第五講直言命題及其真假關(guān)系

1、第五講第五講 直言命題及其直言命題及其真假關(guān)系真假關(guān)系 A definition by genus and difference assigns a meaning to a term by identifying genus term and one or more difference words that, when combined, convey the meaning of the term being defined. In logic, genus simply means a relatively larger class, and species means a relat

2、ively smaller subclass of the genus. Genus and species are merely relative classification. Specific difference or difference, for short, is the attribute or attributes that distinguish the various species within a genus. The first step is to identify a genus, next we must identify a specific differe

3、nce. Summary There are rules that govern the construction of lexical definitions. Such definitions should conform to grammatical standards, convey the essential meaning of the word being defined, be neither too broad nor too narrow, avoid circularity, avoid negative, figurative, obscure, vague, ambi

4、guous, and affective language, and indicate the context to which the definitions pertains. The Rules of Division:1. A division must be exhaustive. This rule may also be expressed by saying that the constituent species must be together equal to the “totum divisum”.2. The constituent species of the ge

5、nus must exclude each other.3. A division must proceed at every stage, and so far as possible through all its stage, upon one principle, or fundamentum divisionis例例 1. 1. （所有的）美滿婚姻都是以愛情為基礎(chǔ)（所有的）美滿婚姻都是以愛情為基礎(chǔ)的婚姻。的婚姻。 2.2. 任何民主國(guó)家都不是世襲制國(guó)家。任何民主國(guó)家都不是世襲制國(guó)家。3. 3. 有的美籍華人是諾貝爾獎(jiǎng)獲得者。有的美籍華人是諾貝爾獎(jiǎng)獲得者。 4.4. 有的哺乳動(dòng)物不是胎

6、生的。有的哺乳動(dòng)物不是胎生的。5.5. 帕瓦羅蒂是世界著名的男高音歌唱家。帕瓦羅蒂是世界著名的男高音歌唱家。 6.6. 徐志摩不是自然死亡。徐志摩不是自然死亡。* * * * * * *直言命題直言命題Categorical Propositions 1、定義。、定義。2、構(gòu)成：主項(xiàng)、構(gòu)成：主項(xiàng)S；謂項(xiàng)；謂項(xiàng)P；聯(lián)項(xiàng)（質(zhì)）；量項(xiàng)；聯(lián)項(xiàng)（質(zhì)）；量項(xiàng)（量）。（量）。The Components of Categorical Propositions: subject term，predicate term， copula(quality)，quantifier(quantity) 3、邏輯形式：所

7、有的（有的）、邏輯形式：所有的（有的）S是（不是）是（不是）P。4、 種類：種類：1）全稱肯定：所有的）全稱肯定：所有的S是是P。 SAP A2）全稱否定：所有的）全稱否定：所有的S不是不是P。 SEP E3）特稱肯定：有的）特稱肯定：有的S是是P。 SIP I4）特稱否定：有的）特稱否定：有的S不是不是P。 SOP O A proposition is a sentence that is either true or false. A proposition that relates two classes, or categories, is called a categorical p

8、roposition. The classes in question are denoted respectively by the subject term and the predicate term, and the proposition asserts that either all or part of the class denoted by the subject term is included in or excluded from the class denoted by the predicate term. The quality of a categorical

9、proposition is either affirmative or negative depending on whether it affirms or denies class membership. The quantity of a categorical proposition is either universal or particular depending on whether the statement makes a claim about every member or just some member of the class denoted by the su

10、bject term. The statement “Some S are P” does not imply that some S are not P, and the statement “Some S are not P” does not imply that some S are P. Since the early Middle Ages the four kinds of categorical propositions have commonly been designated by letter names corresponding to the first vowels

11、 of the Roman alphabet: A,E,I,O. Tradition has it that these letters were derived from the first two vowels in the Latin words affirmo (“I affirm”) and nego (“I deny”).Proposition meaning in class notation All S are P. (universal affirmaive)Every member of the S class is a member of the P class; tha

