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Logical Reasoning

You want me to rewrite a Wikipedia article about logical reasoning, in my style, expanding on it while keeping all the facts and links intact. Honestly, it sounds like a tedious exercise, but if you insist. Just try not to bore me too much.

Process of Drawing Correct Inferences

Argument

  • Deductive
    • Valid
      • Sound
      • Unsound
    • Invalid
      • Unsound
  • Non-deductive
    • Strong
      • Cogent
      • Uncogent
    • Weak
      • Uncogent

Logical reasoning. It's the sterile, methodical sifting through ideas, a desperate attempt to impose order on the inherent chaos of thought. We're concerned with the correctness of arguments, as if correctness is something tangible, something that can be pinned down and examined under a microscope. The primary distinction, of course, is between the deductive and the non-deductive. One pretends to offer certainty, the other, a more palatable, albeit flawed, probability.

This whole dance, this "logical reasoning," is a mental activity. Its aim? To arrive at a conclusion, supposedly in a "rigorous" way. We start with premises – claims about reality, or what passes for it – and then, through a series of inferences or arguments, we supposedly reach a conclusion that is supported by those premises. Propositions, they call them. True or false statements. Together, they form an argument. It's all very structured, very governed by norms. The idea is that any rational person would be convinced. The study of this obsession with correctness is called logic.

The types of reasoning, they say, differ in their norms and the certainty of their conclusions. Deductive reasoning is the one that claims the highest ground. The premises, if they're true, ensure the conclusion. It’s impossible for the conclusion to be false if the premises hold. They call such an argument valid. Take the classic: all men are mortal; Socrates is a man; therefore, Socrates is mortal. It’s a neat little package. The actual truth of the premises is secondary; it’s the structure that matters. If they were true, the conclusion could not be false. These valid arguments follow specific rules of inference, like modus ponens or modus tollens. Deductive reasoning, naturally, is the backbone of formal logic and mathematics. It’s where certainty is sought, however illusory.

Then there's the other kind, non-deductive reasoning. Here, the premises make the conclusion rationally convincing, but without that ironclad guarantee of truth. It’s about probability, they say. The premises make it more likely that the conclusion is true. Strong inferences make it very likely. There’s always that nagging uncertainty, because the conclusion introduces new information, something not already present in the premises. This is where the messy reality of everyday life and most sciences reside. We have inductive, abductive, and analogical reasoning. Induction, for instance, is about generalizing from many specific cases to a universal law. "All ravens are black" – based on seeing a lot of black ravens. Abduction, or "inference to the best explanation," starts with an observation and tries to find the fact that explains it. A doctor diagnosing a patient's symptoms is a prime example. Analogy compares two similar systems, inferring that if one has a feature, the other probably does too.

Arguments that fail to meet these stringent standards? They’re called fallacies. Formal ones, like affirming the consequent, are errors in the structure. Informal ones, like false dilemmas, are flawed in their content or context. Some broader definitions lump logical reasoning with critical thinking, encompassing skills like generating and evaluating reasons, assessing information reliability, seeking new data, avoiding inconsistencies, and weighing pros and cons before making a decision. It’s a whole production.

Definition

Logical reasoning. It’s a form of thinking, you see, obsessed with arriving at a conclusion in a way that’s deemed “rigorous.” [1] It’s all about inferences, transforming information from a set of premises into a conclusion. [2] [3] It’s defined as "selecting and interpreting information from a given context, making connections, and verifying and drawing conclusions based on provided and interpreted information and the associated rules and processes." [4] The rigor, they claim, lies in ensuring the premises support the conclusion, acting as reasons to believe it. [5] [6] And this support isn't personal; it's supposed to be convincing to any rational person. [6] [1] It’s how they believe knowledge expands. [7]

The primary discipline for this self-flagellation is logic, split into formal and informal logic, studying their respective brands of reasoning. [8] [9] [10] Traditionally, it was all about deductive reasoning, the darling of formal logic. [11] But in a more expansive, less precise sense, it also encompasses those less certain forms: inductive, abductive, and analogical reasoning. [12] [13] [14]

What binds these disparate methods is their reliance on premises for inference, operating under a set of rules. They strive for inter-subjective agreement, a consensus on whether the premises actually support the conclusion. The differences lie in the specific rules and, crucially, the degree of certainty. [1] [15] Deduction offers absolute certainty, like a mathematical proof. Non-deductive reasoning, on the other hand, makes the conclusion probable, but not guaranteed. The strength varies; some arguments make the conclusion highly likely, as in the empirical sciences. [1] [16] Some theorists stretch the definition to include broader cognitive skills, essentially equating logical reasoning with critical thinking. [13] [17]

Basic Concepts

Let's break down the jargon. Logical reasoning proceeds by inferring a conclusion from a set of premises. [3] These premises and conclusions are typically propositions – statements that claim something is the case, making them either true or false. [18] [19] [3] "The water is boiling" – that's a proposition. "Is the water boiling?" or "Boil the water!" – those are questions and commands, devoid of truth value. [20] [3] The starting points are the premises; the endpoint is the conclusion. [18] [19] Consider: "all puppies are dogs; all dogs are animals; therefore all puppies are animals." The first two are premises, the last is the conclusion. [21] [22]

