The Scandal of Deduction and Aristotle’s Method for Discovering Syllogisms

Rhizomata ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 289-311
Author(s):  
Matthew Duncombe
Keyword(s):  
Deductive Argument

Abstract (1) If a deductive argument is valid, then the conclusion is not novel. (2) If the conclusion of an argument is not novel, the argument is not useful. So, (3) if a deductive argument is valid, it is not useful. This conclusion, (3), is unacceptable. Since the argument is valid, we must reject at least one premise. So, should we reject (1) or (2)? This puzzle is usually known as the ‘scandal of deduction’. Analytic philosophers have tried to reject (1) but have assumed premise (2). I argue here that Aristotle would deny (2). Aristotle thinks that at least some deductive arguments are useful, even though they present no new conclusions. Thus, Aristotle’s view contrasts with analytic philosophers of logic, who assume that all useful deductive arguments present novel conclusions. I don’t claim that Aristotle ‘solves’ the problem: it was never posed in Aristotle’s time. Rather, I suggest that Aristotle does not face the problem because he assumes deductions can be useful, without presenting novel conclusions. Aristotle’s view of deduction tames the scandal.

The basic issue surrounds whether the law has been broken. We have been told Mary has been charged with theft under s 1 of the Theft Act. We are to assume that the three statements provided containing all of the information in this scenario have been produced just for us to read and work on. For the purposes of this exercise we will assume that these statements were produced in ways not calling into doubt their admissibility or credibility. This means therefore that we only have to concentrate on their probative value. (What do they prove?) The seven point approach of Twining and Miers will be used. 1 Standpoint: the standpoint of the Chart is that of the author of this book demonstrating the Wigmore Chart Method for the purposes of demonstrating the method and argument construction. 2 Stages 2, 3 and 4: relate to setting up the propositions and then key listing and charting. The impossibility of approaching each task in an isolated way is immediately perceived as we are going to work from statements. We have to find out the facts before we can draft the UP, PP, and interim probanda. Task: so that you can appreciate the levels of analysis go back to the statements and highlight the key words and phrases that begin to allow you to break into them and locate the story, and the law. Then try to give answers to the following questions: (1) What are the relevant facts? (2) What key phrases in the statements give you clues as to the application of the law? (3) Can you construct the deductive argument for the prosecution? (4) Can you construct the inductive argument for the prosecution? (5) Can you construct the opposing inductive argument for the defence? (6) Are there any conditions of doubt in your mind surrounding the wording of s1(1) of the Theft Act which may apply? (For example questions surrounding the presence of both mens rea and actus reus.) DO NOT PROCEED UNTIL YOU HAVE ANSWERED QUESTIONS (1)–(6).

2012 ◽  
pp. 253-254
Keyword(s):  
Key Words ◽  
Levels Of Analysis ◽  
Mens Rea ◽  
Key Words And Phrases ◽  
Deductive Argument ◽  
Inductive Argument ◽  
Probative Value ◽  
Actus Reus ◽  
The Law ◽  
Key Phrases

Proof Frames of Preservice Elementary Teachers

1989 ◽  
Vol 20 (1) ◽  
pp. 41-51 ◽  
Author(s):  
W. Gary Martin ◽  
Guershon Harel
Keyword(s):  
Elementary Teachers ◽  
Mathematical Proof ◽  
Preservice Elementary Teachers ◽  
Deductive Argument ◽  
Inductive Argument ◽  
Mathematics Course

This study asked 101 preservice elementary teachers enrolled in a sophomore-level mathematics course to judge the mathematical correctness of inductive and deductive verifications of either a familiar or an unfamiliar statement. For each statement, more than half the students accepted an inductive argument as a valid mathematical proof. More than 60% accepted a correct deductive argument as a valid mathematical proof; 38% and 52% accepted an incorrect deductive argument as being mathematically correct for the familiar and unfamiliar statements, respectively. Over a third of the students simultaneously accepted an inductive and a correct deductive argument as being mathematically valid.

Making Geometry A Personal And Inventive Experience

1982 ◽  
Vol 75 (6) ◽  
pp. 442-446
Author(s):  
Richard G. Brown
Keyword(s):  
Mathematics Teaching ◽  
Major Goal ◽  
Deductive Argument ◽  
Personal Process

A major goal of mathematics teaching is the involvement of our students in the personal process of discovering mathe- matical ideas and formulating problems. Students who use educated guesses to solve a problem or to judge whether another student’s hunch is correct are committing themselves to an exhilarating process. This process of an inductive leap followed by a deductive argument has been used during the centuries in the growth of mathematics.