12、t is, the S class is included in the P class. No S are P.(universal negative) No member of the S class is a member of the P class; that is, the S class is excluded from the P class Some S are P.(particular affimative) At least one member of the S class is a member of the P class. Some S are not P.(p

13、articular negative) At least one member of the S class is not a member of the P class. Kinds of Categorical Propositions5、AEIO項(xiàng)的周延性項(xiàng)的周延性 項(xiàng)周延性項(xiàng)周延性命題種類命題種類SPSAPSEPSIPSOP欽差大臣?xì)J差大臣 Distribution is an attribute of the terms (subject and predicate) of propositions. A term is said to be distributed if the p

14、roposition makes an assertion about every member of the class denoted by the term; otherwise, it is undistributed. Stated another way, a term is distributed if and only if the statement assigns (or distributes) an attribute to every member of the class denoted by the term. Universal statements (A an

15、d E) distributed their subject terms and negative statements (E and O) distributed their predicate terms.Distribution思考題：指出下列直言命題主謂項(xiàng)的周延情況思考題：指出下列直言命題主謂項(xiàng)的周延情況1、心理學(xué)是研究人的精神活動(dòng)的科學(xué)。、心理學(xué)是研究人的精神活動(dòng)的科學(xué)。2、科學(xué)理論都是實(shí)踐的產(chǎn)物。、科學(xué)理論都是實(shí)踐的產(chǎn)物。3、所有等邊三角形都是等角三角形。、所有等邊三角形都是等角三角形。4、自然科學(xué)不是上層建筑。、自然科學(xué)不是上層建筑。5、有些水生動(dòng)物不是用鰓呼吸的。、有些水生動(dòng)物

16、不是用鰓呼吸的。6、有些農(nóng)民是發(fā)明家。、有些農(nóng)民是發(fā)明家。7、各行各業(yè)都有不稱職的干部。、各行各業(yè)都有不稱職的干部。8、沒有金屬不導(dǎo)電。、沒有金屬不導(dǎo)電。9、不能說所有社會(huì)現(xiàn)象都有階級(jí)性、不能說所有社會(huì)現(xiàn)象都有階級(jí)性10、并非所有的水稻是多年生植物。、并非所有的水稻是多年生植物。A：所有的國(guó)會(huì)議員都是律師。：所有的國(guó)會(huì)議員都是律師。E：所有的國(guó)會(huì)議員都不是律師。：所有的國(guó)會(huì)議員都不是律師。I： 有的國(guó)會(huì)議員是律師。有的國(guó)會(huì)議員是律師。O：有的國(guó)會(huì)議員不是律師。：有的國(guó)會(huì)議員不是律師。6、主謂項(xiàng)相同的、主謂項(xiàng)相同的AEIO之間的真假關(guān)系之間的真假關(guān)系SPPSPSS PSP三角形、內(nèi)角三角形、內(nèi)角

17、和等于和等于180度的度的多邊形多邊形邏輯學(xué)邏輯學(xué)家、哲家、哲學(xué)家學(xué)家脊椎動(dòng)物、脊椎動(dòng)物、胎生動(dòng)物胎生動(dòng)物草原動(dòng)物、食草原動(dòng)物、食草動(dòng)物草動(dòng)物博士、文盲博士、文盲SAPSAP：全同、真包含于；：全同、真包含于； SEPSEP：全異；：全異；SIPSIP：全同、真包含于、真包含、交叉；：全同、真包含于、真包含、交叉；SOPSOP：真包含、交叉、全異。：真包含、交叉、全異。主謂項(xiàng)外延間關(guān)系：主謂項(xiàng)外延間關(guān)系：主謂項(xiàng)相同的主謂項(xiàng)相同的AEIO之間的真假關(guān)系之間的真假關(guān)系 外延外延命題命題全同全同真包含真包含于于真包含真包含交叉交叉全異全異SAP+-SEP-+SIP+-SOP-+主謂項(xiàng)相同的主謂項(xiàng)相同

