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Formal and informal logic

When understood in the widest sense, logic encompasses both formal and informal logic.[1] Formal logic is the traditionally dominant field.[2] Various problems in applying its insights to actual everyday arguments have prompted modern developments of informal logic.[3][4][5] They often stress its significance for various practical purposes which formal logic on its own is unable to address.[2][5] Both have in common that they aim to provide criteria for assessing the correctness of arguments and distinguishing them from fallacies.[2][6] Various suggestions have been made concerning how to draw the distinction between the two but there is no universally accepted answer. These difficulties often coincide with the wide disagreements about how informal logic is to be defined.[7][5]

The most literal approach sees the terms "formal" and "informal" as applying to the language used to express arguments.[8][3][4][5] On this view, formal logic studies arguments expressed in formal languages while informal logic studies arguments expressed in informal or natural languages.[2] This means that the inference from the formulas "" and "" to the conclusion "" is studied by formal logic while the inference from the English sentences "Al lit a cigarette" and "Bill stormed out of the room" to the sentence "Al lit a cigarette and Bill stormed out of the room" belongs to informal logic. Formal languages are characterized by their precision and simplicity.[8] They normally contain a very limited vocabulary and exact rules on how their symbols can be used to construct sentences, usually referred to as well-formed formulas.[9] This simplicity and exactness in turn make it possible for formal logic to formulate precise rules of inference that determine whether a given argument is valid.[9] This approach brings with it the need to translate natural language arguments into the formal language before their validity can be assessed, a procedure that comes with various problems of its own.[10][11][5] Informal logic avoids some of these problems by analyzing natural language arguments in their original form without the need of translation.[3][6] But it faces related problems of its own, associated with the ambiguity, vagueness, and context-dependence of natural language expressions.[12][13][2][5] A closely related approach applies the terms "formal" and "informal" not just to the language used, but more generally to the standards, criteria, and procedures of argumentation.[14]

Another approach draws the distinction according to the different types of inferences analyzed.[15][3] This perspective understands formal logic as the study of deductive inferences in contrast to informal logic as the study of non-deductive inferences, like inductive or abductive inferences.[3] The characteristic of deductive inferences is that the truth of their premises ensures the truth of their conclusion. This means that if all the premises are true, it is impossible for the conclusion to be false.[2][16] For this reason, deductive inferences are in a sense trivial or uninteresting since they do not provide the thinker with any new information not already found in the premises.[10][17] Non-deductive inferences, on the other hand, are ampliative: they help the thinker learn something above and beyond what is already stated in the premises. They achieve this at the cost of certainty: even if all premises are true, the conclusion of an ampliative argument may still be false.[10][18][19]

One more approach tries to link the difference between formal and informal logic to the distinction between formal and informal fallacies.[14][5][3][20] This distinction is often drawn in relation to the form, content, and context of arguments. In the case of formal fallacies, the error is found on the level of the argument's form, whereas for informal fallacies, the content and context of the argument are responsible.[21][22][23][24] This is connected to the idea that formal logic abstracts away from the argument's content and is only interested in its form, specifically whether it follows a valid rule of inference.[25][26] It also concerns the idea that it's not important for the validity of a formal argument whether its premises are true or false. Informal logic, on the other hand, also takes the content and context of an argument into consideration.[2][5][8] A false dilemma, for example, involves an error of content by excluding viable options, as in "you are either with us or against us; you are not with us; therefore, you are against us".[22][27] For the strawman fallacy, on the other hand, the error is found on the level of context: a weak position is first described and then defeated, even though the opponent does not hold this position.[22][12]

Other accounts draw the distinction based on investigating general forms of concepts in contrast to particular instances, on the study of logical constants instead of substantive concepts, on the discussion of logical topics with or without formal devices, or on the role of epistemology for the assessment of arguments.[2][5]

Examples for possible inclusion

  • Informal logic would talk about the inference from the English sentences "Al lit a cigarette" and "Bill stormed out of the room" to the sentence "Al lit a cigarette and Bill stormed out of the room", formal logic would address the inference from the formulas "" and "" to the conclusion "".
  • Then go on to talk about generality (though I'm not sure how that's handled in informal approaches).
  • To illustrate context-dependence of natural language, then you could mention that order of conjuncts alters meaning in natural language (e.g. Al smoking caused Bill to get mad vs Bill getting mad caused Al to need a smoke) but that order doesn't matter in (classical) logic.

