---
title: "Logic"
chunk: 2/11
source: "https://en.wikipedia.org/wiki/Logic"
category: "reference"
tags: "science, encyclopedia"
date_saved: "2026-05-05T03:56:39.118518+00:00"
instance: "kb-cron"
---

Formal logic uses formal languages to express, analyze, and clarify arguments. They normally have a very limited vocabulary and exact syntactic rules. These rules specify how their symbols can be combined to construct sentences, so-called well-formed formulas. This simplicity and exactness of formal logic make it capable of formulating precise rules of inference. They determine whether a given argument is valid. Because of the reliance on formal language, natural language arguments cannot be studied directly. Instead, they need to be translated into formal language before their validity can be assessed.
The term "logic" can also be used in a slightly different sense as a countable noun. In this sense, a logic is a logical formal system. Distinct logics differ from each other concerning the rules of inference they accept as valid and the formal languages used to express them. Starting in the late 19th century, many new formal systems have been proposed. There are disagreements about what makes a formal system a logic. For example, it has been suggested that only logically complete systems, like first-order logic, qualify as logics. For such reasons, some theorists deny that higher-order logics are logics in the strict sense.

=== Informal logic ===

When understood in a wide sense, logic encompasses both formal and informal logic. Informal logic uses non-formal criteria and standards to analyze and assess the correctness of arguments. Its main focus is on everyday discourse. Its development was prompted by difficulties in applying the insights of formal logic to natural language arguments. In this regard, it considers problems that formal logic on its own is unable to address. Both provide criteria for assessing the correctness of arguments and distinguishing them from fallacies.
Many characterizations of informal logic have been suggested but there is no general agreement on its precise definition. The most literal approach sees the terms "formal" and "informal" as applying to the language used to express arguments. On this view, informal logic studies arguments that are in informal or natural language. Formal logic can only examine them indirectly by translating them first into a formal language while informal logic investigates them in their original form. On this view, the argument "Birds fly. Tweety is a bird. Therefore, Tweety flies." belongs to natural language and is examined by informal logic. But the formal translation "(1) 
  
    
      
        ∀
        x
        (
        
          B
          i
          r
          d
        
        (
        x
        )
        →
        
          F
          l
          i
          e
          s
        
        (
        x
        )
        )
      
    
    {\displaystyle \forall x(\mathrm {Bird} (x)\to \mathrm {Flies} (x))}
  
; (2) 
  
    
      
        
          B
          i
          r
          d
        
        (
        
          T
          w
          e
          e
          t
          y
        
        )
      
    
    {\displaystyle \mathrm {Bird} (\mathrm {Tweety} )}
  
; (3) 
  
    
      
        
          F
          l
          i
          e
          s
        
        (
        
          T
          w
          e
          e
          t
          y
        
        )
      
    
    {\displaystyle \mathrm {Flies} (\mathrm {Tweety} )}
  
" is studied by formal logic. The study of natural language arguments comes with various difficulties. For example, natural language expressions are often ambiguous, vague, and context-dependent. Another approach defines informal logic in a wide sense as the normative study of the standards, criteria, and procedures of argumentation. In this sense, it includes questions about the role of rationality, critical thinking, and the psychology of argumentation.
Another characterization identifies informal logic with the study of non-deductive arguments. In this way, it contrasts with deductive reasoning examined by formal logic. Non-deductive arguments make their conclusion probable but do not ensure that it is true. An example is the inductive argument from the empirical observation that "all ravens I have seen so far are black" to the conclusion "all ravens are black".
A further approach is to define informal logic as the study of informal fallacies. Informal fallacies are incorrect arguments in which errors are present in the content and the context of the argument. A false dilemma, for example, involves an error of content by excluding viable options. This is the case in the fallacy "you are either with us or against us; you are not with us; therefore, you are against us". Some theorists state that formal logic studies the general form of arguments while informal logic studies particular instances of arguments. Another approach is to hold that formal logic only considers the role of logical constants for correct inferences while informal logic also takes the meaning of substantive concepts into account. Further approaches focus on the discussion of logical topics with or without formal devices and on the role of epistemology for the assessment of arguments.

== Basic concepts ==

=== Premises, conclusions, and truth ===

==== Premises and conclusions ====