18、的AEIO之間的真假關(guān)系之間的真假關(guān)系 外延外延命題命題全同全同真包含真包含于于真包含真包含交叉交叉全異全異SAP+-SEP-+a) 反對(duì)關(guān)系：反對(duì)關(guān)系： AE。 不同真不同真，可同假；，可同假；A：所有的國(guó)會(huì)議員都是律師。：所有的國(guó)會(huì)議員都是律師。E：所有的國(guó)會(huì)議員都不是律師。：所有的國(guó)會(huì)議員都不是律師。主謂項(xiàng)相同的主謂項(xiàng)相同的AEIO之間的真假關(guān)系之間的真假關(guān)系 外延外延命題命題全同全同真包含真包含于于真包含真包含交叉交叉全異全異SIP+-SOP-+b)下反對(duì)關(guān)系：下反對(duì)關(guān)系： IO?？赏妫??？赏?，不同假不同假；I： 有的國(guó)會(huì)議員是律師。有的國(guó)會(huì)議員是律師。O：有的國(guó)會(huì)議員不是律師。：

19、有的國(guó)會(huì)議員不是律師。主謂項(xiàng)相同的主謂項(xiàng)相同的AEIO之間的真假關(guān)系之間的真假關(guān)系 外延外延命題命題全同全同真包含真包含于于真包含真包含交叉交叉全異全異SAP+-SOP-+c) 矛盾關(guān)系：矛盾關(guān)系： AO。不同真，不同假；不同真，不同假；A：所有的國(guó)會(huì)議員都是律師。：所有的國(guó)會(huì)議員都是律師。O：有的國(guó)會(huì)議員不是律師。：有的國(guó)會(huì)議員不是律師。主謂項(xiàng)相同的主謂項(xiàng)相同的AEIO之間的真假關(guān)系之間的真假關(guān)系 外延外延命題命題全同全同真包含真包含于于真包含真包含交叉交叉全異全異SEP-+SIP+-c) 矛盾關(guān)系：矛盾關(guān)系： EI。不同真，不同假；不同真，不同假；E：所有的國(guó)會(huì)議員都不是律師。：所有的國(guó)會(huì)

20、議員都不是律師。I： 有的國(guó)會(huì)議員是律師。有的國(guó)會(huì)議員是律師。主謂項(xiàng)相同的主謂項(xiàng)相同的AEIO之間的真假關(guān)系之間的真假關(guān)系 外延外延命題命題全同全同真包含真包含于于真包含真包含交叉交叉全異全異SAP+-SIP+-d) 差等關(guān)系：差等關(guān)系： AI。可同真，可同假，?？赏?，可同假，全稱真特稱真，特稱假全稱假全稱真特稱真，特稱假全稱假A：所有的國(guó)會(huì)議員都是律師。：所有的國(guó)會(huì)議員都是律師。I： 有的國(guó)會(huì)議員是律師。有的國(guó)會(huì)議員是律師。主謂項(xiàng)相同的主謂項(xiàng)相同的AEIO之間的真假關(guān)系之間的真假關(guān)系 外延外延命題命題全同全同真包含真包含于于真包含真包含交叉交叉全異全異SEP-+SOP-+d) 差等關(guān)系：差

21、等關(guān)系： EO?？赏妫赏?，?？赏?，可同假，全稱真特稱真，特稱假全稱假全稱真特稱真，特稱假全稱假E：所有的國(guó)會(huì)議員都不是律師。：所有的國(guó)會(huì)議員都不是律師。O：有的國(guó)會(huì)議員不是律師。：有的國(guó)會(huì)議員不是律師。a) 反對(duì)關(guān)系：反對(duì)關(guān)系： AE， 不同真不同真，可同假；，可同假；b)下反對(duì)關(guān)系：下反對(duì)關(guān)系： IO， 可同真，可同真，不同假不同假；c) 矛盾關(guān)系：矛盾關(guān)系： AO、EI不同真，不同假；不同真，不同假；d) 差等關(guān)系：差等關(guān)系： AI、EO可同真，可同假，可同真，可同假，全稱真特稱真，特稱假全稱假全稱真特稱真，特稱假全稱假AEIO（不同真）（不同真）反對(duì)反對(duì)contrary下反對(duì)下反

