Basic Logical Concepts

Basic Logical Concepts

• Logic distinguishes correct from incorrect reasoning through methods and principles.
• Reasoning involves producing arguments with reasons to justify beliefs, though not all reasons are valid.
• Evaluating an argument requires assessing if the conclusion logically follows from the assumed premises using objective criteria.
• People support assertions using reasoning, appealing to emotion or authority, or relying on habits, while logic requires correct reasoning.

Propositions and Arguments

• Propositions are the building blocks of reasoning, asserting something is or is not the case, being either true or false.
• A proposition is a statement, typically asserted using a declarative sentence, that is either true or false, although the truth value may be unknown
• A statement is typically what has been asserted by a declarative sentence, although it is distinct from the sentence itself.
• Sentences in different languages can convey the same proposition.
• A sentence can assert different propositions in various contexts.
• Propositions can be simple or compound.
• Conjunctive propositions assert all components are true.
• In disjunctive propositions, none of the components are asserted as true.
• Conditional propositions do not assert the truth of their components, only the "if-then" relationship.
• Arguments consists of one or more premises and a conclusion.
• Arguments are the chief concern of logic.
• An inference is drawn when one proposition is inferred from others, forming the basis of an argument.
• Conclusion is the proposition claimed to be supported by the premises..
• Premises are propositions assumed to provide support for the conclusion.
• The arrow symbol from premises to conclusion indicates direction of inference.
• Logicians focus on the form of an argument to determine how well the premises support the conclusion.

Recognizing Arguments

• Identifying arguments requires distinguishing argumentative passages, which can be challenging due to varied language formulations.
• Conclusion indicators signal the conclusion of an argument.
  • Ex: therefore, hence, so, accordingly, consequently, proves that, as a result, for this reason, thus
• Premise indicators mark the premises of an argument.
  • Ex: since, because, for, as, as indicated by, the reason is that, may be inferred from
• Arguments can be recognized by meaning or setting, even without indicators.
• Premises can be in the form of rhetorical questions, which suggest or assume an answer that serves as a premise.
• Imperatives can serve as a conclusion with the reasons to perform a given act set forth as premises.

Unstated Propositions

• Arguments sometimes imply unstated propositions that are assumed to understood.
• Arguments that are stated incompletely are called enthymemes.
• The audience knowing a proposition is false may cause the speaker to create an enthymeme as the falsehood is already known to be false with the audience.

Arguments and Explanations

• Passages may appear as arguments but are explanations depending on the authors intent.
• Explanations account for why something is the case.
• Distinguishing between arguments and explanations depends on the context and purpose, with emphasis on the intention to persuade or inform.

Deductive and Inductive Arguments

• A deductive argument claims its conclusion is conclusively supported by the premises.
• Deductive arguments either achieve their claim or don't.
  • If they achieve their claim, then they are valid.
  • If they do not achieve their claim, they are invalid.
• An inductive argument does not make the claim that its conclusion is conclusively supported by its premises.
• With inductive reasoning, empirical investigations help to discover the facts that decisions can be based upon.
• The ability to strengthen or weaken the argument is a characteristic of inductive arguments.
• Deductive arguments either succeed or fail in having relation between premises and conclusion.
  • If a deductive argument succeeds, it is valid and no additional premises can add to the strength of the argument.

Validity and Truth

• Validity is a characteristic of the deductive argument that cannot have all true premises and a false conclusion.
• Truth is the attribute of those propositions that assert what really is the case.
• The validity resides in the inference relation between the premises and conclusion.
• A valid deductive argument cannot have all premises and a false conclusion.
• If an argument us valid and the premises are all true, then the conclusion must also be true.
• A proposition can be truthful while the argument isn't valid.
• An argument is sound when an argument is valid and all of its premises are true.
  • The conclusion of a sound argument must be true and only a sound argument can establish the truth of its conclusion.