But no scientific method establishes, say, the axiom of extentionality:



Nor the axiom of the power set:



Nor any of the others in ZFC. Nor could one imagine how any scientific investigation even could, in principle, establish any of these axioms. One suspects that the very vocabulary here is wrong, that there is a mistake of grammar at work.

Let's not forget: logic is just a formalisation of rules for inference making. There are multiple logics, not all of which are compatible with each other, depending on what it is you'd like to do. It's just a series of games, like chess and checkers: it simply makes very little sense - it's not even wrong - to speak of the scientific method in establishing the rules for those games - likewise logic.

Perhaps you mean to speak of something other than logic.

But no scientific method establishes, say, the axiom of extentionality — StreetlightX

I'm not familiar with the axioms that you speak of, but if we define the scientific method as this:



Would it have been possible to have discovered the functional capabilities of those axioms without the use of this cycle?

One suspects that the very vocabulary here is wrong, that there is a mistake of grammar at work. — StreetlightX

If you're suggesting that I am misunderstanding what I am trying to say, it is very possible that you're right lol.

Let's not forget: logic is just a formalisation of rules for inference making. There are multiple logics, not all of which are compatible with each other, depending on what it is you'd like to do. It's just a series of games, like chess and checkers: it simply makes very little sense - it's not even wrong - to speak of the scientific method in establishing the rules for those games - likewise logic. — StreetlightX

I agree, but is the use of the scientific method not subject to those rules as well?

Is the act of formulating a hypothesis not just abductive reasoning, testing said hypothesis deductive, and developing theories inductive?

I think what you're missing is the specificity of logic: logic is a very specific thing, a bunch of formal rules for making inferences (modern logic anyway). One can establish a system of logic without a single reference to any real life constraint, or scientific result. You can literally make the rules up from thin air as you go along, which is kind of what logicians have mostly done, although some have at least tried to make it amenable to math. Logic is more or less entirely disconnected from the empirical: that's exactly its strength.

One can establish a system of logic without a single reference to any real life constraint, or scientific result. Logic is more or less entirely disconnected from the empirical — StreetlightX

When you say this, are you referring to deductive reasoning exclusively, or do you include informal logic as well? And if logic is separate from real life constraints, does it have any value outside of paving the way for its application to the real world? Would a good analogy for the relationship be "logic is 'pure logic' and science is 'applied logic', in comparison to pure and applied mathematics"?

Pure science - science without reference to the empirical - is an oxymoron, so I don't think it's appropriate to say logic is pure science, and science has a specificity to it that exceeds anything in logic so I don't think it's appropriate to call science applied logic. Basically I think you're trying to make more hay than can be done with regard to any connection between science and logic. My suggestion is to look further into what logic is: it's a formal discipline that has alot of specificity to it, and I think your'e in for a hard time trying to discuss anything sensibly if you're aren't familiar with even the actual axioms of logic themselves, when that's what you're trying to talk about! I don't mean this harshly, but only as a suggestion for study.

I mistyped when I said pure science and went back and changed it to logic being pure logic and science being applied logic.

My suggestion is to look further into what logic is: it's a formal discipline that has alot of specificity to it — StreetlightX

Here is my understanding of logic. Logic is a formalization of the concept of reasoning that has been slowly built over time by people trying to more effectively make sense of things. It's main categorizations are informal and formal logic. Informal including inductive reasoning, and abductive reasoning. Formal mainly being deductive. Attempts to improve the rigor of deductive reasoning led to the creation of propositional, first-order, modal, and other similar formal systems. The scientific method is the cycle of these three forms of reasoning according to Charles Sanders Peirce and it seems to me that is an accurate statement. My main question, is there an application of logic that falls outside this cycle?

I think your'e in for a hard time trying to discuss anything sensibly if you're aren't familiar with even the actual axioms of logic themselves — StreetlightX

What are you referring to when you say the axioms of logic?

I don't mean this harshly, but only as a suggestion for study! — StreetlightX

Lol you don't have to worry about me getting offended about potentially being wrong. If it seems like I'm taking an aggressive stance, that's just how I can come off sometimes. But I'm just trying to develop my ideas further and it helps to have them written out and criticized by other people.

What are you referring to when you say the axioms of logic? — MonfortS26

These for example:

https://en.m.wikipedia.org/wiki/Zermelo%E2%80%93Fraenkel_set_theory#Axioms

The scientific method is the cycle of these three forms of reasoning according to Charles Sanders Peirce and it seems to me that is an accurate statement. — MonfortS26

Without commenting on Peirce, what's missing in this characterization of the scientific method is the minimal condition of what the philosopher of science Ian Hacking calls intervening. Science acheives its results by intervening in the world somehow, by making a change in things. Science works by encountering - and overcoming - worldy resistance, intransigence: such are scientific experiments. No such intervention is required by logic, which can freely float above world in perpetuity without in the least encountering any worldy resistence.

These axioms should be ideally be grounded in the scientific method. — MonfortS26

Line 3 is where you fall down...

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".

For the sake of completeness, I should remind that Peirce was famously working on a logic of vagueness. So that was about the unbreaking of broken symmetries.

