Science is just a re-branding of logic

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.

Quoting StreetlightX

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

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?

Quoting StreetlightX

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

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

Quoting StreetlightX

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.

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

Reply to StreetlightX 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.

Quoting StreetlightX

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

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.

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

Quoting StreetlightX

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

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?

Quoting StreetlightX

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

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

Quoting StreetlightX

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

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.

Quoting MonfortS26

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

These for example:

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

Quoting MonfortS26

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.

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.

Quoting MonfortS26

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

Line 3 is where you fall down...

Quoting MonfortS26

It's main categorizations are informal and formal logic. Informal including inductive reasoning, and abductive reasoning. Formal mainly being deductive.

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.

Quoting StreetlightX

No such intervention is required by logic, which can freely float above world in perpetuity without in the least encountering any worldy resistence.

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.

Quoting MonfortS26

My main question, is there an application of logic that falls outside this cycle?

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".

Reply to MonfortS26 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.

Quoting apokrisis

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.

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.

Reply to Akanthinos 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.

Reply to MonfortS26 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.

Quoting apokrisis

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

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

Reply to Akanthinos 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.

Quoting Akanthinos

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

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:

E R Doherty: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.”

Quoting MonfortS26

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

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).

MonfortS26: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?

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.

Quoting Galuchat

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.

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?

Quoting Galuchat

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.

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

MonfortS26: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?

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).

Quoting MonfortS26

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

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.

Quoting MonfortS26

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

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.

Quoting andrewk

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.

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.

Quoting apokrisis

Not really. We would choose it because it works.

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

Quoting apokrisis

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

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.

Quoting Wayfarer

except for -well - any general noun.

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.

Quoting Akanthinos

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

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.

Quoting Wayfarer

The rest is typical nominalist evasion.

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

Reply to andrewk We can know that it worked and so it’s opposite didn’t work.

Inductively, we thus have no good reason to think that the story would reverse itself in the future.

It still might. But we would have no good reason to think it would.

Quoting apokrisis

Inductively, we thus have no good reason to think that the story would reverse itself in the future.

What is the role of the 'Inductively' at the beginning of this sentence? If it means, 'using the principle of induction' then it is assuming the conclusion - i.e. the validity of that principle. If not, I can't see the word contributing anything to the sentence.

I agree we have no good reason to think the process would reverse, just like we have no good reason to think it won't reverse - assuming that 'good' means 'grounded and logical' (and if not that then what does it mean?). We don't have any logical reason to have any expectations about the future, which is the whole problem.

Reply to Akanthinos I’m confused. You say generality and particularity are points of view. I agree.

Then you make some further suggestion about individual worldly processes that produce entities en masse.

Apart from coke bottles and model T fords, did you have some natural process in mind here.

What kind of process produces beaches for instance? There are loads of those everywhere.

Do grains of sands run about and gang together at dead of night to build the beach you visit? Or were you thinking of something general like erosion and currents as the processes responsible?

Quoting andrewk

just like we have no good reason to think it won't reverse

But we do. We have inductive evidence that inductive principles have prevailed to date. This view has the weight of historic evidence. It’s abductive guess remains unfalsified. And the opposite guess has an equivalent lengthy history of not being true,

Quoting apokrisis

Then you make some further suggestion about individual worldly processes that produce entities en masse.

Apart from coke bottles and model T fords, did you have some natural process in mind here.

What kind of process produces beaches for instance? There are loads of those everywhere.

I'm not a physicist, but I would assume a constant in the action of water currents upon small particules in relation to geographical features? The entirety of philogeny would be the explanation of the process leading to a current living being.

It's because those processes leads to mass production of similar entities that we are warranted in speaking of category and kinds, not because the world is structured categorically. In the same way, predication is only seen as so central to our worldview because it is the most natural format of value-attribution for us to handle. All statements can be reduced to non-predicative forms without loss of meaning, and all basic attributive statements can be reduced to existential judgements à la Brentano. Again, imho.

Quoting Akanthinos

I would assume a constant in the action of water currents upon small particules in relation to geographical features?

