ACT

Diagrams

In diagrams, always write the number given to the conclusion at the bottom of the diagram.

Skepticism

Like relativism, skepticism flies in the face of common sense. Skepticism is also in similar difficulty to relativism when it is turned on itself: if nothing can be known, then not even skepticism itself can be known, and there is something definitely odd about any view which by itself can't be known. Simply put, skepticism is that knowledge is impossible and nothing can be known.

Inference indicators

- A word used by the speaker to indicate that they are drawing an inference (conclusion) from stated or implicit premises.

The unstated premise (assumption)

- An argument may rely on unstated premises. - Sometimes the stated premises all sound convincing, but once the unstated premise is uncovered, the weakness of the argument is revealed.

Rhetorical Questions

- For example, "what kind of a fool do you think I am?". - Questions that are NOT meant to be answered. - They look like requests for information, but are really to state information or make a point.

Categorical Forms

- Some means 'at least one'. - "Some S is P" means that 'there exists at least one S which is P'. - "Some S is not P" means that 'there exists at least one S which is not P'. - However, in logic 'all' does not imply 'at least one'. - "All S are P" and "No S are P" mean that 'if any S exist they are/aren't P'.

Mill's Methods

- The Method of Agreement. - The Method of Difference. - The Method of Concomitant Variation.

Quotes

- Used to talk about words or phrases. - Inner and outer quotes. - Scare or shudder quotes.

Deduction

- We speak of deductive inferences/arguments as being valid or invalid. - In a deductive argument, the arguer is putting forward premises, the truth of which is supposed to force the truth of the conclusion. - Whether or not they do force the truth of the conclusion depends on whether the argument in fact has a valid form.

Syllogism (example)

No horses are insects, Some insect is green. So, no horses are green. - Subject (minor) term = horses. - Predicate (major) term = green. - Middle term = insects.

The clear conclusion

Provides all the premises and sub conclusions needed to support the conclusion.

The Dilemma

The dilemma is an extremely useful form of argument known to the Greeks. Two types are distinguished.

The Dilemma - Rejecting one of the other premises

This is often easier to do. Rejecting another premise may or may not be true and as a result further arguments could develop.

Criteria for a good explanation - Falsifiability

This is related to predictive power. Independently of the desire for predictive success, one would like one's hypothesis to be able to be tested, that it be the kind of hypothesis that could be tested. This is known as being falsifiable.

Method of counter example (example)

"If the premier knew about the child abuse allegations at the school, then the premier acted irresponsibly in not ensuring they were properly dealt with. The premie did not know about the allegations. Thus, the premier did not act irresponsibly". - Suppose that: "A senior public servant had in the months prior pressed the premier in his role as Minister of Education to monitor more closely how schools and the Department of Education process and report on abusing events in schools, but the premier ignored this advice".

Categorical Forms - A and E forms

- "All S are P" and "No S are P" do not imply that at least one S exists. - The A and E forms mean that 'if any S exist they are P' and 'if any S exist they are not P' respectively.

Definition - Circular

- A definition is circular if the same word occurs on both sides. - For example "taking a sleeping pill" because of its "dormant power".

Definition - Too broad

- A definition is too broad when there are things falling under the term doing the definition which do not fall under the term being defined. - For example, "motor car" means "wheeled self-propelled vehicle". This is too broad because aeroplanes, motor cycles and other vehicles fall under the same definition.

Definition - Too narrow

- A definition is too narrow when there are things falling under the term being defined which do not fall under the term doing the defining. - For example, "siblings" means "male offspring of the same parents". This is too narrow because siblings can be female too. - Note that the same definition can be both too broad and too narrow.

Premise

- A statement offered as reason to believe the conclusion of an argument. - The reasons given to convince you of a point. - Preceding statements that give support to the conclusion, hence amounting to reasons for accepting the conclusion.

Cause and Effect

- A sufficient cause is used in the sense that its occurrence is a sufficient condition. - Another distinction between causes can be called the distinction between an immediate cause and a remote cause. - We say that an immediate cause is one close to its effect in time, while a remote cause is further away in time.

Categorical Forms (Aristotle)

- AEIO. - A form (Universal affirmative): "All S are P". - E form (Universal negative): "No S are P". - I form (Particular affirmative): "Some S is P". - O form (Particular negative): "Some S is not P". - S is called the subject term and P is called the predicate term.

Argument

- An attempt to justify or prove a conclusion. - A set of statements (claims), one of which is identified as a conclusion, and the rest of which are reasons (premises) that are meant to support the conclusion. - A series of statements, at least one of which is offered as a reason to believe another.

