1) Any three angles of a triangle add up to 180 degrees.
2) Science informs us of the structure of the common reality we all inhabit, and which for the large part exists independent of what people say and think of it.
Both of are ‘reasonable’ but not interchangeably so. Let’s disregard the common analytic/synthetic dichotmy between these propositions (see Immanuel Kant note at bottom of post), not because I disagree with Kant just that I do not find that division very illuminating for the topic at hand. These two propositions of reason are distinct in another way: the first derives its truth-value from an abstract formal system analysis whereas the second does not. The truth-value in proposition 2 is, I will argue, born out of mental deliberation. While we tend to use the same word to denote both reasoning as an abstract process and reasoning as a mental activity the two usages are grammatically incommensurable. A formal system, insofar as it is self-consistent, demands rigid adherence to articulated rules, whereas mental deliberation, an admittedly muddled description of a cognitive event, allows unfiltered intuitive judgment to affect analysis. One could also describe this distinction as one between the abstract and the existential aspects of ‘reasoning’.
The allure of analytic reasoning is that it can demonstrate its proofs step by step in accordance with the formal system it applies to, delineated by the rules of the inference imposed. Existential reason has no such clear divisions built into its process of mediation (in the act of deliberation the rules of inference are only half-glimpsed).
Proposition 1 fits the first category, abstract reason, in that the truth-value can be determined formally within the boundaries set by Euclidean geometry. There is no coinciding formal system which can sufficiently prove proposition 2 because it pertains to an existentially-derived rationalization, using an ad hoc reasoning that is enabled by intuitive judgment (I will return to this point). The aforementioned grammatical error occurs when one blurs the two kinds of reasoning, treating the mental act of reasoning as synonymous with the integrity of formal abstractions. Perhaps as a consequence of the allure of the hard sciences, the rational component of the mental act becomes more pronounced even when it lacks essential soundness.
The mistaken rationalist may argue, for example, that while something like 2% intuition is involved in the determining process of proposition 2 - as the leap of faith necessary to draw the associations between the abstracted proofs with the existential reality - there remains 98% remaining authority of the articulated proofs that carry over and justify the decision. This is a complete misunderstanding of how formal reasoning derives its authority. Bridging the gap between the formal system and the existential world is a derived rule which lacks the formal authority of the proofs it is supposed to enable. Another way to put this would be to say the external applicability of a formal proof is nowhere authorized by the proof. The derived rule is the leap of faith which entirely enables the real-world application of the formal reasoning. Therefore without the 2% involvement of intuition one does not have 98% soundness to the external application of the formal proof, one has zero percent.
Let me describe this a different way: suppose a formal system of logic was programmed into a computer and the rules of inference, the axioms, the theorems were all clearly laid out so as to delineate the boundaries of which the system could necessarily comprehend. Considering this formalism was a logical one requiring self-consistency it would tend to adopt as some of its rules of inferences the law of bivalence and the law of non-contradiction, and further abstractions could be imposed depending on the end desire of the content. Terms would be clearly defined so as to prevent passive connotations of their common parlance to infect the integrity of the formalism (this is an inevitable difficulty of linguistic calculus, something even Euclidean was done in by in his geometry). Already there is a disparity emerging between language in its lived sense of expression and what is required for the sake of the formal system.
Now suppose we input into this computer program an existential question, i.e. a question that pertains to our direct experience of reality, one which is not filtered for the needs of the program, say: is there such thing as a soul? Can a formalized set of rules sufficiently interpret the semantic meaning of the term ‘soul’? If there had been some term denoted ‘soul’ within the program it could not have any property that extended beyond the limits of the rules of inference, nor that had passive connotations. It would be a semantic error to call such a thing ‘soul’ as it is abstracted from, and therefore filtered from, its experiential context. Such a computer program expression of soul is merely nominal, in word only, having excluded from its potential expression all characteristics that are associated with it pre-abstraction. The formalized ‘soul’ could only tautologically describe itself in parody of what it is supposed to signify. Were the system sophisticated enough to identify this disparity it would respond with a syntax (semantic) error, a zero sum output. There would be no partial formal value to be salvaged from the experiment that could then substantiate the meaning of ‘soul’ as it exists outside of the system. The limited understanding of language and concepts used inside the formal system would have no precedent for the language of the external, existential question, and in a very real way could not elicit a response. What bridges this disparity is not something inside the formal system but something without.
Due to our lack of such a puritanical computational system at our disposal when ad hoc formal analysis is done in our minds, we tend to confuse the abstract and existential aspects of what it is ‘to reason’ or ‘understand something as reasonable’ when justifying a belief. Authorities are isomorphically carried over where there would have only been error messages. The half-glimpsed boundaries of the system get blurred and the output, while perhaps seeming rationally convincing, consists of a combination of analytic and intuitive sources of knowing. This other source is sometimes thought of as intuition, instinct, tacit knowledge, morality, etc. Although the source of authentication is all too often irrational this does not exclude the possibility that it is mediated in such a way as to be consistent and tied with objective rules beyond our comprehension. What is deemed irrational may only be a small part of the whole we can view critically, our limited scope of the formal system (if one exists) which extends far beyond our ability to grasp rationally. Much more emphasis needs to be placed on this instinctual component of our judgments, of which abstract reasoning is only a small component.
Returning to the original propositions:
proposition 1 is right insofar as it adheres to the rules within a clearly defined formal system. It satisfies the rules of an abstract reason.
proposition 2 is right or wrong insofar as we glean the truth-value of the statement from our existential reasoning, a reasoning that is affected by intuitive judgment.
Similarly, any reason-based argument which attempts to disprove the existence of the soul overextends the integrity of its logic, mistaking the rationale as something formally sound when in fact it is entirely informal and thus incommensurable with the alleged proofs. Though incommensurable this does not exclude the possibility that some sort of purposeful agreement can occur implicitly between the ‘proofs’ and the mental act of conviction. That which is valuable in the sciences depends on it.
[Immanuel Kant had formulated two distinct categories of judgments: analytic and synthetic. An analytic judgment is one that does not add anything to what is included in the concept (a simple reiterating subject predicate relationship, i.e. all bachelors are unmarried). A synthetic judgment is one which extends beyond the concept, wherein the predicate adds something not already included in the definition of the subject, usually as a result of an empirical observation (i.e. water boils at 100 C). Another way to think of it is an analytic judgment is one based on a tautology (or contradiction), self-describing itself, whereas a synthetic judgment associates a concept with something outside its definition. It is not the greatest distinction and it has lead to some pretty murky philosophical digressions, and so I bring it up only to indicate that I am aware of it, but I prefer my distinctions.]