But you mentioned a causal process that generally produces entities. Being particulate doesn’t seem a cause of a beach as such. The generality of currents as a process do.

Quoting Akanthinos

t's because those processes leads to mass production of similar entities that we are warranted in speaking of category and kinds, not because the world is structured categorically

So if a general process produces particular entities, then how does this structural fact about nature not justify a categorical representation of the situation in logic? Why would that picture fail?

Quoting MonfortS26

Would a good analogy for the relationship be "logic is 'pure logic' and science is 'applied logic', in comparison to pure and applied mathematics"?

Yes, this is how I see the relationship between logic and (empirical) science too. Logic defines all possibilities while empirical observation, that is, interaction with our environment, helps us find out in which logical possibilities we happen to live.

It is better to follow Wittgenstein's example and argue that logic reduces to the practical use of ordinary language with additional constraints to describe a more precise (but not infinitely precise) collection of states of affairs and associated behaviours.

If for any sentence written in logic we cannot think of a use for it, then we can signify this by baptising its negation with the name "logically-necessary".

I have a number of issues here so bear with me please.

Reply to MonfortS26

Logic should be used in circumstances of uncertainty. In order to have a formal deductive logic, axioms must be set. These axioms should be ideally be grounded in the scientific method. It is fair to claim that the scientific method is itself, grounded in its own axioms, but the reproducibility and outside application of its results is reason enough to believe in its merit.

Um, no. Science uses mathematics, which is constructed via axioms which seem plausible and useful in mathematics. Mathematicians reason according to particular formal systems which they choose to use. The dominant such system of the day is Zermelo-Frankel set theory + Classical Logic (despite the name, Classical Logic was invented in the late 1800s, not the classical period, lol). And I assure you, science did not play a role in why this system rose to prominence (although there are a number of competing systems worth study). ZFC & CL gained prominence due to issues in *mathematics*, not science. Such as (with ZFC) the attempt to regiment mathematics axiomatically (ended up failing but the system is useful), such as understanding infinity and number theory etc. Classical Logic was the result of trying to find what rules for reasoning would be needed to overcome the inability of Aristotlean Logic to account for how mathematicians actually reasoned.

Science had nothing to do with it and it's difficult to see how it could itself determine the rules for reasoning when you have to use reasoning (and math) in science. The situation is more complicated than I've made out so far, but I'll get to that soon.

The same argument can be applied to the concept of logic as well. In situations where an axiom is not grounded in scientific reasoning, for my personal use, the best option is to create arguments and attempt to decide what is more probable based on said arguments. This is a process that can only be done with intuition. The merit of those arguments, if not eventually supported by scientific progress, can be measured through the durability of those claims due to public scrutiny. Logic is only useful in determining future behavior. When trying to determine what the best course of action is, the first step is to make observations, based on those observations, you ask yourself questions. Once you have your questions, you create a set of axioms that are logically consistent with each other and use deductive reasoning in order to determine the best outcome. Finally, if things do not go as planned, you come back and question those initial axioms and go back and change them as necessary. Then repeat the cycle.

How on earth are you doing probability without reasoning? What is the axiom in question that you are questioning? Arguments need to be constructed in particular ways (the correct rules for reasoning) to be valid. Now one *can* disagree about which rules are correct for reasoning (Classical Logic, Intuitionistic Logic, Paraconsistent Logic, etc.), but to settle logical disagreements one has to appeal to a model of theory choice and decide based which theory of logic is the best theory of reasoning (determined by the usual criterion of theory choice).


Intuition is a terrible idea here since people's intuitions aren't all the same, nor is there any inherent reason why intuition allows one to reach a true conclusion better than anything else. And isn't this kind of odd? You say science must do X Y & Z and yet you say we have to resort to intuition?

And besides, what observations are going to bear on logic? Look, logic isn't about the world, the world isn't logical. A logic is a formal system that maps out a particular consequence relation. The world is... whatever the heck it is, I don't know (ask a metaphysician). Outside a formalism, one simply reasons. If there is a relationship between logic and reality, it's not obvious what that relationship is.