Bringing Politics into SAI

2017 ◽  
Vol 31 (4) ◽  
pp. 501-506 ◽  
Author(s):  
Sikina Jinnah ◽  
Douglas Bushey
Keyword(s):  
The Political ◽  
Climate Engineering ◽  
Deductive Argument ◽  
Ethical Argument ◽  
Political Implications ◽  
Politics And Law ◽  
Complex Subject

AbstractIn order to advance a neatly deductive argument, Christopher J. Preston must make a number of assumptions and framing decisions that exclude important practical points from the scope of his analysis. We do not criticize him for doing so, as these simplifications allow him to advance a concise argument about an ethically complex subject. However, as scholars of politics and law, we are interested in what this ethical argument means—and does not mean—for the messy politics of climate engineering. Accordingly, in our response we unpack the political implications of some of Preston's assumptions and framing decisions in an effort to add a layer of practical richness to the abstraction of Preston's analysis.

scholarly journals Personal and Objective Ethics: How to Read the Crito

Philosophy ◽  
2021 ◽  
pp. 1-24
Author(s):  
Hiroshi Ohtani
Keyword(s):  
Moral Imagination ◽  
Deductive Argument ◽  
Personal Story ◽  
Objective Understanding ◽  
First Time ◽  
Cora Diamond

Abstract Dominant interpretations of Plato's Crito attempt to reconstruct the text deductively, taking the arguments in the famous Laws’ speech as consisting solely in the application of general principles to facts. It is thus conceived that the principles and facts are grasped independently of each other, and then the former are applied to the latter, subsequently reaching the conclusion that Socrates must not escape. Following the lead of Cora Diamond, who argues against this ‘generalist interpretation’, I argue that the Laws’ speech essentially involves an exercise of our moral imagination through which both principles and the facts to which they apply are grasped. This is not to say that a deductive argument is absent from the Laws’ speech. Rather, for the first time, we understand how the deductive arguments in the Laws’ speech can function through imagining a life in which these arguments make sense. The Crito is an attempt to exercise the readers’ imagination, thereby presenting ethics that is both personal and objective. Understanding the Laws’ arguments essentially requires the readers’ imaginative involvement with Socrates’ personal story, but they still have objective import.

Necessity Lost

2019 ◽  
Author(s):  
Sanford Shieh
Keyword(s):  
Analytic Philosophy ◽  
Logical Positivism ◽  
Bertrand Russell ◽  
Gottlob Frege ◽  
Deductive Argument ◽  
Analytic Tradition

A long tradition, going back to Aristotle, conceives of logic in terms of necessity and possibility: a deductive argument is correct if the truth of its conclusion follows necessarily from the truth of its premises or, put differently, if it is not possible for the conclusion to be false when the premises are true. A relatively unknown feature of the analytic tradition in philosophy is that, at its very inception, this venerable conception of the relation between logic and modality was put into question. The founders of analytic philosophy, Gottlob Frege and Bertrand Russell, held that there are no genuine distinctions among the necessary, the possible and the actual. In this first of a two-volume book, I investigate the grounds and consequences of this anti-modal position. The grounds lie in doctrines on truth, thought, and knowledge, as well as on the relation between mind and reality, that are central to the philosophies of Frege and Russell, and are of enduring philosophical interest. The main consequence is that logic is fundamental, and, to be coherent, modal concepts would be reconstructed in logical terms. This rejection of modality in early analytic philosophy remains of contemporary significance. The coherence of modal concepts is rarely questioned nowadays, because it is assumed that suspicion of modality derives from logical positivism, which has not survived philosophical scrutiny. The anti-modal arguments of Frege and Russell, however, have nothing to do with positivism, and remain a challenge to the contemporary acceptance of modal notions.

through the premises. The conclusion is logically compelled and cannot be attacked. The major premise, however, may be targeted for argument. The major premise of the deductive syllogism that has been considered in this chapter (see Figure 7.12, above) was expressed as: • To steal is to act contrary to the Theft Act. This can be expressed in a more specific manner and still remain general: • It is contrary to s1(1) of the Theft Act to dishonestly appropriate property belonging to another with the intention of permanently depriving that other. The entire de ductive argument can then be set out as shown in Figure 7.14, below. Figure 7.14: a deductive argument Major premise (general) • It is contrary to s1(1) of the Theft Act to dishonestly appropriate property belonging to another with the intention of permanently depriving that other. Minor premise (particular) • Anna dishonestly appropriated a book the property of X store with the intention of permanently depriving the store of it. Conclusion (compelled) • Anna has acted contrary to s1(1) of the Theft Act. We could still attack the minor premise by using it as the thesis of inductive reasoning. However, this time we want to attack the major premise. One way of doing this is to check the interpretation of the words and phrases in the major premise in so far as they replicate s1(1) of the Theft Act. What do you consider to be the meaning of the phrases: • intention to permanently deprive (mens rea); • dishonestly (actus reus); • property (actus reus). These are important words and phrases that may well become the focus of legal argument in the court. We will note later in this chapter how these words and phrases are of major importance in a theft case. In order to explore their meaning, it is necessary to consult other cases where these words and phrases in the Theft Act 1968 have been discussed. Figure 7.15, below, sets out two opposing deductive arguments: one affirming the central deductive argument and one setting out to deny it. This type of structure is the skeleton of the majority of arguments revolving around the use of facts and legal authority to resolve legal dispute in a trial scenario.

2012 ◽  
pp. 236-236
Keyword(s):  
Inductive Reasoning ◽  
Mens Rea ◽  
Legal Authority ◽  
Major Premise ◽  
Legal Argument ◽  
Deductive Argument ◽  
Minor Premise ◽  
Specific Manner ◽  
Actus Reus
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