Formal Logic

One of the two main kinds of logic. Formal logic deals with the form of an argument rather than its content, and it studies language, deduction and reasoning. It is closely related to mathematics.F36

One of its core rules is modus ponens (“the affirming mode”): a technical term sometimes used by students as a brand name for the whole of formal logic, as in “modus ponens and all that”. Modus ponens is an inference from two premises. The first premise is conditional, consisting of an “antecedent” and a “consequent”; the second premise simply confirms that the antecedent applies in this case. Example:

1. If you get some ducks [antecedent], your slug problem will be resolved [consequent].

2. You are getting some ducks [the antecedent is confirmed].

3. Therefore your slug problem will be resolved [conclusion].

The counterpart to this is modus tollens (“the denying mode”), in which a similar first premise is followed by a second premise that denies the consequent. Example:

1. If Mary is at home [antecedent], her car will be outside [consequent].

2. Her car is not outside [the consequent is denied].

3. Therefore she is not at home [conclusion].

It sounds banal, but the syllogisms of formal logic are the building blocks of reasoning which—in combination with a series of conditions, affirmed or denied in sequence and in parallel—can develop into a problem-solving capacity of great complexity, used as the logical structure on which artificial intelligence is based.F37

Informal logic is, of course, the junior partner in all this, since it depends on the reasoning of formal logic, and its mixing up of logic and content is exactly what you cannot do with formal logic. On the other hand, without content, logic has no purpose. Formal logic is the road; informal logic is the journey.


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David Fleming
Dr David Fleming (2 January 1940 – 29 November 2010) was a cultural historian and economist, based in London, England. He was among the first to reveal the possibility of peak oil's approach and invented the influential TEQs scheme, designed to address this and climate change. He was also a pioneer of post-growth economics, and a significant figure in the development of the UK Green Party, the Transition Towns movement and the New Economics Foundation, as well as a Chairman of the Soil Association. His wide-ranging independent analysis culminated in two critically acclaimed books, 'Lean Logic' and 'Surviving the Future', published posthumously in 2016. These in turn inspired the 2020 launches of both BAFTA-winning director Peter Armstrong's feature film about Fleming's perspective and legacy - 'The Sequel: What Will Follow Our Troubled Civilisation?' - and Sterling College's unique 'Surviving the Future: Conversations for Our Time' online courses. For more information on all of the above, including Lean Logic, click the little globe below!

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