# Is logic always coherent

## consistency

A lot of statements are there consistent (consistent) if necessary no contradiction can be derived from them. We have already seen that consistency is an elementary requirement that must be made of theories. The same requirement applies to any scientific text.

In each argument it has to be shown how the second step follows from the first. In the case of assertions one therefore refers back to their presuppositions (which can be found in an earlier chapter). Such a logical connection exists, for example, between the theory introduced in the introduction, the analytical principles derived from it, the analysis itself and its results. An argument whose conclusion does not follow from the premises is inconsistent (more precisely, a non sequitur).

From propositional logic there are a number of argumentation or conclusion figures (traditional modes called), which for logical reasons always work. Here are two examples:

• Mode tollendo ponensFor example, if the premise is that one alternative (i.e. one of two contradicting statements) is true, then one can show that one of the two statements is false, and thus one has proven that the other is true.
• Mode romping: If, for example, the premise is that a second statement follows from one statement, then one can show that the second is false, and thus one has proven that the first must also be false.

To the extent that you stick to logic in your argument, you ensure its consistency.

A text is coherent (connected) iff. its parts are interrelated. In detail:

• Assertions must not stand side by side without being connected, hypotheses cannot be plucked out of thin air. You don't sprinkle bits of thought into the text and you don't suddenly change the subject.
• Papers whose relevance to the topic of the work is unclear lead to incoherence.
• Terms, symbols, diagrams, tables of values, etc., which are placed in front of the reader without explanation, lead to misunderstanding.
• Unnecessary repetitions are redundant. Inadvertent repetition confuses the reader because he does not know what the author is trying to do with it. If something has to be repeated (e.g. because it is too far back), this must be made explicit with reference to the first occurrence.
• Questions cannot simply be left open, gaps cannot simply be left unfilled. The author has questions that the reader is forced to answer in advance and either to put them off to the later treatment or to admit that he cannot answer them.
• Classification criteria must be justified by recourse to the definitions of terms. Then it must first be explained how the criterion can be operationalized in a test and how the results of the test are interpreted. Only then can the criterion be applied.

The parts of a scientific paper must be at all levels in a certain way balance or a reasonable proportion:

• The foreword must be shorter than the introduction.
• Introduction and summary must be shorter than the main part.
• There can be no more presentation than a separate train of thought.
• There can be no more data presentation than analysis and discussion of data.
• In general, the effort involved in the survey and investigation must be in a reasonable proportion to the results.
• The chapters or sections on the same hierarchical level must be reasonably equally long. E.g. a thirty-page paper cannot normally have a main chapter the size of one page.
• Where there is parallelism in terms of content, the length should also be parallel.
• Paragraphs should have a reasonable mean length. Both the tendency to make every sentence a paragraph and the failure to make at least one paragraph per page suggest a lack of conceptual structure.