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Argument (the subject-matter of Logic) - Coggle Diagram

- - - - :check: (if it's true that:) If it's a Blind Lemon Jefferson album, then it's a Blues album.
        :check: (and it's true that:) It's a Blind Lemon Jefferson album.
        Therefore,
        :check: (It must be true that) It's a Blues album.
        
        Logic is not really about the way things actually are in the world. Rather, logic is about argument. So far as logic is concerned, Blind Lemon Jefferson might be a classical pianist, a punk rocker, a rapper, or a country and western artist, and the argument would still be valid.
        
        In a valid argument, true input guarantees true output.
        
        :pushpin: However, validity is certainly not synonymous with truth.
        So, not every valid argument is going to be a good argument.
        
        Soundness
        Sound arguments are good arguments
        
        Because a sound argument is a valid argument with true premises, the conclusion of every sound argument must be a true sentence.
        
        Can't we say simply that sound arguments are definitely, indeed, definitively good arguments?
        
        Well, this is a controversial claim. After all, there are many blatantly circular arguments which are certainly sound but which are not so certainly good.
        
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        As an example, if one or even all of the premises are false in actual fact it is still perfectly possible that the argument is valid.
        
        Furthermore, it is perfectly possible for a false conclusion to be validly drawn.
        
        :forbidden: If I do no work then I'll pass my logic exam.
        :forbidden: I'll do no work.
        Therefore,
        :forbidden: I'll pass my logic exam.
        
        Moreover, valid arguments with false premises can also have actually true conclusions.
        
        :forbidden: My uncle's cat is a reptile.
        :forbidden: All reptiles are cute, furry creatures.
        Therefore,
        :check: My uncle's cat is a cute, furry creature.
        
        :old_key: Validity is a property of arguments. Truth is a property of individual sentences.
        
        Change the name of the supposed bluesman as you will, the form of argument remains exactly the same. So, logic is not really about particular matters of fact and it is not really about particular bluesmen either. Rather, formal logic is about argument-forms (logically enough).
        
        Formal logic
        
        For example, consider the Blind Lemon Jefferson argument. Clearly, it is a valid argument. If the premises are true the conclusion must be true. But, as we have just seen, we can change the name of the bluesman or even substitute the name of any band and still get a valid argument.
        
        Moreover, we can in fact change the most basic sentences which make up the premises and conclusion and still produce a valid argument. What makes this possible is the fact that the validity of this argument does not depend on particular matters of fact or particular bluesmen. Rather, it is the form and structure of the sentences in the argument and the relations between those sentences which guarantee that we cannot have true premises with a false conclusion in any such argument.
        
        :pushpin: It follows that any argument of that particular logical form will also be a valid argument. Thus, formal logicians use the notion of logical form to investigate the concept of validity. Indeed, many formal logicians will now encourage us to replace the intuitive definition of validity we have been working with so far in favour of the following purely formal definition of validity:
        An argument is valid if, and only if, it is an instance of a valid logical form.
        Hence, formal logic is fundamentally concerned with valid logical forms of argument. Formal logic, we might say, investigates formal validity.
        
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        :pushpin: (...) formal logic constitutes a set of rules and standards, ideals of inference, or norms, independent of the thinking of any actual individual, in terms of which we appraise and assess the actual inferences which individuals make. So, in its concern with the ways in which people do actually argue, logic is scientific but in so far as logic provides standards of argument it is also normative.
        
        To sum up, formal logic is fundamentally concerned with the form and structure of arguments and not, primarily, with their content. In terms of the chess analogy, it is the study of the rules of the game, not of the strategies of any particular player.
      - The Hardness of the Logical 'Must'
        Logic as the 'science of thought'
        
        What is it about a valid argument with true premises which compels us to accept the conclusion of that argument?
        
        Logical force, the force of reason
        
        Valid arguments establish their conclusions conditionally upon the truth of all their premises.
        
        :check: All human beings are mortal.
        :check: Prince is a human being.
        Therefore,
        :check: Prince is mortal.
        
        If all human beings are mortal and if Prince is a human being, then it must follow that Prince is mortal.
        
        :old_key: If I do not accept (force) the truth of the conclusion having accepted the truth of the premises, then I have blatantly contradicted myself. It cannot be rational to believe contradictions. I must accept the truth of the conclusion, on pain of irrationality.
        
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      - Invalidity
    - - To show that an argument fails to preserve truth across the inference from premises to conclusion is precisely to show that the argument is invalid.
- - - - Induction
        Traditionally, while deduction is just that kind of reasoning associated with logic, mathematics and Sherlock Holmes, induction is considered to be the hallmark of scientific reasoning, the hallmark of scientific method.
        
        Particular :arrow_right: General
        Records of personal experience (e.g. observation-statements)
        
        These are singular sentences in the sense that they concern some particular individual, fact or event which has actually been observed.
        
        Logic student #1 is very industrious
        Logic student #2 is very industrious
        Logic student #3 is very industrious
        .
        .
        .
        Logic student #10 is very industrious
        Therefore,
        Every logic student is industrious.
        
        From a finite list of singular observation-statements about particular individuals we go on to infer a general statement which refers to all such individuals and attributes to those individuals a certain property.
        
        Charles Sanders Peirce: inductive arguments are 'ampliative arguments', i.e. the conclusion goes beyond, ‘amplifies’, the
        content of the premises
        
        But, if that is so, isn’t there a deep problem with induction? After all, isn’t it perfectly possible that the conclusion is false here even if we know that the premises are true?
        
        :pushpin: Certainly, the industriousness of ten logic students does not guarantee the industriousness of every logic student. And, indeed, if that is so, induction is invalid, i.e., it simply does not provide the assurance of the truth of the conclusion, given the truth of the premises, which is definitive of deductive reasoning.
        
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