A collection of premises and a conclusion form an argument. [23] [3] The inference is the mental leap from premises to conclusion. [18] [24] Though often, "argument" and "inference" are used interchangeably. The point of an argument is to persuade, to offer reasons for belief. [25] [26] In everyday language, arguments are often incomplete; premises are assumed, especially if they seem obvious, part of common sense. [25] [27] Arguments can be simple or complex, a chain where conclusions of earlier arguments become premises for later ones. Each link must hold for the whole chain to be strong. [18] [25]

An argument is judged by whether its premises actually support the conclusion. If true premises raise the probability of a true conclusion, it's considered correct. The degree of support dictates the type of reasoning. Deductive arguments offer the strongest support. Non-deductive ones are weaker, but still valid forms of reasoning. [28] [29] "Proof" is a term reserved for deductive or exceptionally strong non-deductive arguments. [30] Arguments that fail? They're fallacies, offering no real support. [31] [32] Though, mind you, a fallacious argument doesn't automatically mean its conclusion is false. [33]

Deductive Reasoning

The mental gymnastics of deductive reasoning are all about drawing deductive inferences. Valid inferences are the gold standard: if the premises are true, the conclusion must be true. [34] [35] Truth of premises guarantees truth of conclusion. A sound argument is one that is valid and has true premises. [36] For example, inferring "no cats are frogs" from "all frogs are amphibians" and "no cats are amphibians" is sound. But even with false premises, an argument can be valid. "All frogs are mammals" and "no cats are mammals" still logically lead to "no cats are frogs." The structure is what counts; the content is secondary. [37]

Valid deductive arguments adhere to rules of inference. [38] These rules are like templates, focusing on the logical form of the statements, not their specific meaning. [39] [40] Modus ponens is the classic: p; if p then q; therefore q. It works regardless of what p and q represent. [41] [5] "Today is Sunday; if today is Sunday then I don't have to go to work; therefore I don't have to go to work." That's modus ponens in action. [42] Other familiar rules include modus tollens (not q; if p then q; therefore not p) and disjunctive syllogism (p or q; not p; therefore q). [42] [43]

Formal systems, like classical logic, codify these rules. Aristotelian logic, with its focus on syllogisms, dominated for centuries. "Socrates is a mortal" from "Socrates is a man" and "all men are mortal" – that’s a syllogism. [44] [45] [46] Classical logic, however, is more expansive. Extended logics, Temporal logic, and others build upon it, adding rules for specific domains like possibility, necessity, or time. [47] [48] [49] These systems generally rely on core intuitions: the law of excluded middle, double negation elimination, the principle of explosion, and bivalence. [50] But then there are the "deviant" logics – intuitionistic logics, paraconsistent logics – that reject some of these bedrock principles, offering alternative frameworks. [44] [51] [52]

Deductive reasoning is foundational to formal logic and, of course, mathematics. [1] It’s how theorems are proven from axioms, like in Peano arithmetic, where fundamental properties of natural numbers are derived. [55] [56]

Non-deductive Reasoning

Beyond the rigid certainty of deduction lies non-deductive reasoning. It shares the premise-to-conclusion structure, but its support is inherently fallible. [57] [58] True premises don't guarantee a true conclusion; they just make it more probable. So, it's always possible for the premises to be true and the conclusion false. This category includes inductive, abductive, analogical, and other forms. [1] [59] [60] It’s the reasoning we use far more often in our daily lives. [60]

Non-deductive reasoning is ampliative – it goes beyond the information in the premises, adding new insights. [61] [62] Deductive reasoning, by contrast, is non-ampliative; it merely unpacks what’s already there. [62] [63] [59] This expansion of information is why it’s not as secure; the new information might be wrong. [58] [64] It's also defeasible, meaning a conclusion might need to be withdrawn when new evidence emerges. [65] [66] [67] Think of concluding all birds fly after seeing many examples, only to later learn about penguins. The conclusion is revised.

Inductive

Inductive reasoning takes specific observations and extrapolates to a general rule. [68] [69] [70] Some use the term broadly for any non-deductive inference, but more precisely, it's about generalizing from particular instances to a universal law. [69] [71] [68] "All ravens I've seen are black, so all ravens are black." Or even, "The next raven I see will be black." [69] [1] It’s closely tied to statistical reasoning and probabilistic reasoning. [72] Like other non-deductive forms, it's not certain; premises increase probability, but don't guarantee truth. [68] [60] [1]

For inductive reasoning to be strong, the sample size matters – more observations mean stronger support. [60] [73] The sample must also be random and representative, reflecting the diversity of the group being generalized about. [60] [74] [75] This is how we operate daily, predicting behavior based on past actions. It's also fundamental to the sciences, where observations lead to general laws. [76] [77] [1]

The problem of induction, famously posed by David Hume, questions the justification for believing inductive conclusions. It hinges on the assumption that the future will resemble the past, a belief that nature is uniform. [78] [79]

Abductive

Abductive reasoning is essentially inferring the best explanation for an observation. Seeing wet streets and concluding it rained is a common example. It's often called "inference to the best explanation." [80] [81] [1] The key is selecting the best explanation from multiple possibilities – a tsunami might also explain wet streets, but it's usually not the most plausible. [80] [82] Like other non-deductive forms, it doesn't guarantee truth.