He could have gone beyond his musing about abduction if he had crystallised that logic. But we can see its outlines in the way he opposes vagueness to generality in terms of the three laws of thought.

Vagueness is that to which the PNC does not apply - to be vague is to be such that saying something of it is neither true nor false. (While generality is that to which the LEM fails to apply - a generality excludes neither one nor the other.)

And then Peirce also sought to move beyond regular logical methods by founding logic in diagrammatic argument. So rather than an algebra of symbols, he felt that a geometry of constraints or relations drilled down to the deepest level. It is in diagrams that reasonableness of logical truths becomes the most self-evident and undeniable.

Again, this was a move to strengthen the connection between human constructed principles of thought and the way the world physically exists.

Spencer-Brown famously picked up this move in his laws of form.

So formal predicate logic - the focus of your typical philosophy course - is a rather restrictive view of logical relations and their possible models. There is a heck of a lot that seems "outside" of that, as Peirce was so good at showing.

The simple answer is this, that what is logical to one person may not be to the next, whilst they may both equally be logical thinkers, that logic is not sufficiently specialized to define science. I`ve no idea why you are doing all of that hard work over something this easy, what happens when the difficult questions start? You do n`t require evidence for anything, just the answer, and an ability to wake up to it.

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. — apokrisis

This is where we part. "S is P" is not the structure of the world, it's just the easiest format of valuation we can operate with.

What, the world isn’t structured by categorical relations? The notion of generals and particulars fails the test of naturalness? We are merely imagining that reality is organised hierarchically?

I find that hard to believe.

My personal view is that logic is learned as opposed to it being innate.

Take the famous Pavlov dog experiment. Dogs were trained to associate the sound of a bell to food. After some time dogs were found to salivate just by the sound of the bell. Logic, very loosely, is a learned mental behavior. In short, we're logical because our world is. This is important.

The scientific method is fundamentally about basing our theories of the world on actual observation and experiment. If this is so then logic and science seem to be both empirical in foundation. Both are learned from the world.

The notion of generals and particulars fails the test of naturalness? — apokrisis

Well, I've never met a general anything, so there's that. :)

When you go to the seaside, do your encounter a beach as well as the grains of sand?

Think about how you would naturally reply if a friend asked where you went at the weekend.

I've never met a general anything, so there's that. — Akanthinos

except for -well - any general noun.

'I like apples.' 'Which kind?' 'Oh, Delicious, in particular. Please pass me that one.'

Pause

'That's not an apple, it's a peach. What's the matter with you, don't you understand English?'
**

As far as a general description of science is concerned, I find this one hard to fault:

Modern science emerged in the seventeenth century with two fundamental ideas: planned experiments (Francis Bacon) and the mathematical representation of relations among phenomena (Galileo). This basic experimental-mathematical epistemology evolved until, in the first half of the twentieth century, it took a stringent form involving (1) a mathematical theory constituting scientific knowledge, (2) a formal operational correspondence between the theory and quantitative empirical measurements, and (3) predictions of future measurements based on the theory. The “truth” (validity) of the theory is judged based on the concordance between the predictions and the observations. While the epistemological details are subtle and require expertise relating to experimental protocol, mathematical modeling, and statistical analysis, the general notion of scientific knowledge is expressed in these three requirements.

Science is neither rationalism nor empiricism. It includes both in a particular way. In demanding quantitative predictions of future experience, science requires formulation of mathematical models whose relations can be tested against future observations. Prediction is a product of reason, but reason grounded in the empirical. Hans Reichenbach summarizes the connection: “Observation informs us about the past and the present, reason foretells the future.” — E R Doherty

the first step is to make observations, based on those observations, you ask yourself questions. — MonfortS26

No, the first step is to posit a consistent nature or essence for a thing, then you deduce necessary conclusions for experience (or likely conclusions, if there are likely to be other, unknown factors involved) conditional on fiddling about with the object in some way - i.e. you deduce what would happen if the thing is the way you're positing it to be and if you were to fiddle about with it in some specified way, and then you fiddle about with it in the specified way (experiment).

Then you observe, to see if experience pans out as expected. If yes, you're done for now (until some anomaly crops up); if not, modify the essence or dream up another.

It's generate-and-test all the way up and down. That's how "blind" evolving nature works, that's how the brain works, how the immune system works, how epistemology works, how everything works (so far as we can tell).

The scientific method is the cycle of these three forms of reasoning according to Charles Sanders Peirce and it seems to me that is an accurate statement. My main question, is there an application of logic that falls outside this cycle? — MonfortS26

Yes.

In Einstein's epistemology..."the axiomatic structure (A) of a theory is built psychologically on the experiences (E) of the world of perceptions. Inductive logic cannot lead from the (E) to the (A). The (E) need not be restricted to experimental data, nor to perceptions; rather, the (E) may include the data of Gedanken experiments. Pure reason (i.e., mathematics) connects (A) to theorems (S). But pure reason can grasp neither the world of perceptions nor the ultimate physical reality because there is no procedure that can be reduced to the rules of logic to connect the (A) to the (E). Physical reality can be grasped not by pure reason (as Kant has asserted), but by pure thought."

