It's main categorizations are informal and formal logic. Informal including inductive reasoning, and abductive reasoning. Formal mainly being deductive. — MonfortS26
I agree if what you are saying is that reasoning has this natural psychological structure that Peirce describes. The same method applies across the board in critical thinking as an epistemic necessity. So the three stages are really fundamental.
But as you say, abduction and inductive confirmation are informal. So you will come up against resistance from those who want to refer only to the formal part as "logic". At this point, it becomes a meaningless argument over terminology.
No such intervention is required by logic, which can freely float above world in perpetuity without in the least encountering any worldy resistence. — StreetlightX
Sure, rules are just rules. Generalised syntactical structures are by design separate from the semantics that particular grammatically-correct statements may claim. So floating freely above the world is central to the semiotic deal. It provides a general means to structure propositions.
But then to interpret a sentence does reconnect the whole business to the world. The act of measurement or inductive confirmation is where logic meets resistance from potential falsification.
So the world is present in the grammar of predication, or whatever. It is present in its most generalised possible form. It is a view of how the world works boiled down to a most abstract view about the necessity of certain relations.
It floats above the world as pure form - or as pure and immaterial as we can imagine it. (A Turing machine still needs the physics of a gate and tape, a Boolean circuit still needs connections and switches. So the divorce is never absolute.)
But then the grammar gets particularised as some material claim. It becomes some actual structure of constraints that "say something meaningful" - or not, as the case may prove to be.
My main question, is there an application of logic that falls outside this cycle? — MonfortS26
I can't think of any. Although again, the question might be better phrased as to whether there is any other reasonable method of reasoning.
:)
The live issue is probably that we don't have a good handle on abduction. Even Peirce was notoriously mystical sounding about the psychological details.
So somehow we seem to be unreasonably good at jumping towards the most productive guesses when it comes to finding the right foundational generalisations, whether it be hypotheses, axioms or principles.
It happens too often just to be luck - a random search algorithm. And we can't really go along with supernatural inspiration.
But there are semi-formalisable processes for taking abductive leaps, nevertheless.
What we are usually trying to do is guess the general causal mechanism - the wider rule - behind some particular state of affairs. So we are trying to unbreak a broken symmetry. We are trying to de-individuate some individuated state of being. And this is where logical methods - like dialectics - come into play. We can think retroductively, looking backwards from the variety of the particulars to the generality of some dichotomy which had to be the initial breaking of a symmetry.
So retroduction seems a semi-formal logic to me. There is a method behind the apparent freely inspired guessing. You know what you are seeking to get things started. Generality is a symmetry. And you want to see through the variety, the detail, to recover the dichotomy that must be at root of that variety. The simple break represented by that which was "mutually exclusive and jointly exhaustive".
That is, abduction already knows where it wants to land. It must leap backwards from the particular to the general. It must leap from the fractured variety back towards the first fracture. It is looking for a complementarity of opposed possibility that is always the starting point for any process of development or evolution.
So - as Peirce was sort of saying in citing Galileo's
il lume naturale - the psychological architecture of human reasoning works because it mirrors the actual evolutionary logic of the Cosmos.
It all starts with a symmetry or a vague and undifferentiated potential. Then the symmetry gets broke in some dialectical fashion and unleashes a flood of direct consequences. Constraints or regularities emerge from this confusion to create some persisting order. The broken symmetry achieves an equilibrium, a global rule of habit or law.
So nature itself expresses this reasoning method. It starts with a symmetry breaking - the primal leap that is the retroductive target of abductive thought. It follows with a direct mechanical unfolding of consequences - the deterministic interactions that are "deductively" played out. Then finally some global rule of law emerges as the symmetry breaking finds its steady equilibrium. The world is now in a position to inductively confirm its own existence. It has habits that measure its state of being and check that local individuated actions are "in line" with its "beliefs".