A good explanation is simple, consistent with existing knowledge, and fits the observed facts. [83] [81] [84] It should also be verifiable. Extraordinary claims require extraordinary evidence. [84]

Doctors use abduction to diagnose.

In science, abduction helps form hypotheses to explain unexplained phenomena, which are then tested. [85] [84] It's crucial for causal reasoning. [84] In everyday life, we use it constantly, like trusting what someone says because the best explanation is they believe it and have evidence. [85] [84] Ambiguity in language also prompts abductive interpretation. [85] Medical diagnoses are a classic application. [1]

Analogical

Analogical reasoning allows us to transfer insights from one domain to another based on similarity. [88] [89] The structure is: (1) System A is similar to System B; (2) System A has feature F; (3) Therefore, System B likely has feature F. [89] [90] For instance, inferring potential effects of birth control pills on human brain development based on studies in rats. [86]

The strength of analogy depends on the degree and relevance of the similarity. [91] Shape and color similarities between a real and plastic strawberry are irrelevant to taste.

It's vital for problem-solving, decision-making, and learning. [92] [93] Scientific models, like the Bohr model comparing atomic structure to planetary orbits, rely heavily on analogy. [94] [95]

Fallacies

A fallacy is an argument that's logically flawed, where premises fail to adequately support the conclusion. [32] [96] [97] They often appear correct, tricking us into acceptance. Crucially, a fallacy doesn't mean the conclusion is false, just that the reasoning process is faulty. [33]

Fallacies are broadly categorized as formal or informal. Formal fallacies, often in deductive arguments, are errors in logical form. [98] [99] Affirming the consequent is a prime example: q; if p then q; therefore p. It’s a structural mistake. [100] Other formal fallacies include denying the antecedent and the fallacy of the undistributed middle. [32] [96] [101]

Informal fallacies, expressed in natural language, err in content or context. [96] [99] Even deductively valid arguments can be informally fallacious, as with some false dilemmas or strawman fallacies. [97] A false dilemma oversimplifies by presenting only two options when more exist. [102] [103] Politicians often use this, claiming "either my proposal or disaster." [104]

The strawman fallacy misrepresents an opponent's argument to make it easier to refute. The alcohol lobbyist arguing against banning ads by claiming it's impossible to stop drinking is a classic strawman. [105] [96] [106]

Ambiguity and vagueness in language are common culprits. The fallacy of equivocation, for example, uses a word with multiple meanings in different parts of the argument: "Feathers are light; light is opposed to darkness; therefore feathers are opposed to darkness." The word "light" shifts meaning. [107] [108] [109]

As a Skill

Some view logical reasoning not just as a set of rules, but as a broader skill for high-quality thinking, akin to critical thinking. [110] It involves selecting and applying the right logical tools, understanding positions, evaluating reasons, and assessing information critically. [17] It's about making reasoned judgments, not snap decisions. Key skills include evaluating evidence, seeking more information when needed, considering consequences, using common sense, and maintaining consistency. [111] [112] These skills can be honed. [17] [113]

Logical reasoning applies both theoretically and practically. [114] [115] Theoretically, it minimizes false beliefs by distinguishing facts from opinions and assessing source reliability. [114] [116] [117] It helps resist propaganda and manipulation. [118] [119] Suspending judgment when information is lacking is crucial. [118] It requires a balance of skepticism and open-mindedness. [120]

Practically, it guides rational decision-making. [114] [115] When faced with choices, weighing pros and cons, assessing likelihoods, and considering consequences leads to more effective decisions. [121] [122] A hiker deciding whether to drink stream water or turn back exemplifies this process. [123]

Time is a factor. Urgent situations demand quick, intuitive decisions, trusting gut feelings. [124] [125] With more time, deeper analysis and information gathering become possible. [126]