Statements

- An expression that is capable of being true or false. - Arguments offer some statements to gain acceptance of another statement - the "conclusion" - on the basis of accepting the preceding statements.

Fallacy of Begging the Question/Circular argument

- Another type of fallacy, not a form of genetic fallacy, is called circular argument, or "begging the question". - Basically, begging the question or circular arguments amounts to assuming what you have to prove. - A traditional example is the claim "this drug will make you sleep because of its dormitive power". If we ask what the words "dormitive power" , we find that they mean "power to make you sleep". Thus, this drug will make you sleep because of its power to make you sleep. - This kind of circle is not uncommon in disputes about political ideologies or metaphysical systems or other large and complex doctrines. - Circular arguments are useless in a route to knowing the truth.

Accidental connection

- Another way a definition can fail is that it can fail to give the meaning of a word, giving instead something that is only accidentally connected with the concept. - For example, "cow" means "the sacred animal of the Hindus in India". This may be neither too broad, too narrow nor circular. But all the same it does not give a phrase which supplies the meaning, since one could perfectly well know the meaning of "cow", be an expert in its use, and yet not know anything about the Hindu religion.

Soundness

- Arguments which have a valid form and true premises are truth preserving. - These are good arguments. - We call arguments deductively sound when they have a valid form and true premises. - To go against the conclusion of such an argument is to go against the authority of reason. - An argument is deductively sound if and only if it is both valid and has premises, all of which are true.

Complex arguments

- Consists of more than one inference (premise/s to sub conclusion/s to one conclusion). - Inference from single or multiple premises to sub conclusion/s. - Sub conclusion/s to one conclusion. - Diagramming: more than two levels (premise/s, sub conclusion/s, conclusion).

Simple arguments

- Consists of only one inference (premise/s to conclusion). - One inference from one or several premises to a conclusion. - Diagramming: two levels (premise/s to conclusion).

Categorical statements

- Correspond to fundamental forms of thought and categorical logic concerns the logical relations of categorical propositions or statements. - Are about classes, sets, or whole categories of things. - Vary in quality and quantity (whether they are universal, particular, affirmative and negative).

Three types of arguments

- Correspond to three types of reasoning, all of which involve premises which can be true or false. - When we speak of "moving" from premise/s to a conclusion, we mean we are inferring something or making an inference.

Different forms of inference

- Deduction. - Induction. - Abduction. - We should be persuaded by an argument only when it is a good argument. - Logic helps us understand what makes an argument good. - Each of deductive, inductive and adductive arguments are good (or bad) in different ways. - The only way an argument can be bad is to have a false premise. However, there are even more ways. - Some ways of being bad have nothing to do with the truth or falsity of the premises. Sometimes premises do not support conclusions adequately, even if they are true.

Independent Premises

- Each provides direct support to the conclusion. - The conclusion is supported by either one of the premises, but the argument is strengthened by combining the two premises.

Performatives

- For example, "I now pronounce you husband and wife". - Promises, bets, official verbal actions.

Exclamation

- For example, "Ooooh, I can fly!". - Requirements, commands, suggestions.

Imperatives

- For example, "have a nice day!". - Requirements, commands, suggestions.

Assertion

- For example, "the book Harry Potter and the Philosophers Stone is much better than the film". - Unsupported claim.

Guilt by association

- Here, the second speaker attempts to discredit the original claim by suggesting that it is the kind of claim made by some group whose views taken as a whole are presumed to be obnoxious. - Such arguments are rarely spelled out in detail for the very good reason that they are patently bad: in full they amount to something like "you say X. Communists say X".

Validity

- If the premises are true, the conclusion is true. - It is impossible for the premises of valid arguments to be true and the conclusion false at the same time. - Validity is purely a matter of the form that the argument has, where the form of an argument is the general pattern of reasoning that it instantiates. - Validity and invalidity are purely a matter of the form of an argument. All arguments of a given form are either valid or invalid but not both.

Premise indicators

- Inference indicators used before premises are called premise indicators. - Since, because, for, my reason is, on account of, the justification is, is confirmed by, it follows from, given that, etc.

Invalid arguments

- Invalidity can be demonstrated by using the method of logical analogy ("you might just as well argue that..."). - It can also be demonstrated by using the method of counterexample ("suppose that..."). - Venn diagrams and categorical logic demonstrate validity/invalidity.

Arguments - what are they?

