神世界。人的精神世界依附于人类的文化,即人的实践活动及其成果的总和。当人类文化呈现出多样性的统一状态时,包括逻辑思维在内的精神世界不仅有共性,也有由民族地域不同而显现的个性。在中国,先秦文化不同于古希腊文化,它的核心是伦理政治与社会人事,它的主要内容是伦理尺度与治国纲纪的构想、建立和实践,它的基本思维取向是现实的需要以及实践中的经验。以“类同”为依据进行“以类取,以类予”推演的“推类”,成为先秦时期逻辑思维中居主导地位的推理类型,同时也成为先秦逻辑学研究的主要内容。中国古代逻辑学是有别于欧洲传统演绎逻辑的。研究中国逻辑离不开对欧洲传统逻辑的借鉴,在这种借鉴研究中,应用比较法的关键有三：第一,被比较的诸对象都把与之相比较的对象视为平等的他者,而不是对立者或规范者;第二,在见其同异中,比较以见其相异乃更为重要。第三,对研究对象的异点给出制约因素的分析,就中国逻辑研究而言,就是“历史分析与文化诠释”。     

Frege on the generality of logical laws

Frege claims that the laws of logic are characterized by their “generality,” but it is hard to see how this could identify a special feature of those laws. I argue that we must understand this talk of generality in normative terms, but that what Frege says provides a normative demarcation of the logical laws only once we connect it with his thinking about truth and science. He means to be identifying the laws of logic as those that appear in every one of the scientific systems whose construction is the ultimate aim of science, and in which all truths have a place. Though an account of logic in terms of scientific systems might seem hopelessly antiquated, I argue that it is not: A basically Fregean account of the nature of logic still looks quite promising.     

The covering law model of historical explanation

It is often argued (as by Hempel and Nagel) that genuine historical explanations — if these are to be had — must exhibit a connection between events to be explained and universal or probabilistic laws (or ‘hypotheses'). This connection may take either a ‘strong’ or ‘weak’ form. The historian may show that a statement of the event to be explained is a logical consequence of statements of reasonably well‐confirmed universal laws and occurrences linked by the laws to the event to be explained. Or the historian may show that a statement of the event to be explained has high inductive probability conferred upon it given statements of reasonably well‐confirmed probabilistic laws and occurrences so linked by the laws to the type of event to be explained that one finds the occurrence of the particular event likely. This essay focuses on ‘strong’ explanations which meet a ‘deducibility’ requirement (for reasons given in the body of the article). It is argued that explanations in history (at least where it is plausible to construe them as ‘non‐rational') may meet a ‘deducibility’ requirement and count as genuine historical explanations although they do not meet a ‘covering law’ requirement (i. e. none of the premises of these explanations state universal or probabilistic hypotheses). It is required, however, that at least one premise in such explanations assert a reasonably well‐confirmed condition (e. g., a co‐variation) which can be taken as a sign or indication of the presence of laws. Rather than appealing to laws, the historian may appeal to the well‐founded possibility of laws.     

The Logicality of Language: A new take on Triviality, “Ungrammaticality”, and Logical Form*

Recent work in formal semantics suggests that the language system includes not only a structure building device, as standardly assumed, but also a natural deductive system which can determine when expressions have trivial truth‐conditions (e.g., are logically true/false) and mark them as unacceptable. This hypothesis, called the ‘logicality of language’, accounts for many acceptability patterns, including systematic restrictions on the distribution of quantifiers. To deal with apparent counter‐examples consisting of acceptable tautologies and contradictions, the logicality of language is often paired with an additional assumption according to which logical forms are radically underspecified: i.e., the language system can see functional terms but is ‘blind’ to open class terms to the extent that different tokens of the same term are treated as if independent. This conception of logical form has profound implications: it suggests an extreme version of the modularity of language, and can only be paired with non‐classical—indeed quite exotic—kinds of deductive systems. The aim of this paper is to show that we can pair the logicality of language with a different and ultimately more traditional account of logical form. This framework accounts for the basic acceptability patterns which motivated the logicality of language, can explain why some tautologies and contradictions are acceptable, and makes better predictions in key cases. As a result, we can pursue versions of the logicality of language in frameworks compatible with the view that the language system is not radically modular vis‐á‐vis its open class terms and employs a deductive system that is basically classical.     