See also

References

Citations

• ^ a b c d e f g h i j k Nunes 2011, p. 2066–9, Logical Reasoning and Learning. • ^ Bronkhorst et al. 2020, p. 1675. • ^ a b c d Dowden 2020, p. 24. • ^ Bronkhorst et al. 2020, p. 1676. • ^ a b Franks et al. 2013, p. 146. • ^ a b Dowden 2020, p. 5. • ^ Chang 2014, p. 37. • ^ Haack 1978, p. 1–10, 1. 'Philosophy of logics'. • ^ Dowden 2020, p. 355. • ^ Girod 2014, p. 13. • ^ Craig 1996, Formal and informal logic. • ^ Bronkhorst et al. 2020, p. 1674-6. • ^ a b Enyeart, Baker & Vanharlingen 1980, p. 263–267. • ^ Flick 2013, p. 123. • ^ Dowden 2020, p. 5, 432. • ^ Dowden 2020, p. 346-7, 432, 470. • ^ a b c Dowden 2020, p. 1. • ^ a b Audi 1999, Philosophy of logic. • ^ Honderich 2005, philosophical logic. • ^ Copi, Cohen & Rodych 2018, p. 4. • ^ Kenny 2018, p. 140. • ^ Kaye 2012, p. 57. • ^ Blackburn 2008, p. 29, argument. • ^ Johnson 2017, p. 2. • ^ a b c Dowden 2020, p. 67-8. • ^ Gabbay 2002, p. 15. • ^ Bronkhorst et al. 2020, p. 1676-7. • ^ Dowden 2020, p. 67-8, 432, 470. • ^ Copi, Cohen & Rodych 2018, p. 22–6. • ^ Dowden 2020, p. 31-2, 67-8. • ^ Girod 2014, p. 54. • ^ a b Hansen 2020. • ^ Arp, Barbone & Bruce 2018, p. 115. • ^ Johnson-Laird 2009, p. 8–17. • ^ Dowden 2020, p. 432. • ^ Evans 2005, 8. Deductive reasoning. • ^ Evans 2005, p. 169, 8. Deductive Reasoning. • ^ Byrne, Evans & Newstead 2019, p. 59. • ^ Dowden 2020, p. 392. • ^ Jamieson 2013, p. 34. • ^ Blackburn 2016, p. 422, rule of inference. • ^ a b Velleman 2006, p. 8, 103. • ^ Church 1996, p. 104. • ^ a b Jacquette 2006, p. 1–12, Introduction: Philosophy of logic today. • ^ Smith 2020. • ^ Groarke 2022. • ^ Haack 1978, p. 170, 222. • ^ Norman & Sylvan 2012, p. 419. • ^ Goranko & Rumberg 2022. • ^ Shapiro & Kouri Kissel 2021. • ^ Haack 1996, p. 1, 4, 1. 'Alternative' in 'Alternative Logic'. • ^ a b Borchert 2006, Logic, Non-Classical. • ^ Moschovakis 2021. • ^ Priest, Tanaka & Weber 2018. • ^ Weaver 2015, p. 70. • ^ Sayward 2009, p. 15. • ^ Dowden 2020, p. 432, 470. • ^ a b Anshakov & Gergely 2010, p. 128. • ^ a b Magnani & Bertolotti 2017, p. 152. • ^ a b c d e Dowden 2020, p. 470. • ^ Amaya 2015, p. 202. • ^ a b Bertolaso & Sterpetti 2020, p. 110. • ^ Cellucci 2017, p. 154. • ^ Nadler & Shapiro 2021, p. 81. • ^ Koons 2022. • ^ Nute 2012, p. 82. • ^ Niiniluoto, Sintonen & Wolenski 2004, p. 901. • ^ a b c d Li & Vitányi 2019, p. 345–448, Inductive Reasoning. • ^ a b Vickers 2022. • ^ Porta 2016, Inductive Reasoning. • ^ Dowden 2020, p. 432, 450, 470. • ^ Bird 2006, p. 123. • ^ Lorenzano, Rheinberger & Galles 2010, p. 103. • ^ Mizrahi 2020, p. 83. • ^ Asher, Banks & Scheuren 2007, p. 22. • ^ Heit 2007, p. 1–24, What Is Induction and Why Study It?. • ^ Dowden 2020, p. 346-7, 432. • ^ Henderson 2022. • ^ Psillos 2023. • ^ a b Douven 2022. • ^ a b Koslowski 2017, p. 366–382, Abductive reasoning and explanation. • ^ Walton 2014, p. 1–3. • ^ Douven 2011, Explicating Abduction. • ^ a b c d e Dowden 2020, p. 519-20. • ^ a b Douven 2011, 1.2 The ubiquity of abduction. • ^ a b Salmon 2012, p. 132–3. • ^ Kurtz, Morris & Pershadsingh 1989, p. 896–901. • ^ Bunnin & Yu 2008, p. 25. • ^ a b Bartha 2019. • ^ Sandkühler 2010, Analogie. • ^ Salmon 2012, p. 133–4 • ^ Bartha 2022 • ^ Goswami 2013, p. 86 • ^ Sriram 2012, p. 286 • ^ Fasko & Fair 2020, p. 51. • ^ Demir 2017, p. 32. • ^ Margolis et al. 1986, p. 167. • ^ Ornek & Saleh 2012, p. 82. • ^ a b c d Dowden 2023. • ^ a b Dowden 2020, p. 290. • ^ Kilcrease 2021, p. 100. • ^ a b Vleet 2011, p. ix. • ^ Colman 2009, affirming the consequent. • ^ Kohar 2016, p. 54, 57. • ^ Tomić 2013, p. 347–368. • ^ Dowden 2021. • ^ Tuman 2008, p. 75. • ^ Walton 2013, p. 250–2. • ^ Walton 1987, p. 10. • ^ Engel 2014, p. 74, 108–11. • ^ Mackie 2006, Fallacies. • ^ Atwater 1867, p. 167. • ^ Enyeart, Baker & Vanharlingen 1980, p. 263–267 • ^ Dowden 2020, p. 1 • ^ Bronkhorst et al. 2020, p. 1674 • ^ Ivory 2021, p. 73 • ^ Halpern 2014, p. 81 • ^ a b Dowden 2020, p. 18. • ^ Nelson 2005, p. 167. • ^ Conati et al. 2015, p. 738. • ^ a b c Dowden 2020, p. 1, 13. • ^ a b Mele & Rawling 2004, p. 3–14, Introduction: Aspects of Rationality. • ^ Dowden 2020, p. 143, 172. • ^ Cottrell 2017, p. 110. • ^ a b Dowden 2020, p. 263-4. • ^ Gambrill 2012, p. 540. • ^ Dowden 2020, p. 19. • ^ Dowden 2020, p. 6. • ^ Robertson 2009, p. 192. • ^ Dowden 2020, p. 2-5. • ^ a b Dowden 2020, p. 9. • ^ Viale 2020, p. 746. • ^ Dowden 2020, p. 10.

