Philosophy: Conceptual Analysis & Arguments

• Philosophy investigates the foundational concepts and principles of any subject matter
• Methodological tools for conceptual analysis include: Hypotheses, INJS conditions, Thought Experiments, Logic & Arguments
• The Utilitarian Principle (UP) relates to: Consequentialism, Welfarism, Weak Pareto, Cardinal Comparability, and Transitional Equity

Conceptual Analysis & Arguments

• Conceptual analysis of X seeks to formulate, test, and revise principles for X using thought experiments to increase understanding
• A knowledge principle: If A knows that p, then p is true
• Most principles are not self-evident and require philosophers present arguments to explain why to accept a principle or statement

Arguments

• An ensemble of propositions, which can be true or false
• Propositions which provide reasons to believe or accept the conclusion
• Arguments in standard form list the premises, then state the conclusion
• "Real life arguments" converted into standard form to asses them

Conversion to Standard Form

• Conclusion indicators include: therefore, so, hence, thus, it follows that, as a result, consequently
• Premise indicators include: because, since, by, from which it follows, for these reasons

What is a Good Argument?

• Good arguments occur when premises provide a good reason to believe or accept the conclusion
• The conclusion "follows from" the premises
• Inductive, abductive, and deductive inferences can be identified

Inductive Arguments

• Premises provide a fairly good reason to accept its conclusion
• The conclusion "follows from" the premises on the basis of frequencies, statistics or generalization
• The conclusion doesn't necessarily follow from its premises

Abductive Arguments

• Premises provide a fairly good reason to accept its conclusion
• The conclusion "follows from" the premises because it is a plausible explanation of those premises
• The conclusion doesn't necessarily follow from its premises

Deductive Arguments

• Premises provide a very good reason to accept its conclusion
• Considered a valid argument
• If the premises are true, then the conclusion must be true as well
• The conclusion necessarily follows from its premises

Good Arguments and Validity

• Arguments can be "good" in different ways: inductive, abductive, deductive, and analogical arguments
• Logic focuses on deductive goodness and validity

C.S. Peirce

• Peirce introduced the term 'abduction' and the study of abductive arguments

Valid Arguments

• In every situation in which all premises are true, the conclusion is true as well
• No situation in which all premises are true and the conclusion is false
• The conclusion necessarily follows from the premises
• Logic is the study of the (in-)validity of arguments

Sound Argument

• To be sound, an argument needs to be valid and all premises must be true

Enthymeme

• An invalid argument with suppressed premises that, when added, render the argument valid
• Suppressed premise is implicitly accepted by a proponent of the argument

Atheism

• Valid reasoning
• Not clear whether soun

Validity

• Argue that if A1,..., An are true, then B must be true
• Analyse what it means that the premises are true, and from that analysis, infer that the conclusion must be true as well

Reductio ad Absurdum

• Is a proof or argument of reasoning whereby assumption leads to a contradiction, so the assumption cannot be true To show that B follows logically from A1,..., An:
• Assume that all of the premises are true
• Assume B is false
• Derive a contradiction from the ensemble of the premises and the falsification of B
• Conclude: if A1,..., An are true, then B must be true as well ("on pain of contradiction")

How to Show Invalidity

• Counterexample: A situation in which the argument's premises are true and its conclusion false.
• In conceptual analysis, done referring to real cases (empirical work) and potential situations (thought experiments)
• For both (i) and (ii), rely on intuitions to see if the concepts in question apply

When is an Argument Valid on Formal Grounds?

• Modus Tollens is an argument form for arguments like Payoffs and Bankruptcy
• The arguments are all valid in virtue of their form

Argument Forms and Poems

• Abstract from everything but the "end-sound" of it sentences

Logical Form

• The logical form of an argument is abstracting from specific propositions
• Objects, properties, and relations in the argument, leaving only the logical terms in place: words such as "all", "some", "and", "not", "or", "if... then...", etc
• Obtain logical form by replacing all non-logical terms (those terms refer to events and objects in some external reality) with letters that function as variables
• A particular type of logical form is an argument's propositional form, where another type of logical form is an argument's predicate form
• Therefore, propositional logic and predicate logic can be distinguished

Formal Validity and Logic

• (Formal) Logic deals with arguments that are valid solely in virtue of their logical form
• Logical terms include propositional connectives, quantifiers, and modalities

Atomic Propositional Form

• Obtained by replacing atomic propositions that occur in the argument with letters, using the same letter for atomic propositions that occur more than once

Validity of Form

• Valid arguments
• Valid in virtue of their form, and the standard meaning of "no" and "if..., then..."
• Well-known names include: Disjunctive Syllogism, Modus Ponens, Modus Tollens

Disjunctive Syllogism

• To be valid and substitutable, arguments need to be for any propositions p and k where the valid form is: α or β. Not-α. So, β, where α and β are arbitrary (not necessarily atomic) propositions
• Disjunctive Syllogism is the name for a valid (propositional) argument form

Modus Ponens

• To be valid and substitutable, arguments need to be for any propositions α and β where the valid form is: If α then β. Moreover, α. So, β
• This argument is valid in virtue of its Modus Ponens form
• Budget Cuts has Modus Ponens form: α: Budget cuts are approved, and β: There will be a strike

Denying the Antecedent

• if p, then q and not-p, it does not follow that not-q
• Thus, "Only if p, then q" actually means: "if q, then p"! (i.e. q cannot be true without p also being true.)

Modus Tollens

• To be valid and substitutable, the arguments need to be for any propositions α and β where the valid form is: If α then β. Not-β. So, not-α
• "" Modus Ponens is another person's Modus Tollens.

Affirming the Consequent

• To be valid and substitutable, the arguments P1, P2 and c CANNOT be in the valid form, as this does not affirm Modus Tollens

Validity Beyond Propositional Form

• A valid argument must instantiates a valid propositional form

Musician (Propositional Form)

• valid, but does not instantiate a valid propositional form
• Keith Jarrett, Jarrett is the greatest living jazz pianist. This box is green. So, 2 + 2 = 5

Predicate Form

• valid because it instantiates a valid predicate form
• For every object j and properties M, R, that substitute in this form, the resulting argument is valid
• Predicate logic for reasoning about objects, properties and relations
• Predicate logic is the logic of "all", "some", "none"

Logical Forms and Validity

• The logical form of an argument is what is abstracted from specific propositions, objects, properties, and relations in the argument
• Only leaving the logical terms in place: words such as and, not, or, if then, if and only if, all, some, necessarily, possibly
• The validity of these logical forms are studied (Propositional logic, Predicate logic, (Propositional) Modal logic)
• Various argument forms used in one go while relying on the meaning of non-logical terms