2第二讲 科学推理
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第一格 MP SM 第二格 PM SM 第三格 MP MS 第四格 PM MS
SP
SP
SP
SP
• 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。
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.
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."
• Arguagement 2
– – – – Matter attracts matter; Apples are matter; The earth is matter;源自文库All apples are attracts by earth.
2.1 assessment of arguments
• Arguagement 3
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.
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；
– – – – 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.
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。
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.
• 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.
– assessment of validity: valid or invalid
• a inductive arguagement claims that the premises provide some grounds for the acceptance of the conclusion.
• 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.
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
1.1 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.
– assessment of reasonableness: reasonable or unreasonable
2.2 valid arguments
• Arguagement 5
– All humans are mortal; – All Greeks are humans; – All Greeks are mortal.
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
3.1 induction by simple enumeration
• 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.
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.
SP
SP
SP
SP
• 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。
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.
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."
• Arguagement 2
– – – – Matter attracts matter; Apples are matter; The earth is matter;源自文库All apples are attracts by earth.
2.1 assessment of arguments
• Arguagement 3
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.
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；
– – – – 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.
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。
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.
• 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.
– assessment of validity: valid or invalid
• a inductive arguagement claims that the premises provide some grounds for the acceptance of the conclusion.
• 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.
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
1.1 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.
– assessment of reasonableness: reasonable or unreasonable
2.2 valid arguments
• Arguagement 5
– All humans are mortal; – All Greeks are humans; – All Greeks are mortal.
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
3.1 induction by simple enumeration
• 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.
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.