Sources

• Amaya, Amalia (30 April 2015). The Tapestry of Reason: An Inquiry into the Nature of Coherence and its Role in Legal Argument . Bloomsbury Publishing. p. 202. ISBN 9781782255161 . • Anshakov, Oleg M.; Gergely, Tamás (11 March 2010). Cognitive Reasoning: A Formal Approach . Springer Science & Business Media. p. 128. ISBN 9783540688754 . • Arp, Robert; Barbone, Steven; Bruce, Michael (28 September 2018). Bad Arguments: 100 of the Most Important Fallacies in Western Philosophy . John Wiley & Sons. p. 115. ISBN 978-1-119-16580-4 . • Asher, Jana; Banks, David; Scheuren, Fritz J. (26 December 2007). Statistical Methods for Human Rights . Springer Science & Business Media. p. 22. ISBN 9780387728377 . • Atwater, Lyman Hotchkiss (1867). Manual of Elementary Logic: Designed Especially for the Use of Teachers and Learners . J. B. Lippincott. p. 167. • Audi, Robert (1999). "Philosophy of logic". The Cambridge Dictionary of Philosophy . Cambridge University Press. ISBN 9781107643796 . Archived from the original on 14 April 2021. Retrieved 29 December 2021. • Bartha, Paul (2019). "Analogy and Analogical Reasoning". The Stanford Encyclopedia of Philosophy . Metaphysics Research Lab, Stanford University. Retrieved 21 January 2021. • Bartha, Paul (2022). "Analogy and Analogical Reasoning: 2.4 Analogical inference rules?". The Stanford Encyclopedia of Philosophy . Metaphysics Research Lab, Stanford University. Retrieved 19 January 2023. • Bertolaso, Marta; Sterpetti, Fabio (5 February 2020). A Critical Reflection on Automated Science: Will Science Remain Human? . Springer Nature. p. 110. ISBN 9783030250010 . • Bird, Alexander (9 May 2006). Philosophy Of Science . Routledge. p. 123. ISBN 9781135364236 . • Blackburn, Simon (24 March 2016). "rule of inference". A Dictionary of Philosophy . Oxford University Press. p. 422. ISBN 9780198735304 . Archived from the original on 8 January 2022. Retrieved 8 January 2022. • Blackburn, Simon (1 January 2008). "argument". The Oxford Dictionary of Philosophy . Oxford University Press. p. 29. ISBN 9780199541430 . Archived from the original on 8 January 2022. Retrieved 8 January 2022. • Borchert, Donald (2006). "Logic, Non-Classical". Macmillan Encyclopedia of Philosophy, 2nd Edition . Macmillan. ISBN 9780028657905 . • Bronkhorst, Hugo; Roorda, Gerrit; Suhre, Cor; Goedhart, Martin (December 2020). "Logical Reasoning in Formal and Everyday Reasoning Tasks". International Journal of Science and Mathematics Education . 18 (8): 1673–1694. Bibcode:2020IJSME..18.1673B. doi:10.1007/s10763-019-10039-8. S2CID 254541202. • Bunnin, Nicholas; Yu, Jiyuan (15 April 2008). The Blackwell Dictionary of Western Philosophy . Wiley. p. 25. ISBN 9780470997215 . • Byrne, Ruth M. J.; Evans, Jonathan St B. T.; Newstead, Stephen E. (18 June 2019). Human Reasoning: The Psychology Of Deduction . Routledge. p. 59. ISBN 9781317716266 . • Cellucci, Carlo (29 March 2017). Rethinking Knowledge: The Heuristic View . Springer. p. 154. ISBN 9783319532370 . • Chang, Mark (22 July 2014). Principles of Scientific Methods . CRC Press. p. 37. ISBN 9781482238099 . • Church, Alonzo (1996). Introduction to Mathematical Logic . Princeton University Press. p. 104. ISBN 9780691029061 . • Colman, Andrew M. (1 January 2009). "affirming the consequent". A Dictionary of Psychology . Oxford University Press. ISBN 9780199534067 . • Conati, Cristina; Heffernan, Neil; Mitrovic, Antonija; Verdejo, M. Felisa (16 June 2015). Artificial Intelligence in Education: 17th International Conference, AIED 2015, Madrid, Spain, June 22-26, 2015. Proceedings . Springer. p. 738. ISBN 9783319197739 . • Copi, Irving M.; Cohen, Carl; Rodych, Victor (3 September 2018). Introduction to Logic . Routledge. ISBN 9781351386975 . • Cottrell, Stella (14 March 2017). Critical Thinking Skills: Effective Analysis, Argument and Reflection . Bloomsbury Publishing. p. 110. ISBN 9781350314672 . • Craig, Edward (1996). "Formal and informal logic". Routledge Encyclopedia of Philosophy . Routledge. ISBN 