The square of opposition — A new approach

Summary The theory of the square of opposition has been worked out many centuries ago as a part of Aristotelian logic of terms.In spite of its inexactness (for instance it is not possible to decide whether the termsquare of opposition is a logical or a metalogical term) this theory is included without any changes in the usual elementary course of logic.The author defines the square of opposition in the language of the logic of propositions (see Def. 1.000) and derives from this definition the usual laws of the square of opposition and several new theorems.     

What is the axiomatic method?

The modern notion of the axiomatic method developed as a part of the conceptualization of mathematics starting in the nineteenth century. The basic idea of the method is the capture of a class of structures as the models of an axiomatic system. The mathematical study of such classes of structures is not exhausted by the derivation of theorems from the axioms but includes normally the metatheory of the axiom system. This conception of axiomatization satisfies the crucial requirement that the derivation of theorems from axioms does not produce new information in the usual sense of the term called depth information. It can produce new information in a different sense of information called surface information. It is argued in this paper that the derivation should be based on a model-theoretical relation of logical consequence rather than derivability by means of mechanical (recursive) rules. Likewise completeness must be understood by reference to a model-theoretical consequence relation. A correctly understood notion of axiomatization does not apply to purely logical theories. In the latter the only relevant kind of axiomatization amounts to recursive enumeration of logical truths. First-order “axiomatic” set theories are not genuine axiomatizations. The main reason is that their models are structures of particulars, not of sets. Axiomatization cannot usually be motivated epistemologically, but it is related to the idea of explanation.     

Ecosystems and society: Implications for sustainable development

Human systems are interacting with, and dependent on, the global ecosystem. These complex interconnected systems have to obey natural laws and system laws in order to remain viable in the long‐term. “Sustainable development” therefore has to adhere to certain principles and constraints which derive partially from physical conditions, partially from principles of (evolving) ecosystems, partially from principles applying to human systems with conscious actors and normative standards. Although “sustainable development” constrains the spectrum of permissible processes, it does not define a final steady state. The development process must be guided by reference to an ethical principle and to the balanced satisfaction of the basic orientors resulting from a system's interaction with its environment. The systems perspective required encompasses a wide range of scientific disciplines, for which a comprehensive bibliography is provided.     

Measurability And Physical Laws

I propose and motivate a new account of fundamental physical laws, the Measurability Account of Laws (MAL). This account has a distinctive logical form, in that it takes the primary nomological concept to be that of a law relative to a given theory, and defines a law simpliciter as a law relative to some true theory. What makes a proposition a law relative to a theory is that it plays an indispensable role in demonstrating that some quantity posited by that theory is measurable. In Section 1, I motivate the project of seeking a philosophical account of fundamental physical laws, as opposed to laws of nature in general. In Section 2, I motivate seeking an account with the distinctive logical form of the MAL. In Section 3, I present the MAL and illustrate the way it works by applying it to a simple example.     

What Is It to Make Clear the Working of Our Language?1

In The Logical Basis of Metaphysics, Dummett articulates and develops his “fundamental assumption” that the introduction rules for a logical constant determine its meaning. According to Dummett, logical laws in harmony with the introduction rules are justified, while logical laws not in harmony with the introduction rules are unjustified. This powerful picture enables Dummett to criticise certain aspects of our linguistic practice, such as the Law of Excluded Middle and the metaphysics of realism he believes it embodies, as not remaining responsible to the meanings of the logical constants. Against Dummett's fundamental assumption, I bring to bear what in the Tractatus Wittgenstein describes as his “fundamental thought” that the logical constants do not represent. Properly understood, Wittgenstein's point is that since the logical constants may be eliminated from the propositional signs of a fully precise logical notation, the constants do not express meanings to which our use of expressions containing the constants is responsible. I then apply Wittgenstein's fundamental thought to Dummett's proof‐theoretic notation to show that far from determining the meanings of the logical constants, the introduction rules merely allow the constants to be edited from certain inferences, leaving Dummett with no semantic kernel with which to criticise other sentences or inferences featuring the constants. Thus, his picture of what it is to make clear the working of our language collapses.