2第二讲 科学推理

• Arguagement 8
– All X are Y; – All a are X; – All a are Y.
2.2 valid arguments
• the notions of validity and truth • a. validity applies to arguments and only to arguments, not to statements. • b. validity signifies a certain relationship between a group of statements and one other statement, and this relationship depends on the contents of the premises and the conclusion rather than on their truth or falsity. • the validity of an arguagement usually comes from its form rather than from its content.
1.1 what is a hypotheses
• Greeks: Hypotheses is the starting point of a debate. • us：Hypotheses is a statement which we doubt its truth status.——relativity • hypotheses are statements of assertions and judgments, their essential characteristic is that the are either true of false. • empirical hypotheses: hypotheses whose truth of falsity would make a difference in what we should expect in our experience. • hypotheses and fact • scientific statement and metaphysical statement.
2 deductive reasoning
• the study of the notion of deduction and associated notions such as logical consequence, consistency, and contradiction belongs to the discipline know as deductive logic. • deduction is a kind of argument. • an argument has two components: the premises and the conclusion. • P1, P2, P3, ...→ C • read as "P1, P2, P3, ...therefore C."
– – – – Angle A1 contained in semicircle K1 is a right angle; Angle A2 contained in semicircle K2 is a right angle; Angle A3 contained in semicircle K3 is a right angle; All angles contained in semicircles are right angles.
• Arguagement 4
– All isosceles(等腰) triangles have equal base angles. – The angle sum of any triangle is two right angles. – All angles contained in semicircles are right angles.
– assessment of reasonableness: reasonable or unreasonable
2.2 valid arguments
• Arguagement 5
– All humans are mortal; – All Greeks are humans; – All Greeks are mortal.
2.1 assessment of arguments
• Areguagement 1
– – – – Apple A1 when unsupported falls downward; Apple A2 when unsupported falls downward; Apple A3 when unsupported falls downward; All apple when unsupported falls downward.
1.3 logic of indirect test
• from hypothesis to implication • H→I • if H is true, then I is true. But I is found to be false. therefore, H is false. • if H is true, then I is true. I is indeed found to be true. therefore there are some grounds for the truth of H. • H: the figure is a square. • I: it has 4 corners.
第一格 MP SM 第二格 PM SM 第三格 MP MS 第四格 PM MS
SP
SP
SPSPLeabharlann • 三段论的格，三段论的式
2.4 演绎法的意义
• 演绎的可靠性与前提、结论的真假无关，演绎法只是一个 概念游戏。 • 演绎法的前提不能通过演绎得到，演绎出来的结论已经包 含在前提之中，所以演绎法不能产生新知识。 • 所以，演绎法没有实际意义？ • 首先，演绎法是科学阐述的主要方式； • 其次，演绎法也是理论检验的必要手段； • 最后，演绎法可以发现新的规律、提出新的概念。
3 inductive reasioning
• • • • • • 老师第一周点名了； 老师第三周点名了； 老师第五周点名了； 老师第七周点名了； …… 老师每逢单周点名，所以我们单周不能跷课。
3 inductive reasioning
• • • • • • • • • • 西方哲学史总共点了两次名； 中国哲学史总共点了两次名； 马克思主义哲学史总共点了两次名； 西方哲学原著总共点了两次名； 中国哲学原著总共点了两次名； 马克思主义哲学原著选读总共点了两次名； …… 所以，科学技术哲学总共也会点两次名。 老师已经点了两次名了； 所以他不会再点名了。
• but not
– true premises and false conclusion
P T T F F Q T F T F P→Q T F T T
2.3 演绎法的一个误区
• 演绎法是从一般到个别的推理。 • A=B， B=C， 则A=C；这是从一般到个别吗？ • • • • • 关于三段论 A：所有S均为P； E：所有S均为非P； I：有的S为P； O：有的S为非P；
Basic Types of Reasoning in Science
主讲人：万小龙、冉奎
本节内容
• • • • hypotheses：假说是科学推理中的一个基本概念。 deductive Reasoning：演绎推理 inductive Reasoning：归纳推理 statistical and Probabilistic Reasoning：概率推理
2.1 assessment of arguments
• deductive arguagements and inductive arguagements • a deductive arguagement claims that the premises provide conclusive grounds or reason for the acceptance of the conclusion.
• Arguagement 2
– – – – Matter attracts matter; Apples are matter; The earth is matter; All apples are attracts by earth.
2.1 assessment of arguments
• Arguagement 3
– assessment of validity: valid or invalid
• a inductive arguagement claims that the premises provide some grounds for the acceptance of the conclusion.
• Arguagement 7
– All tigers are mortal; – All Greeks are tigers; – All Greeks are mortal.
• Arguagement 6
– All humans are lions; – All Greeks are humans; – All Greeks are lions.
3.1 induction by simple enumeration
2.2 valid arguments
• from argument 5-7, we know that valid arguments allow the following possibilities:
– (i) true premises and true conclusion – (ii) false premises and false conclusion – (iii) false premises and true conclusion
1 hypotheses
• • • • • • • • • everything is made of water. matter is continuous and infinitely divisible. the earth is fixed at the center of the universe. the earth moves around a stationary sun. light is made up of little particles. light is made up of waves. it will rain tomorrow. it rained last night. it is raining now.
1.2 problems of hypotheses
• motivations: explain things; unify phenomena. • problem of discovery • problem of justification
– direct test: match the given hypothesis with reality • "the tower of Pisa is red." – indirect test: comparing a logical consequence of the hypothesis with reality. • "the earth is round." • logical consequence: the shadow of the earth is round. – 严格来说，没有绝对的直接检验，这种区分是相对的。