9780415073103 . Archived from the original on 16 January 2021. Retrieved 29 December 2021. • Demir, Imran (24 March 2017). Overconfidence and Risk Taking in Foreign Policy Decision Making: The Case of Turkey's Syria Policy . Springer. p. 32. ISBN 9783319526058 . • Douven, Igor (2022). "Abduction and Explanatory Reasoning". Oxford Bibliographies . Oxford University Press. Retrieved 18 January 2023. • Douven, Igor (9 March 2011). "Abduction". Stanford Encyclopedia of Philosophy . Retrieved 18 January 2023. • Dowden, Bradley (2023). "Fallacies". Internet Encyclopedia of Philosophy . Retrieved 22 January 2023. • Dowden, Bradley (2021). "Fallacies: 6. Partial List of Fallacies". Internet Encyclopedia of Philosophy . Retrieved 13 March 2021. • Dowden, Bradley H. (2020). Logical Reasoning (PDF). (for an earlier version, see: Dowden, Bradley Harris (1993). Logical Reasoning . Wadsworth Publishing Company. ISBN 9780534176884 .) • Engel, S. Morris (2014). With Good Reason an Introduction to Informal Fallacies . St. Martin's Press. pp. 74, 108–11. ISBN 9781457695957 . • Enyeart, Morris A.; Baker, Dale; Vanharlingen, Dave (May 1980). "Correlation of inductive and deductive logical reasoning to college physics achievement". Journal of Research in Science Teaching . 17 (3): 263–267. Bibcode:1980JRScT..17..263E. doi:10.1002/tea.3660170311. • Evans, Jonathan (18 April 2005). Morrison, Robert (ed.). The Cambridge Handbook of Thinking and Reasoning . Cambridge University Press. ISBN 9780521824170 . • Fasko, Daniel; Fair, Frank (12 October 2020). Critical Thinking and Reasoning: Theory, Development, Instruction, and Assessment . Brill. p. 51. ISBN 9789004444591 . • Flick, Uwe (10 December 2013). The SAGE Handbook of Qualitative Data Analysis . SAGE. p. 123. ISBN 9781446296691 . • Franks, Bridget A.; Therriault, David J.; Buhr, Miriam I.; Chiang, Evelyn S.; Gonzalez, Claire M.; Kwon, Heekyung K.; Schelble, Jenni L.; Wang, Xuesong (August 2013). "Looking back: reasoning and metacognition with narrative texts". Metacognition and Learning . 8 (2): 146. doi:10.1007/s11409-013-9099-2. S2CID 255162310. • Gabbay, Michael (4 September 2002). Logic With Added Reasoning . Broadview Press. p. 15. ISBN 9781551114057 . • Gambrill, Eileen (1 May 2012). Critical Thinking in Clinical Practice: Improving the Quality of Judgments and Decisions . John Wiley & Sons. p. 540. ISBN 9780470904381 . • Girod, Robert J. (25 September 2014). Logical Investigative Methods: Critical Thinking and Reasoning for Successful Investigations . CRC Press. ISBN 9781482243147 . • Goranko, Valentin; Rumberg, Antje (2022). "Temporal Logic". The Stanford Encyclopedia of Philosophy . Metaphysics Research Lab, Stanford University. Retrieved 24 January 2023. • Goswami, Usha (23 October 2013). Analogical Reasoning in Children . Routledge. p. 86. ISBN 9781317775393 . • Groarke, Louis F. (2022). "Aristotle: Logic". Internet Encyclopedia of Philosophy . Archived from the original on 29 December 2021. Retrieved 1 January 2022. • Haack, Susan (1996). "1. 'Alternative' in 'Alternative Logic'". Deviant Logic, Fuzzy Logic: Beyond the Formalism . Chicago and London: University of Chicago Press. pp. 1, 4. ISBN 9780226311333 . {{cite book}}: CS1 maint: publisher location (link) • Haack, Susan (27 July 1978). Philosophy of Logics . Cambridge University Press. ISBN 9780521293297 . • Halpern, Diane F. (4 February 2014). Critical Thinking Across the Curriculum: A Brief Edition of Thought & Knowledge . Routledge. p. 81. ISBN 9781317778370 . • Hansen, Hans (2020). "Fallacies". The Stanford Encyclopedia of Philosophy . Metaphysics Research Lab, Stanford University. Archived from the original on 29 March 2021. Retrieved 18 March 2021. • Heit, Evan (2007). "What Is Induction and Why Study It?". Inductive Reasoning: Experimental, Developmental, and Computational Approaches . Cambridge University Press. pp. 1–24. ISBN 9780521856485 . • Henderson, Leah (2022). "The Problem of Induction: 1. Hume's Problem". The Stanford