Occam's razor in the teaching of phylogenetics (Dec. 21, 2022)
During my TA for BIOL 201 (Ecology and Evolution), Occam's razor was mentioned every time the parsimony principle of phylogenetic analysis was taught, and the purpose may be to offer a philosophical basis. However, I think this is a misuse and misunderstanding of Occam's razor.
Based on Wiki, although Occam's razor is credited to William of Ockham (1287-1347), the original statement restricted the principle to a monotheistic position as "Plurality must never be posited without necessity". The principle was then extended to science. The most popular version, "Entities are not to be multiplied without necessity" was formulated by the Irish Franciscan philosopher John Punch in 1639. Ernst Mach formulated a stronger version in physics: "Scientists must use the simplest means of arriving at their results and exclude everything not perceived by the senses."
From all these various versions of the principle, we can see that Occam's razor is a pragmatic as opposed to an epistemological principle. Specifically, if we can construct different models to explain a phenomenon, then we should choose the simplest one (e.g., less assumptions, less parameters/variables). It also seems to imply that a more general and concise model is better than a more specific one, as the latter often captures more entities. Nevertheless, Occam's razor never means that the simplest model or hypothesis will be more likely the correct one. Considering phylogeny, Occam's razor is irrelevant to the justification of parsimony because which phylogenetic tree is more likely to be true is not a pragmatic problem.
It may be argued that the constructing phylogenetic trees is the same as constructing alternative models to explain the current character states. However, different trees are not different models, but merely different contents of the same model, since a model should be classified based on form instead of content. Therefore, a tree with few transitions is not any more concise than a tree with many transitions. Each tree is a unique possible state of the model and thus is actually not comparable and should be treated equally! What we can say is merely that one tree has less transitions than another tree, but not anything about conciseness.
Perhaps a more crucial point for phylogenetic construction is that the real history can never be known, so Occam's razor is not relevant because we even do not know whether the theory really matches the reality or not.
Also, Occam's razor itself can be debated. Considering how our human intuition allows the comparability of things to be possible, one may doubt that the comparability between models is just a misleading illusion. Models are actually not comparable, but merely bear different characteristics. Stating that one model is simpler than the other is the same as stating that apple is simpler than pineapples. If we adopt this view, there are only models with more factors and less factors, but no concept of which model is simpler than others.
One example may be Chinese calligraphy. People can see great complexity from a "simple" character 三 written by a master than from a "complicated" character 懿 written by a beginner. Here we have at least two levels of complexity. In terms of the number of strokes, 懿 is more complicated than 三. However, in terms of spatial arrangement by the calligrapher, which is more subtle, 三 can be more complicated than 懿. This is similar to modelling. We often compare the complexity of models by counting the number of entities involved, but different models also have different structures, that is, how entities interact. However, as comparability relies on quantifiability, as the structure of the model is less quantifiable, it is thus not comparable. This means we compare things by abstracting the aspect that is easy to quantify, which can be biased, incomplete, and even misleading.
It should be noted that I am not saying we should not use parsimony principle during phylogeny, but merely arguing Occam's razor is not a relevant justification. Perhaps what is left to us is that the choice of models is merely an aesthetic taste. In fact, there is really no reason why conciseness is better than complexity, so the preference for conciseness is actually also an aesthetic taste. Now that we have different models that lead to the same results, why not choose the most beautiful one?
Based on Wiki, although Occam's razor is credited to William of Ockham (1287-1347), the original statement restricted the principle to a monotheistic position as "Plurality must never be posited without necessity". The principle was then extended to science. The most popular version, "Entities are not to be multiplied without necessity" was formulated by the Irish Franciscan philosopher John Punch in 1639. Ernst Mach formulated a stronger version in physics: "Scientists must use the simplest means of arriving at their results and exclude everything not perceived by the senses."
From all these various versions of the principle, we can see that Occam's razor is a pragmatic as opposed to an epistemological principle. Specifically, if we can construct different models to explain a phenomenon, then we should choose the simplest one (e.g., less assumptions, less parameters/variables). It also seems to imply that a more general and concise model is better than a more specific one, as the latter often captures more entities. Nevertheless, Occam's razor never means that the simplest model or hypothesis will be more likely the correct one. Considering phylogeny, Occam's razor is irrelevant to the justification of parsimony because which phylogenetic tree is more likely to be true is not a pragmatic problem.
It may be argued that the constructing phylogenetic trees is the same as constructing alternative models to explain the current character states. However, different trees are not different models, but merely different contents of the same model, since a model should be classified based on form instead of content. Therefore, a tree with few transitions is not any more concise than a tree with many transitions. Each tree is a unique possible state of the model and thus is actually not comparable and should be treated equally! What we can say is merely that one tree has less transitions than another tree, but not anything about conciseness.
Perhaps a more crucial point for phylogenetic construction is that the real history can never be known, so Occam's razor is not relevant because we even do not know whether the theory really matches the reality or not.
Also, Occam's razor itself can be debated. Considering how our human intuition allows the comparability of things to be possible, one may doubt that the comparability between models is just a misleading illusion. Models are actually not comparable, but merely bear different characteristics. Stating that one model is simpler than the other is the same as stating that apple is simpler than pineapples. If we adopt this view, there are only models with more factors and less factors, but no concept of which model is simpler than others.
One example may be Chinese calligraphy. People can see great complexity from a "simple" character 三 written by a master than from a "complicated" character 懿 written by a beginner. Here we have at least two levels of complexity. In terms of the number of strokes, 懿 is more complicated than 三. However, in terms of spatial arrangement by the calligrapher, which is more subtle, 三 can be more complicated than 懿. This is similar to modelling. We often compare the complexity of models by counting the number of entities involved, but different models also have different structures, that is, how entities interact. However, as comparability relies on quantifiability, as the structure of the model is less quantifiable, it is thus not comparable. This means we compare things by abstracting the aspect that is easy to quantify, which can be biased, incomplete, and even misleading.
It should be noted that I am not saying we should not use parsimony principle during phylogeny, but merely arguing Occam's razor is not a relevant justification. Perhaps what is left to us is that the choice of models is merely an aesthetic taste. In fact, there is really no reason why conciseness is better than complexity, so the preference for conciseness is actually also an aesthetic taste. Now that we have different models that lead to the same results, why not choose the most beautiful one?