Einstein, A. (1933). On the Method of Theoretical Physics. Lecture delivered on 10 June 1933 at Oxford University.

"Less certain is the connection between the (S) and the (E). If at least one correspondence cannot be made between the (A) and (S) and (E), then the scientific theory is only a mathematical exercise. Einstein referred to the demarcation between concepts or axioms and perceptions or data as the 'metaphysical original sin' (1949); and his defense of it was its usefulness."

Miller, A. (1984). Imagery in Scientific Thought. Birkhauser Boston, Inc.

In Einstein's epistemology..."the axiomatic structure (A) of a theory is built psychologically on the experiences (E) of the world of perceptions. Inductive logic cannot lead from the (E) to the (A). The (E) need not be restricted to experimental data, nor to perceptions; rather, the (E) may include the data of Gedanken experiments. — Galuchat

But even if the (E) is the data of Gedanken experiments, is that not to some extent the result of abductive reasoning? If we define abductive reasoning as a form of logical inference which starts with an observation then seeks to find the simplest and most likely explanation, isn't that synonymous with the statement above which you proposed?

Einstein referred to the demarcation between concepts or axioms and perceptions or data as the 'metaphysical original sin' (1949); and his defense of it was its usefulness. — Galuchat

Was he saying that the sin was the separation of the two concepts or the lack of separation?

But even if the (E) is the data of Gedanken experiments, is that not to some extent the result of abductive reasoning? If we define abductive reasoning as a form of logical inference which starts with an observation then seeks to find the simplest and most likely explanation, isn't that synonymous with the statement above which you proposed? — MonfortS26

I didn't propose a statement, I quoted Einstein. And in that quote, he is referring to the faculty of imagination, not reason, in arriving at (A).

These axioms should be ideally be grounded in the scientific method. — MonfortS26

That sounds like an axiom. That leads us to ask what it is grounded on.

There is no escape from the necessity of having to choose groundless axioms. That being the case, we may as well choose axioms of logic and set theory, like those referred to by Streetlight.

Why choose those? Because in the past they have worked very well for us.

Why should the fact that they have worked well in the past imply anything about how well they will work in the future?

..... enter Hume, and the Problem of Induction.

We can defuse that problem by choosing an Axiom of Induction.

But then why choose that axiom? We could try to say because it has worked well in the past, but that would be circular, as Hume pointed out.

So instead I would say that we cannot help but assume that axiom, because it is innate. We accept as a brute fact the fact that we inevitably accept the axiom of induction.

Having accepted the axiom of induction, we can then justify accepting the axioms of logic and set theory, because they have worked well for us in the past. Having bootstrapped ourselves up in that way, we can go on from there and soon get back to business as usual, including the scientific method.

Logic as a discipline preceded science, so I could see science evolving as a variation of logic.

But everybody in this thread seems to treat logic as something other than an intellectual discipline created by humans.

Seems anthropocentric to me. Humans uncover some things that work for them and then say that those things are how everything in existence is organized.

It seems like the scientific method is just the application of logic, reduced to 'scientific' axioms — MonfortS26

Well, if it is, then Frege, Russell, Carnap and al. sure lost a hell of a lot of time trying to build-up their lingua characteristica.

But then why choose that axiom? We could try to say because it has worked well in the past, but that would be circular, as Hume pointed out. — andrewk

Not really. We would choose it because it works. It become safe to think the past predicts the future once you are in that future.

So we know what works vs what doesn’t work. It’s a historical fact. There is inductive confirmation of any abductive leap we might have made.

Not really. We would choose it because it works. — apokrisis

That can't be a reason, because we can never know whether it works. All we can ever know is that it worked.

do your encounter a beach as well as the grains of sand? — apokrisis

Gotta say, this stomped me for a while. I had to ponder the fuck outta that one.

If I encounter a beach or if I encounter a grain of sand depends not on the world itself, but of a combination of the scale of my being, of my perceptive expectations and of my linguistic performance. Same thing for a forest and the trees. I can't distinguish between a drop of water and the sea unless I take them apart, because I'm not constituted in such a way that it is relevant for me to do so naturally. Same thing with air. This does not say anything about the world, but about the conditions of my relation to the world within such a scale. In the same way, the propensity of lumping in kinds entities does not, imho, speak of the world, but of our cognitive capacities in regard to that world.

If individual worldly processes tends to produce entities en masse, then that is something that can be attributed to the world.

except for -well - any general noun. — Wayfarer

Well, is it phenomenologically correct to say that you encounter a general noun? What you encounter is text, its only once interpreted that you attribute to a certain piece of text the role of being a general noun. It is more an operation on the text than an encounter of any kind, really.

Well, is it phenomenologically correct to say that you encounter a general noun? — Akanthinos

Sure, I encountered one reading that very sentence. The rest is typical nominalist evasion. General nouns rely on there being generalisations, which are in a sense Universals.

The rest is typical nominalist evasion. — Wayfarer

Damn. You got me. Like a spotlight on my nominalistic villainy. :-}