Stefano Gattei

1. Stefano Gattei LOGIC andARGUMENTATION THEORY PhD programmes in CSE, EMI, MDCH and PSIC IMT Institute for Advanced Studies, Lucca2011 stefano.gattei@imtlucca.ithttp://www.imtlucca.it/stefano.gattei

2. BRIEF DESCRIPTION The aim is to provide a (short) guide to correct reasoning that is, the basic tools in order to construct, defend and assess an argument

3. What is an argument? • What are its main components, and how do they work together? • What is a valid argument? • What makes an argument fallacious? • What is the difference between a valid and a convincing argument? • How do we counteract an opposing argument? • What is a possible strategy in order to ‘win’ a discussion?

4. We are constantly subjected to messages of the most various kinds and we have actually lost both our ability to recognize a good argument and the taste for arguing correctly. Every day we listen to all sorts of things and speak about all sorts of things, often basing our positions on statements such as: “I believe that…”“My own sense is that…”“They say that…”“Mr X said that…”“Lei non sa chi sono io… [You don’t know who I am…]” BUT what is important is not what we believe, or what we personally feel about something – what is really important are ideas and the way we argue for or against them.

5. Of course, our ideas are not and cannot be separated from what we believe or feel. But what we believe or feel should not be enough. By contrast, all our private beliefs or personal convictions should always be argued for. In Karl Popper’s terminology, personal feelings are part of World 2, whereas ideas (and particularly scientific theories) are part of what he calls World 3. Only World 3 members can aim at Kant’s surrogate for objectivity, that is, inter-subjectivity. World 3, in other words, is the realm of rational confrontation and critical debate – the only environment in which our knowledge can grow.

6. The Beginning (1984) Two Greeks converse. Socrates and Parmenides, perhaps. We may never know their names; the story, thus, will be more [mysterious and tranquil. The theme of the dialogue is abstract. At times they allude to myths, [which they both distrust. The reasons they advance may abound in fallacies and have no end. They do not quarrel. And they wish neither to persuade nor to be [persuaded; they think of neither win or loss. They agree on one single thing: they know that discussion is the [not-impossible path to reach a truth. Free of myth and metaphor, they think or try to. We shall never know their names. This conversation of two unknowns somewhere in Greece is the capital [event in History. They forgot prayer and magic.

7. 1. WHAT IS AN ARGUMENT? The practice of rationality takes place through the construction of arguments. An argument is an organized structure of statements; statements are made of terms. Arguing implies the use of language, but not any use of language is an argument: an argument is an organized use of language, structured so as to produce correct reasonings.

8. TERMS “John”, “white”, “run” are terms. Generally speaking, nouns, verbs, adverbs and adjectives are terms. “The car is red” is a sentence made by terms. There are also other terms: articles, prepositions, conjunctions, etc. These latter terms do not have a meaning per se, but they mean something only if and when they are referred to other terms. Therefore, we have: - categorematic (or semantic) terms: terms that have a meaning when standing by themselves - syncategorematic (or synsemantic) terms: terms that have no meaning when standing by themselves

9. STATEMENTS A statement is a linguistic form that is characterized by its having a subject, a copulative conjunction and a predicate. Statements are made of terms, but whereas terms cannot be true or false, statements can be either true or false. We know what the term “book” means. But if we only utter “book”, this is neither true nor false. “The book is on the table” is something that is either true or false. In other words: when we construct a sentence that either affirms or denies certain relations among terms, we can speak of truth or falsehood.

10. Furthermore, we can distinguish: statements (or sentences): the linguistic expressions about which we can talk about truth or falsity (e.g., “the book is on the table”) propositions: the contents of a sentence (what “the book is on the table” actually means, namely, that the book is actually on the table) judgments: the mental acts of which the propositions are the expressions It is an important distinction, for it highlights that our reasoning is structured at three levels at least: - the mental level, at which we produce judgments - the logic level, at which we structure propositions - the linguistic level, at which we choose a particular language to state or deny something

11. There is one final distinction: affirmative statements, that affirm a given state of affairs negative statements, that deny a given state of affairs Each of these statements can be either: singular, referring to a precise individual (“Bill is a tall man”) universal, referring to all those that are characterized by a given feature (“all ravens are black”, or “each swan is white”) particular (or existential), referring to a part of those that are characterized by a given feature (“some birds fly” or “there are some brown rabbits”)

12. REASONINGS A reasoning, or inferential process, is a succession of statements linked by inferences. They can be divided into three kinds: - the statement(s) from which the reasoning develops, that is, the premise(s) of the reasoning - the statement with which the reasoning concludes, that is, the conclusion of the reasoning - the intermediate statements that allow to move from given premise(s) to the conclusion By “reasoning” or “inferential process” we mean a process by which we move from a set of given premises to a given conclusion through a number of intermediate statements (steps).

