Logic

Logic is the study of the principles and methods of valid reasoning

  1. Arguments and Logic
  2. Examples of Arguments
  3. Branches of Logic
    1. Formal (Symbolic) Logic
    2. Informal (Practical, Applied) Logic

Arguments and Logic

  • Reasoning is the process of endeavoring, by rational means, to answer a question, resolve an issue, solve a problem, or make a decision.  Logic is the study of the rational means by which thinkers ought to reason. 
  • The focus of Logic is the evaluation of arguments.
    • An argument is an instance of reasoning, from premises to a conclusion.
    • Arguments are typically set forth to establish their conclusions.

Examples of Arguments

  • The core of the Declaration of Independence is the following argument:
    1. The people have the right to alter or abolish a government if it violates basic human rights such as the rights to life, liberty and the pursuit of happiness.
    2. The British government of the colonies has violated those rights.
    3. Therefore the American people have a right to alter or abolish the British government of the colonies.
  • Before he flew a kite in a thunderstorm, Benjamin Franklin presented an argument that lightning was electrical in nature.
    1. Lightning and sparks are alike in the following respects:
      • 1. Giving light, 2. Color of the light, 3. Crooked direction, 4. Swift motion, 5. Being conducted by metals, 6. Crack or noise in exploding, 7. Subsisting in water or ice, 8. Rending bodies it passes through,  9. Destroying animals, 10. Melting metals, 11. Firing inflammable substances, 12. Sulphureous smell
    2. A spark is electrical in nature.
    3. Therefore, lightning is likely electrical in nature.
      • “Let the experiment be made.”
  • The New York Times presented this argument against capital punishment:
    1. Fallible governments should refrain from inflicting irreversible punishments
    2. Capital punishment is irreversible.
    3. Governments are fallible.
    4. Therefore, governments should refrain from inflicting capital punishment.
  • Hypothesis testing is one kind of statistical inference.
    1. In a blind taste test, a wine connoisseur, who claims she can taste the difference between French and California Cabernets, correctly identified 15 out of 20 glasses of the wines.
    2. The probability she correctly identified at least 15 out of 20 glasses by chance is 1/50. (In statistical jargon, the p-value = 1/50.)
    3. Therefore, she can probably taste the difference between French and California Cabernets.
  • The Britannica is an authoritative source.
    1. In its article on swans the Britannica says there are black swans in Australia.
    2. The Britannica is a reliable source of information.
    3. Therefore, black swans exist.

Branches of Logic

  • Formal Logic is the theoretic study of the principles of valid reasoning within a formal (symbolic) language.
  • Informal Logic is the practical study of the methods of valid reasoning (within a natural language such as English).

Formal (Symbolic) Logic

  • Formal (Symbolic) Logic is the theoretic study of the principles of valid reasoning within a formal (symbolic) language.
What Formal Logic looks like
  • Consider the argument:
    • If Newton’s theory of gravitation were true, the gravitational attraction between Sun and Earth would be instantaneous.
    • The gravitational attraction between Sun and Earth is not instantaneous. (The Sun’s gravitational pull on Earth takes a little over 8 minutes.)
    • Therefore Newton’s theory of gravitation is false.
  • The argument can be “translated” into the language of Propositional Logic (where capital letters stand for sentences) as follows:
    • N → I
    • ~I
    • Therefore, ~N
  • In the “formalized” argument:
    • N stands for “Newton’s theory of gravitation is true.”
    • I stands for “The gravitational attraction between Sun and Earth is instantaneous.”
    • → means “If … then —— “.
    • ~ means “It is false that ….”.
  • It is easily shown in Propositional Logic that the translated argument is valid, that is, ~N follows necessarily from N → I and ~I. The form of argument even has a name: modus tollens.
Pages on Formal Logic

Informal (Practical, Applied) Logic

  • Informal (Practical, Applied) Logic is the practical study of the methods of valid reasoning (within a natural language such as English).
Evaluating Arguments
  • The focus of Informal Logic is the evaluation of arguments as they naturally occur in writing and conversation.
  • Evaluating an argument involves:
    • Reconstructing the argument, i.e. restating the argument so its premises, conclusion, and reasoning are clear.
    • Determining how the premises are supposed to support the conclusion.
    • Determining whether the premises, assuming they’re true, support the conclusion.
    • Determining whether the premises are true, typically beyond a reasonable doubt.
    • Determining how likely the conclusion is based on the premises, e.g. whether the conclusion is certain, beyond a reasonable doubt, very likely, more probable than not, plausible, doubtful, and so on.
Pages on Informal Logic
Topics
  • Arguments
    • An argument is an instance of reasoning, from premises to a conclusion.
    • View Arguments
  • Argument Reconstruction
    • Argument reconstruction is the process of restating a naturally-occurring “real life” argument so its premises, conclusion, and reasoning are clear.
    • View Argument Reconstruction
  • Argumentation (Dialectic)
    • Argumentation (Dialectic) is the exchange of arguments, objections, and replies in the hope of shedding light on the matter at issue.
    • View Argumentation
  • Evidential Probability
    • The evidential probability of a proposition is how much it’s supported by the evidence and arguments.
    • Evidential probabilities are expressed by locutions such as: “it is certain that,” “it is beyond a reasonable doubt that,” “it is likely that,” “it is doubtful that,” and “it is impossible that.”
    • View Evidential Probability
  • Fact-checking
    • Fact-checkers rate claims false, misleading, or unsupported based on the evidence and arguments.
    • View Fact-checking
  • Framework for Determining What’s True
  • Framework for Decision-making
  • Kinds of Arguments
    • Deductive Arguments
      • A deductive argument is an argument whose conclusion (purportedly) follows necessarily from its premises.
      • View Deductive Arguments
    • Evidential Arguments
      • An evidential argument is an argument whose premises are evidence (purportedly) making its conclusion probable.
      • View Evidential Arguments
    • Analogical Arguments
      • An analogical argument is an argument that, because things are alike in certain respects, they are therefore (purportedly) alike in a further respect.
      • View Analogical Arguments
    • Normative Arguments
      • A normative argument is an argument whose premises are (purportedly) reasons why a particular action should (or shouldn’t) be done.
      • View Normative Arguments
    • Defeasible Arguments
      • A defeasible argument is an argument whose premises (purportedly) support its conclusion other things being equal (and which support can therefore be “defeated” by additional information).
      • View Defeasible Arguments
  • Logical (Metaphysical) Modalities
    • The logical modalities are the concepts of necessary truth, logical entailment, logical incompatibility, and logical impossibility that underly deductive logic.
    • View Logical (Metaphysical) Modalities
  • Syllogisms and Venn Diagrams
Pitfalls
  • Anomalies of Language
    • The “mist and veil of words,” using George Berkeley’s phrase, can be a source of confusion that impedes reasoning.
    • View Anomalies of Language
  • Artifices of Deception and Distraction
  • Bias
    • Bias is a predisposition that can result in systematic errors in a process of reasoning.
    • View Bias
  • Conspiracy Theories
    • A conspiracy theory explains events by invoking a secret plot by a group of conspirators.
    • View Conspiracy Theories
  • Disinformation
    • “Those who can make you believe absurdities can make you commit atrocities.” — Voltaire
    • View Disinformation
  • Fallacies
    • A fallacy is an error in reasoning having an air of plausibility.
    • View Fallacies
  • Getting Fooled by Statistics
  • Why people believe irrational things
    • People sometimes believe what they’re predisposed to believe through the process of motivated reasoning.
    • View Motivated Reasoning