Logic

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

Arguments

  • Reasoning is the process of trying to answer a question, resolve an issue, solve a problem, or make a decision by rational means.  Logic is the study of the rational means by which thinkers ought to reason. 
  • The focus of Logic is on the evaluation of arguments.
  • An argument is an instance of reasoning, from premises to a conclusion.
  • Examples:
  • Declaration of Independence:
    • 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.
    • The British government of the colonies has violated those rights.
    • Therefore the American people have a right to alter or abolish the British government of the colonies.
  • Benjamin Franklin
    • 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
    • A spark is electrical in nature.
    • It’s therefore plausible that lightning is electrical in nature.
      • “Let the experiment be made.”
  • Against Capital Punishment
    • Fallible governments should refrain from inflicting irreversible punishments
    • Capital punishment is irreversible.
    • Governments are fallible.
    • Therefore, governments should refrain from inflicting capital punishment.
  • Special Relativity
    • The energy of a particle moving with velocity v is mc2/√(1 – v2/c2)
    • For a particle at rest, where v = 0, √(1 – v2/c2) = 1.
    • Therefore, for a particle at rest, E = mc2.
  • Poker Hand
    • There are 624 card-combinations of four-of-a-kind in five card draw poker.
    • There are 2598960 card-combinations of five cards dealt from a 52-card deck.
    • Therefore the probability of four-of-a-kind in five card draw poker is 624/2598960.
  • In each case the argument is put forth to establish its conclusion, i.e. to establish:
    • That the American people have a right to alter or abolish the British government of the colonies.
    • That it’s plausible that lightning is electrical in nature.
    • That governments should refrain from inflicting capital punishment.
    • That, for a particle at rest, E = mc2.
    • That the probability of four-of-a-kind in five card draw poker is 624/2598960.

Kinds of Arguments

  • A deductive argument is an argument from premises to a logical consequence.
    • Example:
      • John Oliver is not eligible to be president because he’s not a natural-born U.S. citizen (and only natural-born U.S. citizens are eligible).
  • An evidential argument is an argument from evidence to a probable hypothesis.
    • Examples:
      • The suspect’s fingers were in contact with the murder weapon because the suspect’s fingerprints match those on the murder weapon (and a fingerprint match is reliable evidence that the fingerprints belong to the same person).
      • Thomas Jefferson likely fathered some of Sally Hemings’ children because that’s the best explanation of (1) her children’s physical appearance and (2) a one-in-thousand Y-chromosome match between a male descendant of Jefferson’s paternal uncle and a male descendant of one of Hemings’ sons.
  • A normative argument is an argument, based on reasons, that a particular action should (or shouldn’t) be done.
    • Examples:
      • You shouldn’t shoplift because stealing is wrong (and shoplifting is stealing).
      • You shouldn’t shoplift because you might get caught (and getting caught is bad).
  • An analogical argument is an inference from known similarities to a further similarity
    • Examples:
      • Cheating is morally wrong because there’s no morally relevant difference between cheating and surreptitiously changing your grade on the instructor’s spreadsheet (and the latter is morally wrong).
      • Your house will likely sell for about $250,000 because it’s very similar to three recently-sold houses nearby that sold for about that amount.

Branches of Logic

Brief Descriptions

  • Analysis of Knowledge
    • Knowledge as true justified belief.
  • Anomalies of Language
    • The “mist and veil of words”
  • Arguments
  • Argument Reconstruction
    • Argument Reconstruction is the process of restating a naturally-occurring argument so its premises, conclusion, and logic are clear, making it easier to understand and evaluate.
  • Artifices of Deception and Distraction
    • The methods of deception and distraction used to fool people and change the subject
  • Axiom Systems
    • An axiom system is a set of assumptions from which logical consequences are derived.
  • Bias
    • A process of reasoning is biased if it has errors that systematically favor one conclusion over others due to a predisposition of the reasoner. 
    • A statistical study is biased if it has errors that systematically favor one outcome over others due to a flaw in the study’s methodology.
  • Conspiracy Theories
    • A conspiracy theory explains events by invoking a secret plot by a group of conspirators.
    • Ockham’s Razor provides an a priori reason for rejecting conspiracy theories, since the straightforward explanation of events is simpler.
  • Decision-Making
    • Articulate the issue
    • Frame the options
    • Formulate the arguments
    • Evaluate the arguments and decide
  • Determining What’s True
    • Articulate the question
    • Frame competing positions
    • Formulate the arguments for and against the positions
    • Evaluate the arguments
    • Judge the epistemic probabilities of the positions
  • Dialectic (Argumentation)
    • Dialectic is an exchange of arguments to find the truth
  • Disinformation
    • “Those who can make you believe absurdities can make you commit atrocities.” (Voltaire)
  • Decision Theory
    • Alternative courses of action are assessed by the expected value (probability times value) of their projected consequences.
  • Deductive Logic
    • Deductive Logic is the formal theory of deductive reasoning.
  • Epistemic Probability
    • The epistemic probability of a proposition is how reasonable it is to believe.
  • Ethics
    • Ethics is the investigation of right and wrong, good and bad, and what ought to be done
  • Epistemology
    • Epistemology is the investigation of knowledge and rational belief
  • Fact-checking
    • Fact-checkers rate claims true, false, misleading, and unsupported by evaluating the evidence and arguments for and against.
  • Fallacies
    • A fallacy is an error in reasoning having an air of plausibility.
  • History of Philosophy
    • The History of Philosophy is the history of philosophic arguments
  • Fooled by Statistics
    • Because it’s tricky, it’s easy to be fooled by statistics
  • Forecasting
    • Time Series, Regression, Forecasting Models, Expert Opinion, Prediction Markets
  • Logic
    • Tools for formulating and evaluating arguments
  • Logical Equivalences among Why, Because, Reason, Therefore, Explain
    • Their logical equivalences
  • Metaphysics
    • Metaphysics is the investigation of basic questions about reality.
  • Paradoxes
    • A paradox is a seemingly valid instance of reasoning leading to an absurdity.
  • Philosophy
    • Philosophy is the investigation of fundamental issues by rational argument.
  • Political Philosophy
    • Political Philosophy is the normative and conceptual inquiry into forms of government
  • Probability Theory
    • Probability Theory is the formal theory of probability.
  • Scientific Models
    • A model is a simple representation of complex phenomena.
  • Scientific Theories
    • A scientific theory is:
      • designed to explain certain kinds of phenomena
      • defined by its postulates
      • supported or disproved by its predictions
  • Skepticism
    • Skepticism is the disposition to believe based only on rational argument
  • Syllogisms and Venn Diagrams
    • Venn Diagrams are sets of overlapping circles used to determine the validity of syllogisms.
  • Thought Experiments
    • A thought-experiment is a hypothetical scenario set forth either as a puzzlement or as a basis for argument.
  • How People Form Unwarranted Beliefs
    • People believe what they’re predisposed to believe through motivated reasoning

Epistemic Pitfalls