13. The truth of the premises, or of the conclusion, and the validity of the inferential process are two different things. In the former case, we focus on the truth-values of individual statements, whereas in the latter we check the validity, or correctness, of the inference that allows us to move from one statement to another. Therefore, premises (as well as conclusions) can be either true or false, whereas inferences can be valid or invalid. As a consequence, reasonings may have: 1) true premises and valid inferences 2) false premises and valid inferences 3) true premises and invalid inferences 4) false premises and invalid inferences

14. The truth of the premises, or of the conclusion, and the validity of the inferential process are two different things. In the former case, we focus on the truth-values of individual statements, whereas in the latter we check the validity, or correctness, of the inference that allows us to move from one statement to another. Therefore, premises (as well as conclusions) can be either true or false, whereas inferences can be valid or invalid. As a consequence, reasonings may have: 1) true premises and valid inferences[right] 2) false premises and valid inferences [wrong] 3) true premises and invalid inferences [wrong] 4) false premises and invalid inferences [wrong]

15. To sum up: TERMS and STATEMENTS (which are made by terms) have or do not have a meaning. STATEMENTS (including premises and conclusion) only can be either true or false. INFERENCES can be either valid or invalid. REASONINGS can be either right or wrong.

16. DIFFERENT KINDS OF REASONINGS There are various ways of making inferences: EXAMPLE 1A entails Bit is the case that Atherefore B EXAMPLE 2aWhoever is rich is happy; and John is rich; therefore John is happy. EXAMPLE 2bDue to the fact that divorce is legal, the number of failed marriages is growing. EXAMPLE 3If I am in Lucca, then I am in Tuscany.I am in Tuscany, therefore I am in Lucca.

17. EXAMPLE 1 is an instance of demonstrative argument, or proof: it validly applies a deductive inference that allows to move from premises that are taken to be true to true conclusions, in a necessary way. EXAMPLE 2a is different: if we accept the premises (“richness equals happiness” and “John is rich”) then the conclusion follows necessarily. The point, however, is that one of the premises is not true, or it is not true for everybody.The inference is valid, but the premises are not true, or are regarded as true – therefore, it is not a proof. It is an argumentative reasoning. EXAMPLE 2b is yet of another kind: the premise is true (the law actually exists), but the inference is questionable (since a divorce may be due to a variety of causes). Once again, it is an argumentative reasoning, in which the conclusion is not reached necessarily.

18. EXAMPLE 3 is a wrong reasoning, or fallacy (“fallacy of the consequent”): if P then Q if it is a swan, it is whiteQ it is whitetherefore P therefore, it is a swan Indeed, if we are in Tuscany, we may well be also in Pisa, or Florence, or Siena… PROOF: true (or taken to be true) premises, valid inferences and therefore necessary and unquestionable conclusions ARGUMENT: either the premises or the inferences are questionable, therefore the conclusion is not necessary FALLACY: one or more inferences are invalid, therefore the reasoning must be rejected whether the premises are true or not

19. Once accepted, proofs are not questionable. In the case of arguments, however, the passage from the premises to the conclusion does not involve absolute necessity: the conclusion, that is, does not logically follow from the premises – rather, it is argued for on the basis of the premises. Whereas proofs characterize science, arguments characterize philosophy, as well as everyday life. Indeed, appeal to argumentation, rather than to proofs, is far more common, for we are constantly faced with situations in which our rationality is bounded by questionable premises, doubtful passages or complex problem situations. Fallacies, finally, are not proper reasonings, for they are based upon invalid inferences. They are errors we might commit when reasoning.

20. REASONINGS PROOFS ARGUMENTS FALLACIES true premises, necessary inferences not always true premises, invalid inferences not always true premisesand/ornot necessary inferences