We've just examined the conditions under which induction and deduction yield valid results. Now let's consider the errors that result from illegitimate reasoning or fallacies.

One well-known classification of fallacies is that of Bacon, who called them εἴδ⍵λἀ or idola and compared them to phantoms that cloud and muddy our understanding. Bacon distinguished four different forms of fallacy:

1. Idola tribus are errors common to the entire species, which stem from the nature of the human mind itself – from the limits and narrowness of the mind, for example, from the need for harmony inherent in human nature, from the natural errors of our senses, and so on.

2. Idola specus are idols of the cave, which stem from individual defects. Having a predilection for science, we denature nature to transform it in to material for our understanding.

3. Idola fori are errors born of language. The “forum” here refers to the place where conversations occur.

4. Idola theatri are errors born of philosophical sects, stemming from the spirit of various philosophical systems. Bacon always depicted philosophers as actors on a stage.

But these terms used by Bacon (like the ideas they express) are quite vague, so this classification is important only from a historical point of view. It shows that Bacon clearly saw that the cause of error is often subjective. His list of fallacies is neither exact nor complete.

Let's see if we can improve upon this classification.