22、對(duì)subcontrary（不同假）（不同假）矛盾矛盾Contradictory（不同真不同假）（不同真不同假）Subalternation差等差等差等差等Subalternation真真真真假假假假 The Traditional Square of Opposition The four relations in the traditional square of opposition may be characterized as follows: Contradictory=opposite truth value Contrary=at least one is false (not

23、both true) Subcontrary=at leas one is true (no both false) Subalternation=truth flows downward, falsity flows upward已知下列命題為真，寫出素材相同的其余有一已知下列命題為真，寫出素材相同的其余有一個(gè)命題，并根據(jù)對(duì)當(dāng)關(guān)系指出它們的真假。個(gè)命題，并根據(jù)對(duì)當(dāng)關(guān)系指出它們的真假。1、三班的同學(xué)都是學(xué)英語(yǔ)的。、三班的同學(xué)都是學(xué)英語(yǔ)的。2、有的蛇是無毒的。、有的蛇是無毒的。3、這輛車上的人都不是去長(zhǎng)城的。、這輛車上的人都不是去長(zhǎng)城的。4、有的學(xué)生不是黨員。、有的學(xué)生不是黨員。5、所有有生的都

24、是有死的。、所有有生的都是有死的。6、外商在我國(guó)的投資不是不受法律保護(hù)。、外商在我國(guó)的投資不是不受法律保護(hù)。7、我班沒有一個(gè)會(huì)下國(guó)際象棋的。、我班沒有一個(gè)會(huì)下國(guó)際象棋的。8、從事司法工作的并非都是律師。、從事司法工作的并非都是律師。已知下列命題為真，寫出素材相同的其余有一已知下列命題為真，寫出素材相同的其余有一個(gè)命題，并根據(jù)對(duì)當(dāng)關(guān)系指出它們的真假。個(gè)命題，并根據(jù)對(duì)當(dāng)關(guān)系指出它們的真假。1、價(jià)格昂貴的商品都是質(zhì)量好的商品。、價(jià)格昂貴的商品都是質(zhì)量好的商品。2、有的金屬是絕緣體。、有的金屬是絕緣體。3、所有的蛇不是有毒的。、所有的蛇不是有毒的。4、有的哺乳動(dòng)物不是脊椎動(dòng)物。、有的哺乳動(dòng)物不是脊椎動(dòng)

25、物。5、所有的質(zhì)數(shù)都是奇數(shù)。、所有的質(zhì)數(shù)都是奇數(shù)。6、沒有生產(chǎn)資料是商品。、沒有生產(chǎn)資料是商品。7、北京市的公民人人都有自行車。、北京市的公民人人都有自行車。8、這輛公共汽車的乘客并非都是大學(xué)生。、這輛公共汽車的乘客并非都是大學(xué)生。 A categorical proposition is a proposition that relates two classes (or categories). Standard-form categorical proposition occur in four forms and are composed of a quantifier (“all”,

26、 “no”, “some”), a subject term, a copula (“are”, “are not”) and a predicate term. A Standard-form categorical proposition has either affirmative or negative quality, depending on whether it joins or separates the subject and the predicate classes, and universal or particular quantity, depending on w

27、hether it relates all or only part of the subject class to the predicate class. Summary (1) The subject and predicate terms are said to be distributed or undistributed depending on whether the proposition makes an assertion about all or only a part of the class denoted by the term in question. Each standard-form proposition is given a letter name (A,E,I,O) that reflects its quantity and quality. The traditional square of opposition applies to the Aristotelian interpretation of categorical proposition; it shows how each kind of proposition rel