- It refers to an activity of reason or something we do using logical thinking. - Arguments are used as a rational tool to try to solve disputes or disagreements (without force) about what is the case or what we should do. - A form of reasoning that relates propositions or statements. -There are words that we use to indicate that an inference is being made.

Inference

- Made when you draw a conclusion from a premise. - When you draw a conclusion, you make an inference.

Valid arguments

- May have false premises and false conclusions - they can still be valid (though worthless) just so long as they are in a form of argument which guarantees true conclusions if the premises are true. - Thus, whether a specific argument is in fact valid is not established by its premises and conclusions being true. - If the specific argument is of a form which permits some instances of specific arguments of that same form where the premises are clearly true but the conclusion clearly false, that shows the argument form is an invalid form. - In which case the specific argument you were considering is also invalid (because it is an argument of invalid form) even though it happens to have true premises and a true conclusion.

Criteria for a good explanation

- Mechanism. - Predictive Power. - Falsifiability. - Compatibility with other well established hypotheses. - Explanatory Power.

Logical Signposting

- Premise and conclusion indicators (which are inference indicators) are examples of logical signposting. - Note: These indicators don't have to be present for something to be a premise or a conclusion. - A logical signpost is any word/group of words that tell the reader/listener what the relation between the statements is meant to be. - Inference indicators are one kind of logical signpost.

Interdependent Premises

- Premises provide support, in combination, to the conclusion. - Both premises are needed for the conclusion to be true. - Negate one premise and the argument collapses.

Reportive definitions

- Report the ordinary meaning of a word (or at least claims to, though reportive definitions can be wrong). - We usually drop the term "reportive". - They can go wrong in three ways: by being too broad, too narrow or circular.

Fallacy of ad hominem: The Genetic Fallacy

- Such arguments are also called arguments against the person (as opposed to arguing against the truth of their position or the validity of their argument). - They were traditionally called ad hominem arguments, which translates literally as "against the person". This indicates a rough class of arguments, some sound, some not. - The genetic fallacy is, broadly speaking, the error of trying to refute a claim by attacking the source or origin. This style of argument is the staple diet of politicians.

Explanation

- Tells you "why" something is the case or simply "that" something is the case. There is no argument for a conclusion. - An argument tells you "that" something that I am trying to convince you of is the case.

Deductive arguments

- The concepts of validity, invalidity and soundness apply to deductive arguments. - We have learned that 'validity' is a technical term applicable to deductive arguments of a special kind. - Those with argument forms which, if the premises of the argument are true, force the conclusion of the argument to be true also (i.e. are truth-preserving).

Determinism

- The idea that every event has a sufficient cause. - Determinism is not a logical truth, it is possibly true and possibly false. - Our best guess using our most successful basic theories is that determinism is false.

Conclusion indicators

- The kind of inference indicators used before a conclusion are referred to as conclusion indicators. - Therefore, thus, hence, so, consequently, what this justifies/confirm is, it follows that etc.

Definitions

- The primary use of definitions is to give the meaning of a word or phrase by specifying a word or group of words which means the same. - For example, "hectare" means "10 000 square metres". - Errors can occur if quote marks are dropped incautiously, for example "nil" means nothing (this is false). - Definitions can be reportive or stipulative.

Induction

- The topic of induction covers reasoning which aims to uncover causal relationships between phenomena. - Inductive arguments typically argue from premises which appeal to observation, knowledge or experience, and argue to a conclusion which goes beyond experience. - As such, they are invalid. However, it is reasonable to believe the conclusion on the basis of the premises.

The Dilemma - Reject the first premise

- This can be done by arguing that the premise represents what is called a false dichotomy or false alternatives or false disfunction. - For example, if someone says "either you are with us or you are against us", you may reply "are there any alternatives?"

Evaluating arguments

- This is a rational activity too. - It does not depend on whether we like the arguer or like the conclusion. - We also consider the relationships between the premises and the conclusion and the extent of justification for the conclusion. - An argument is an attempt to persuade someone else of the truth of one statement by putting forward at least one other, purportedly true, statement as evidence for it, or as a reason to support of it. - Reasons then are the statements, the truth of which is supposed to contribute a justification for supposing some other statement to be true.

Loaded Question

- This isn't strictly a fallacy as a mistake in argument, so much as a trick designed to get you to admit something you are unwilling to admit. - For example, "have you stopped beating your wife?". Answering yes or no commits you to having once done so, so do not answer either yes or no. - The correct response is to say "that is a loaded question. It presupposes that I once beat my wife, which is untrue". - Reporters aiming to conduct a hostile interview are particularly fond of loaded questions.

