Formal and Material Consequence

The notions of formal and material consequence had me questioning the point of the distinction between the two and how they pertain to our knowledge of philosophy and argumentation. It seemed like something that was common knowledge due to its matter-of-factness and simplicity, but also overemphasising its place in argumentation so much so, that it leant itself to the sense that it was overcompensating for its futility.

I suppose then in keeping with futile descriptions, I will first explain the difference between formal and material consequence before I can explore their significance.

Formal consequence determines the validity of logic through its formal perfection. In other words, the consequence does not rely on the contents of the argument; rather it relies on the unchangeable form. This means that even if we were to substitute certain claims, the argument’s validity would remain uncompromised.

Material consequence, however, relies on the context of the claims made; that is, we need knowledge of the nature of things in order to determine the validity of the consequence. Therefore, if we were to substitute certain claims for others, the validity would be destroyed.

For example: “If it is a whale, it is a mammal”

Our knowledge of the context of the statement allows us to affirm that it is valid to state that a whale is a mammal due to prior knowledge about the whale being a mammal. However, if we were to replace “whale” or “mammal” with, perhaps, “wood”, the validity no longer holds. Therefore, our knowledge of the nature of things is crucial in determining material consequence.

Abelard referred to formal and material consequence as perfect and imperfect consequences, respectively. So, if we say that an argument is perfect, we are implying that our knowledge of its validity is irrespective of our knowledge of the world. This notion seems problematic and reminds me of Galileo Galilei’s Two Kinds of Properties in which he argues for estrangement from the world in order to reach truth. He argues that we make a projective error by mistaking features of our ideas about things for properties of the world itself; and therefore for truth. In short, he thinks that our sensory experience of the nature of things is deceptive; we do not see properties of things, we see our ideas about the properties of things.

We can see this correlation with perfect or formal consequences, in which an estrangement from our knowledge of nature of things is required in order to reach validity. However, my problem with this lies here: if we attain knowledge through experience, and if we experience through the senses, then are our senses simply deceiving us, as Galileo infers? If this is so, and if we maintain that experience and sense perception are inalienable then how do we reach perfect entailments?

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