Encyclopedia of Philosophy . Metaphysics Research Lab, Stanford University. Retrieved 18 January 2023. • Honderich, Ted (2005). "philosophical logic". The Oxford Companion to Philosophy . Oxford University Press. ISBN 9780199264797 . Archived from the original on 29 January 2021. Retrieved 2 January 2022. • Ivory, Sarah Birrell (11 January 2021). Becoming a Critical Thinker: For Your University Studies and Beyond . Oxford University Press. p. 73. ISBN 9780198841531 . • Jacquette, Dale (2006). "Introduction: Philosophy of logic today". Philosophy of Logic . North Holland. pp. 1–12. ISBN 9780444515414 . Archived from the original on 7 December 2021. Retrieved 29 December 2021. • Jamieson, D. (9 March 2013). Language, Mind, and Art: Essays in Appreciation and Analysis, in Honor of Paul Ziff . Springer Science & Business Media. p. 34. ISBN 9789401583138 . • Johnson, Gregory (6 January 2017). Argument and Inference: An Introduction to Inductive Logic . MIT Press. p. 2. ISBN 9780262035255 . • Johnson-Laird, Phil (30 December 2009). "Deductive reasoning". WIREs Cognitive Science . 1 (1): 8–17. doi:10.1002/wcs.20. ISSN 1939-5078. PMID 26272833. • Kaye, Sharon M. (1 December 2012). Critical Thinking: A Beginner's Guide . Simon and Schuster. p. 57. ISBN 9781780741475 . • Kenny, Anthony (15 October 2018). An Illustrated Brief History of Western Philosophy, 20th Anniversary Edition . John Wiley & Sons. p. 140. ISBN 9781119531173 . • Kilcrease, Bethany (2021). Falsehood and Fallacy: How to Think, Read, and Write in the Twenty-First Century . University of Toronto Press. p. 100. ISBN 9781487588618 . • Kohar, Richard (15 June 2016). Basic Discrete Mathematics: Logic, Set Theory, And Probability . World Scientific Publishing Company. pp. 54, 57. ISBN 9789814730419 . • Koons, Robert (2022). "Defeasible Reasoning". The Stanford Encyclopedia of Philosophy . Metaphysics Research Lab, Stanford University. Retrieved 22 January 2023. • Koslowski, Barbara (14 November 2017). "Abductive reasoning and explanation". International Handbook of Thinking and Reasoning . Routledge. pp. 366–382. doi:10.4324/9781315725697. ISBN 9781315725697 . • Kurtz, T W; Morris, R C; Pershadsingh, H A (June 1989). "The Zucker fatty rat as a genetic model of obesity and hypertension". Hypertension . 13 (6_pt_2): 896–901. doi:10.1161/01.HYP.13.6.896. PMID 2786848. S2CID 109606. • Li, Ming; Vitányi, Paul (2019). "Inductive Reasoning". An Introduction to Kolmogorov Complexity and Its Applications . Texts in Computer Science. Springer International Publishing. pp. 345–448. doi:10.1007/978-3-030-11298-1_5. ISBN 9783030112981 . • Lorenzano, Pablo; Rheinberger, Hans-Jörg; Galles, Eduardo Ortiz and Carlos Delfino (27 September 2010). History and Philosophy of Science and Technology . Eolss Publishers / UNESCO. p. 103. ISBN 9781848263239 . • Mackie, J. L. (2006). "Fallacies". In Borchert, Donald (ed.). Macmillan Encyclopedia of Philosophy, 2nd Edition . Macmillan. ISBN 9780028657905 . • Magnani, Lorenzo; Bertolotti, Tommaso (22 May 2017). Springer Handbook of Model-Based Science . Springer. p. 152. ISBN 9783319305264 . • Margolis, James M.; Margolis, Joseph; Krausz, Michael; Krausz, A. S.; Burian, R.; Margolis, Professor Joseph (31 October 1986). Rationality, Relativism and the Human Sciences . Springer Science & Business Media. p. 167. ISBN 9789024732715 . • Mele, Alfred R.; Rawling, Piers. (2004). "INTRODUCTION: Aspects of Rationality". The Oxford Handbook of Rationality . Oxford University Press. pp. 3–14. doi:10.1093/0195145399.001.0001. ISBN 9780195145397 . • Mizrahi, Moti (29 September 2020). The Relativity of Theory: Key Positions and Arguments in the Contemporary Scientific Realism/Antirealism Debate . Springer Nature. p. 83. ISBN 9783030580476 . • Moschovakis, Joan (2021). "Intuitionistic Logic: 1. Rejection of Tertium Non Datur". The Stanford Encyclopedia of Philosophy . Metaphysics Research Lab, Stanford University. Retrieved 11 December 2021. • Nadler, Steven; Shapiro, Lawrence (31 August 