Fallacy of absent evidence

- This kind of argument tends to arise when a conspiracy theory is being advocated. It is not a very persuasive form of argument. - Absence is the mark of non-evidence. Furthermore, you would be prompted to ask: why do I believe in the theory if I agree that the reasons for doing so are so weak? - Ask: Can we investigate more thoroughly? If yes, and we still have no evidence, the best explanation would eventually be that the theory is false. If it were true, you would expect to have found that out by now. Absence is the mark of non- existence.

Contradictories

- Two statements are contradictories of one another if it is impossible for them to be true together, and impossible for them to be false together. - In other words, two statements are contradictories of one another if they cannot have the same "truth-value". - Cannot both be true and false at the same time. - The truth of one excludes the truth of the other. - The falsity of one excludes the falsity of the other. - It is apparent that A and O forms are contradictories of one another. - It is also apparent that E and I forms are contradictories of one another. - Universal statements are also contradictories. - Particular statements are subcontraries.

Stipulative definitions

- Used to declare a definition artificially for the purposes of the present context, in the hope that doing so will clarify the issue, avoid irrelevancy and enable progress to be made. - Stipulative definitions do not report the ordinary meaning of words. Thus, you can go wrong if you are using a stipulative defintion and don't declare that you are doing so, because people will think that you are reporting the ordinary meaning.

Validity Testing

- Validity is a matter of form and structure, referring to how the premises relate to the conclusion. - We can test for invalidity using logical analogy and counter example. - We can test for validity through categorical forms, through expressing premises in a form by which we can evaluate the relation of premises to the conclusion, through Venn diagrams and 2 line arguments.

The Counterdilemma

- Way 2. This proceeds by offering another dilemma designed to show that the opposite conclusion can be drawn from the same alternatives. - Most apparent counter dilemmas are only apparently so (that is, not really counter dilemmas) because the conclusions are really compatible. - One can also criticise the two dilemmas in ways other than with a counter dilemma.

Syllogism

- We can demonstrate validity by focussing on arguments called syllogisms. - A syllogism is a 3-line argument using two categorical statements as premises and one categorical statement as the conclusion. - We can provide a syllogism with Venn diagrams by using three circles. - A syllogism is an argument with two premises and a conclusion, all in categorical form, with three terms occurring twice. - The subject term of the conclusion is also called the subject term of the syllogism, and the predicate term of the conclusion is also called the predicate term of the syllogism. - The third term, which occurs once in each premise but not in the conclusion is called the middle term of the syllogism. - When diagramming, always do the universal term first.

Venn diagrams

- You can use venn diagrams to work out whether an argument made up of categorical forms is valid. - We let each class corresponding to the terms of a categorical statement be represented by a circle. - We represent the information conveyed by the statement with markings in certain areas inside or outside the circle. - Shading indicates 'empty'. - To show that at least one member exists, put a small 'x' in the region. This indicates that a set or sub-class has at least one member. - If there is neither shading not an 'x' in the region, this indicates that we do not have information about it. - If the Venn diagram for the second argument for the second statement shows information that directly contradicts the first categorical statement then you can conclude that the truth value of the second statement will be the opposite of the truth value of the first statement.

Fallacies

Described as "common mistakes in arguments". Not all of these types of fallacy we look at are mistaken arguments, though there are mistakes "nearby" as it were.

Mill's Methods - The Method of Concomitant Variation

If a given phenomenon varies in amount or degree in some regular way with the amount or degree of some phenomenon, then the two phenomena are causally relevant to one another. Thus, if the frequency of lung cancer varies directly with the number of cigarettes smoked, this is evident that they are causally linked. Mill's Methods are vital for the success of science as we know it.

Synthetic

Need to see what's going on in the world to determine the truth/falsity. The truth/falsity is not wholly determined by the meaning of words.

Questions/Interrogations

Requests for information.

Criteria for a good explanation - Explanatory Power

That is, numbers of different kinds of phenomena explained. Hypotheses which unify phenomena, which show them to all be instances of a single law, are thereby better.

Criteria for a good explanation - Mechanism

The explanation proposes a mechanism for how the phenomenon came about. The theory of evolution proposes a particularly good mechanism called "natural selection".

Analytic

True by definition. True solely by the meaning of words.

Categorical Forms - I and O forms

- "Some S is P" and "Some S is not P". - The I and O forms mean that 'there exists at least one S which is/is not P' respectively.

Method of counter example

- "Suppose that...". - Imagines a hypothetical scenario, a possible case, in which the premises of the original argument are true and the conclusion is false at the same time. - We can show this is not a valid form of argument (where truth of premises forces the truth of the conclusion) by supposing the circumstances in which the premises are true but the conclusion false.

