An argument is a structure that comprises a conclusion, namely, a proposition that one wants to uphold, and some premises, as reasons to support the belief in the conclusion. Logic is about whether and how a conclusion follows from the premises. (Location 127)
Example (1) The Law of Identity Example (2) The Law of Excluded Middle Example (3) The Law of Contradiction (Location 155)
Premise-indicators: because, since, for, as, follows from, as shown by, inasmuch as, as indicated by, the reason is that, for the reason that, may be inferred/derived/deduced from, in view of the fact that… • Conclusion-indicators: therefore, so, hence, thus, in consequence, consequently, accordingly, as a result, for this reason, it proves that, it follows that, we may infer, which allow us to infer that, which shows/means/entails/implies that, which points to the conclusion that… (Location 210)
Deduction Induction Achieves certainty: for a deductively valid argument, if the premises are true, then the conclusion must be true. Achieves probability: if the premises are true, then the conclusion is likely to be true, although it does not have to be true. (Location 304)
argument usually consists of several statements, i.e. a conclusion and some premises. A Can a statement (a premise or a conclusion) be valid or invalid? B Likewise, can an argument be true or false? No, they can’t. A statement is true or false; yet only an argument can be valid or invalid. It is because validity is a relation between statements, rather than a property of an individual statement by itself. Validity indicates whether the conclusion follows if the premises are true. Although we sometimes hear of people making ‘valid’ statements in ordinary language, this is in fact a mistake. Similarly, only a statement can be true or false. An argument contains statements which are true or false, but the argument itself is not true or false. If an argument is valid, then its conclusion must be true when the premises are true. However, we say the argument is valid, not that it is true. (Location 335)
I use the term ‘cogent argument’ to refer to any argument (including inductive argument) whose ‘premises are acceptable, relevant to and sufficient for its conclusion’ (Johnson and Blair 1977). (Location 441)
Logic is the study of good and bad reasoning. Reasoning is presented in arguments, which take the form of a conclusion supported by premises. • A statement or a proposition is either true or false. • An argument is evaluated in the following order: validity, soundness and cogency. • A valid argument is one which, if all premises are true, then the conclusion cannot be false. • A sound argument is a valid argument in which all premises are true. • A cogent argument is a strong argument whose premises are evidentially true. (Location 471)
When an expression can be interpreted to have more than one meaning, we call that expression ambiguous. (Location 609)
An expression is vague if it has a core meaning but does not have a clear boundary. Unlike ambiguity, vagueness is not about referring to completely different things, but is about matters of degree relative to a standard or a comparison class. Look at the following examples. Example (7): Woe is me! I am too old for a happy life. Example (8): Bald men are sexy. Example (9): An average 13-year-old boy is short. (Location 621)
The sorites paradox The sorites paradox is also called the paradox of the heap. It is a paradox about vagueness. It runs as follows. One grain of sand does not form a heap. Adding one grain still does not make a heap. Indeed, intuitively no one grain of sand is responsible for changing the status of the existing sum into something completely different. However, if someone keeps repeating the process of adding one grain of sand at a time over and over again, then eventually a heap will be formed. So, when does the heap come into being and what is the boundary between a heap and not a heap? (Location 641)
An expression is obscure when it lacks a core meaning. With vague expressions we are not able to draw a clear boundary in all cases between, say, what is bald and what is not bald, or what is old and what is not old. Yet a competent language user still knows more or less what baldness or old age means; for instance, a person with no hair at all is certainly bald and a person at 100 years old is certainly old. So, a vague expression does have a core meaning. However, an obscure expression is different in that it does not even have a core meaning. Consider the following examples. Example (10): Everything counts. Example (11): You are always right to some extent (or, in some sense). Example (12): There’s something in it. Example (13): It is an interesting argument… (Location 657)
An incomplete expression is an expression in which the domain is not specified. Its reference is often sensibly fixed only by making some contextual adjustment. Example (14): Let’s go to the pub afterwards. Example (15): Everyone is happy. (Location 674)
Idiosyncratic expressions are jargon terms or expressions with unusual usage deviating from ordinary usage without explicit definition. (Location 693)
Emotive words are expressions that would usually arouse particular feelings or judgements. (Location 721)
We can say that an expression denotes certain object(s) in virtue of the property so expressed. (Location 818)
Mill: Denotation versus connotation Frege: Reference versus sense Carnap: Extension versus intension (Location 844)
Indeed, most recursive definitions involve three components; they are called a base case (such as a), an inductive clause (such as b) and an external clause (such as (c)). (Location 971)
Hence, indeed, more information is needed to cash out items such as ‘the principle of justice in acquisition’ and ‘the principle of justice in transfer’, (Location 977)
One may wonder why recursive definition is considered a denotative definition because a recursive definition may contain connotative clauses as constituents (such as 43b, 44a and 44b). Indeed, (44) does not even contain any enumeration or ostensive definition. This is a fair observation. Recursive definition is categorized under denotative definition because the overall aim of a recursive definition is to pick out the complete set of objects falling under the definiendum. How those objects are picked out (say, what principles of justice are involved in (44)) are really beside the point of the definition. (Location 979)
To sum up, denotative definitions pick out objects or events in the world and so they link language to reality. (Location 993)