Refs

  1. ^ Cite error: The named reference HaackLogics1 was invoked but never defined (see the help page).
  2. ^ a b c d e f g h Cite error: The named reference RoutledgeFormalInformal was invoked but never defined (see the help page).
  3. ^ a b c d e f Groarke, Leo (2021). "Informal Logic". The Stanford Encyclopedia of Philosophy. Metaphysics Research Lab, Stanford University. Retrieved 31 December 2021.
  4. ^ a b Audi, Robert. "Informal logic". The Cambridge Dictionary of Philosophy. Cambridge University Press.
  5. ^ a b c d e f g h i Johnson, Ralph H. (1999). "The Relation Between Formal and Informal Logic". Argumentation. 13 (3): 265–274. doi:10.1023/A:1007789101256.
  6. ^ a b Cite error: The named reference Blair was invoked but never defined (see the help page).
  7. ^ van Eemeren, Frans H.; Garssen, Bart; Krabbe, Erik C. W.; Snoeck Henkemans, A. Francisca; Verheij, Bart; Wagemans, Jean H. M. (2021). "Informal Logic". Handbook of Argumentation Theory. Springer Netherlands. pp. 1–45. ISBN 978-94-007-6883-3.
  8. ^ a b c Honderich, Ted (2005). "logic, informal". The Oxford Companion to Philosophy. Oxford University Press.
  9. ^ a b Craig, Edward (1996). "Formal languages and systems". Routledge Encyclopedia of Philosophy. Routledge.
  10. ^ a b c Cite error: The named reference Hintikka was invoked but never defined (see the help page).
  11. ^ Cite error: The named reference Magnus was invoked but never defined (see the help page).
  12. ^ a b Walton, Douglas N. (1987). "1. A new model of argument". Informal Fallacies: Towards a Theory of Argument Criticisms. John Benjamins.
  13. ^ Engel, S. Morris (1982). "2. The medium of language". With Good Reason an Introduction to Informal Fallacies.
  14. ^ a b Blair, J. Anthony; Johnson, Ralph H. (1987). "The Current State of Informal Logic". Informal Logic. 9 (2).
  15. ^ Weddle, Perry (26 July 2011). "36. Informal logic and the eductive-inductive distinction". Argumentation 3. De Gruyter Mouton. ISBN 978-3-11-086771-8.
  16. ^ Cite error: The named reference McKeon was invoked but never defined (see the help page).
  17. ^ D'Agostino, Marcello; Floridi, Luciano (2009). "The Enduring Scandal of Deduction: Is Propositional Logic Really Uninformative?". Synthese. 167 (2): 271–315. ISSN 0039-7857.
  18. ^ Backmann, Marius (1 June 2019). "Varieties of Justification—How (Not) to Solve the Problem of Induction". Acta Analytica. 34 (2): 235–255. doi:10.1007/s12136-018-0371-6. ISSN 1874-6349.
  19. ^ "Deductive and Inductive Arguments". Internet Encyclopedia of Philosophy. Retrieved 4 December 2021.
  20. ^ Hansen, Hans (2020). "Fallacies". The Stanford Encyclopedia of Philosophy. Metaphysics Research Lab, Stanford University. Retrieved 18 March 2021.
  21. ^ Vleet, Van Jacob E. (2010). "Introduction". Informal Logical Fallacies: A Brief Guide. Upa.
  22. ^ a b c Dowden, Bradley. "Fallacies". Internet Encyclopedia of Philosophy. Retrieved 19 March 2021.
  23. ^ Stump, David J. "Fallacy, Logical". www.encyclopedia.com. Retrieved 20 March 2021.
  24. ^ Korb, Kevin (2004). "Bayesian Informal Logic and Fallacy". Informal Logic. 24 (1): 41–70.
  25. ^ Cite error: The named reference MacFarlane2 was invoked but never defined (see the help page).
  26. ^ Cite error: The named reference Corkum was invoked but never defined (see the help page).
  27. ^ Mackie, J. L. (1967). "Fallacies". www.encyclopedia.com. Retrieved 19 March 2021.
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