Method of logical analogy

- "You may just as well argue that...". - Sometimes arguments which appear valid to us in fact instantiate invalid form. - A method is available to assertion whether this is the case. - The method of analogy involves producing an argument of the same form as the original argument (that at first looked okay) with obviously true premises and an obvious fake conclusion.

Ambiguity

A term is ambiguous if it has more than one meaning, and the context doesn't make clear what is meant. One can make mistakes of reasoning if one fails to be aware of ambiguity.

Vagueness

A term is vague when there are some cases which don't clearly fall under the term, and don't clearly fall outside the term, for example "bald". There is no line with vagueness however it can sometimes be inappropriate.

Analogous argument

An argument in the form of true premises and an obviously fake conclusion.

Contradictory

False by definition.

Mill's Methods - The Method of Agreement

Look for the common factor, it will be causally relevant.

Mill's Methods - The Method of Difference

Look for what is different between cases where the effect occurs, and otherwise identical cases where the effect doesn't occur, the factor that differs is causally relevant.

Abuse

- For example, "you are ignorant". - Personal put down.

The charge of having inconsistent beliefs

1. X is true. 2. (You can't say that because) X is inconsistent with other things you say or do. - Person 1 makes a claim X, and Person 2 argues ad hominem that the claim X is inconsistent with another belief which Person 1 is known to have, or another action which Person 1 is known to have performed. - A special case is the "you too" response. This is an example of hypocrisy. - Responses include "the issue of my consistency/inconsistency is irrelevant to the truth/falsity of X, so let's stick to the point".

Fallacy of appeal to authority

1. X. 2. I question the authority on which you base that claim. - Person 1 makes a claim X and Person 2 replies by suggesting that Person 1 is not in a position to know ("you wouldn't know" or "the authority you are citing would not know"). - Note again that such a reply does nothing to show that the stated claim X is false. - Re-evaluating one's reasons is called the reality check. A reality check is not necessarily grounds for following the majority, but it is something of an antidote to solitary madness.

Questioning the speakers veracity

1. X. 2. I question your truthfulness. - A third type of genetic fallacy arises when one questions the speakers words. Whether the speaker is believable all the same, on the grounds that they have a vested interest in whether the matter under discussion is true.

Assumption

A premise that is not made explicit.

Categorical logic

A branch of deduction that involves categorical propositions or statements and goes back to the ancient greek philosopher Aristotle.

Statistics laws

Admit exceptions, such as statistical laws about how children tend to vote the way their parents do, and are common in the social sciences.

Deterministic laws

Admit of no exceptions, such as Newton's Laws of Motion and Gravitation, and are common in both physics and chemistry.

Method of logical analogy (example)

All lions are felines. Leo is a feline. So, Leo is a lion. - You may just as well argue that: All cows are mammals. Felix the cat is a mammal. So, Felix the cat is a cow.

Description

For example, an illustration, it provides you with information.

Arguments - Not all are "good"

Invalid (badly structured), not sound (false premises), containing informal fallacies (an inherently bad arguments).

Criteria for a good explanation - Compatibility with other well established hypotheses

One cannot rely too much on the criteria of a good hypothesis since some hypotheses are truly revolutionary in their effect on existing theory.

False Cause

Person 1: A occurs before B. So, A causes B. - Examples arise in primitive beliefs about the efficacy of political contexts, where an outcome is predicted as a consequence of a certain line of action, and when the outcome occurs it is concluded that the line of action must have been the cause of the outcome.

Fallacy of appeal to ignorance

Person: You can't prove that X is false (that is, you can disprove X) So, X is true. - This can occur, for example, in discussions on religious matters. The general pattern is invalid. - In certain circumstances, however, the conclusion is made more reasonable to believe.

Criteria for a good explanation - Predictive Power

Predictive power in as yet as unobserved circumstances. For example, the theory of evolution states that bacteria will over time become antibiotic resistant.

Conclusion

The statement that premises, or reasons, are offered to support.

Relativism

The truth is subjective, the truth is relative and it all depends on the individual. Schick and Vaughn argue against this, stating that these relavist statements go nowhere.

Teleological explanations

These appeal to some goal state. For example, "the rat left in order to get food" - and are common in the life sciences. Teleological explanations contrast with causal explanations, which cite some law of antecedent cause.

The Dilemma - Show one of the premises false

Way 1. If you can do this then you have shown that the argument is unsound, and thus does not provide a good reason to believe its conclusion.