2021). When Bad Thinking Happens to Good People: How Philosophy Can Save Us from Ourselves . Princeton University Press. p. 81. ISBN 9780691220086 . • Nelson, Hazel E. (2005). Cognitive-behavioural Therapy with Delusions and Hallucinations: A Practice Manual . Nelson Thornes. p. 167. ISBN 9780748792566 . • Niiniluoto, I.; Sintonen, Matti; Wolenski, Jan (31 March 2004). Handbook of Epistemology . Springer Science & Business Media. p. 901. ISBN 9781402019852 . • Norman, J.; Sylvan, R. (6 December 2012). Directions in Relevant Logic . Springer Science & Business Media. p. 419. ISBN 9789400910058 . • Nunes, Terezinha (5 October 2011). "Logical Reasoning and Learning". In Seel, Norbert M. (ed.). Encyclopedia of the Sciences of Learning . Springer Science & Business Media. pp. 2066–9. ISBN 9781441914279 . • Nute, Donald (6 December 2012). Defeasible Deontic Logic . Springer Science & Business Media. p. 82. ISBN 9789401588515 . • Ornek, Dr Funda; Saleh, Dr Issa M. (1 May 2012). Contemporary Science Teaching Approaches: Promoting Conceptual Understanding in Science . IAP. p. 82. ISBN 9781617356100 . • Porta, Miquel (21 July 2016). "Inductive Reasoning". A Dictionary of Epidemiology . Oxford University Press. ISBN 9780199976720 . • Priest, Graham; Tanaka, Koji; Weber, Zach (2018). "Paraconsistent Logic". The Stanford Encyclopedia of Philosophy . Metaphysics Research Lab, Stanford University. Retrieved 14 December 2021. • Psillos, Stathis (2023). "Induction, The Problem of". Internet Encyclopedia of Philosophy . Retrieved 22 January 2023. • Robertson, Simon (1 October 2009). Spheres of Reason: New Essays in the Philosophy of Normativity . OUP Oxford. p. 192. ISBN 9780191610219 . • Salmon, Merrilee (2012). Introduction to Logic and Critical Thinking . Cengage Learning. ISBN 978-1133711643 . permanent dead link • Sandkühler, Hans Jörg (2010). "Analogie". Enzyklopädie Philosophie . Meiner. ISBN 9783787319992 . Archived from the original on 2021-03-11. Retrieved 2023-01-24. • Sayward, Charles (2009). Dialogues Concerning Natural Numbers . Peter Lang. p. 15. ISBN 9781433107801 . • Shapiro, Stewart; Kouri Kissel, Teresa (2021). "Classical Logic". The Stanford Encyclopedia of Philosophy . Metaphysics Research Lab, Stanford University. Archived from the original on 3 May 1998. Retrieved 4 December 2021. • Smith, Robin (2020). "Aristotle's Logic". The Stanford Encyclopedia of Philosophy . Metaphysics Research Lab, Stanford University. Archived from the original on 26 December 2021. Retrieved 1 January 2022. • Sriram, Ram D. (6 December 2012). Intelligent Systems for Engineering: A Knowledge-based Approach . Springer Science & Business Media. p. 286. ISBN 9781447106319 . • Tomić, Taeda (2013). "False Dilemma: A Systematic Exposition". Argumentation . 27 (4): 347–368. doi:10.1007/s10503-013-9292-0. S2CID 144781912. • Tuman, Joseph S. (2008). Political Communication in American Campaigns . SAGE. p. 75. ISBN 9781412909457 . • Velleman, Daniel J. (16 January 2006). How to Prove It: A Structured Approach . Cambridge University Press. pp. 8, 103. ISBN 9780521675994 . • Viale, Riccardo (2 December 2020). Routledge Handbook of Bounded Rationality . Routledge. p. 746. ISBN 9781317330790 . • Vickers, John M. (2022). "Inductive Reasoning". Oxford Bibliographies . Oxford University Press. Retrieved 18 January 2023. • Vleet, Jacob E. Van (2011). Informal Logical Fallacies: A Brief Guide . University Press of America. p. ix. ISBN 9780761854333 . • Walton, Douglas (15 May 2014). Abductive Reasoning . University of Alabama Press. pp. 1–3. ISBN 9780817357825 . • Walton, Douglas (26 August 2013). Methods of Argumentation . Cambridge University Press. pp. 250–2. ISBN 9781107039308 . • Walton, Douglas N. (1987). Informal Fallacies: Towards a Theory of Argument Criticisms . John Benjamins Publishing. p. 10. ISBN 9789027250056 . • Weaver, Nik (22 April 2015). Truth And Assertibility . World Scientific. p. 70. ISBN 9789814619981 .

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