Also, you made an assumption here. Axioms don't have to be "logically consistent with each other", as then you're simply assuming a particular axiom already (the Law of Non-Contradiction). There are formal systems where that law is not a tautology. Namely, dialetheic logics, a type of Paraconsistent Logic.

The problem with this though is where I state that the axioms should be grounded in the scientific method. Correct me if I'm wrong, but I basically just re-transcribed the scientific method. It seems like the scientific method is just the application of logic, reduced to 'scientific' axioms. My question is this, is there any knowledge worth knowing, that cannot be learned through this cycle? Is there any reason not to just follow the scientific method and adjust based on the pragmatic maxim when in times of doubt?

1) There's no such thing a "the" scientific method.
2) Science is basically useless (because it's inapplicable) in formal disciplines like mathematics and logic. And surely we've gained knowledge from mathematics and logic.

This thread makes no sense to me. Logic is not science and science is not rebranded logic. "Pragamtism" is not logic either.

Quoting apokrisis

We have inductive evidence that inductive principles have prevailed to date.

We have observations that inductive principles have served us well in the past. On that I expect we agree.

I can see no way to turn that set of observations into a reason to expect that inductive principles will serve us well in the future, without using the principle of induction itself. And neither could Hume. And neither, to my knowledge, has anybody found a satisfactory answer to that in the intervening centuries.

Reply to andrewk Again, the converse is true. We can see from a history that believing the contrary of the principle of induction would have been as misleading as possible. So to adopt the contrary in regards to the future would be as unreasonable as possible. Hence it is only reasonable to continue to assume the principle.

We are talking about a meta-argument, remember. This is not about some particular belief. This is about the general method of belief. We are no longer talking about just events in the world. We are talking about a habit of mind.

Quoting apokrisis

So to adopt the contrary in regards to the future would be as unreasonable as possible.

This supposes we already have a standard for judging what is reasonable and what is not. What is that standard, and where did we get it from?

Reply to andrewk Experience. A history of what works. Reason seems reasonable as unreason has likewise proved itself as such.

Quoting apokrisis

A history of what works.

We have a history of what worked, not of what works. The difference of tenses is critical.

Reply to andrewk

It seems rather impractical--perhaps even impossible--to operate reasonably under the assumption that the future will work differently from the past. What would (or could) warrant any particular expectation or corresponding course of action?

In any case, induction is justified because its method is such that experience would, sooner or later, correct any erroneous beliefs adopted by following it.

Quoting aletheist

What would (or could) warrant any particular expectation or corresponding course of action?

Nothing. The mistake is to expect, or even demand, a warrant. The answer is to act without warrant.

We act according to our nature, which is to assume the principle of induction, without wasting time futilely seeking a warrant for the assumption.

Reply to andrewk Sigh. The history of what worked up to a nanosecond ago then?

Crucial difference my arse. Pointless pedantry more like.

Quoting apokrisis

Crucial difference my arse. Pointless pedantry more like

Really? If you have to resort to sneering your beliefs must be poorly thought-out indeed.

Reply to andrewk Well prove me wrong by actually making an argument and not merely an assertion.

If the difference in tense is crucial, demonstrate what practical difference it could make.

Quoting apokrisis

If the difference in tense is crucial, demonstrate what practical difference it could make.

Because we know what consequences past actions have had, but we do not know what the consequences will be of future actions, or of actions we are currently undertaking but for which the consequences are not yet observable.

In concrete terms, I am prepared to bet, today, on who won the last papal election, but not on who will win the next one.

Reply to andrewk You said the difference in tense between past and present was crucial - between worked and works.

So what was that about?

Quoting apokrisis

You said the difference in tense between past and present was crucial - between worked and works.

So what was that about?

We have observations about what worked in the past, and that includes observations that the principle of induction worked in the past. I can see no way of logically deducing from those observations a prediction of what will work in the future- including whether the principle of induction will work in future - without using the principle of induction. Neither could Hume. Neither could anybody else since then.

Reply to andrewk So your claim is now about past vs future tense and not past vs present tense. Do you blame me for feeling confused. Especially when you just won’t correct what you said.

But again, if we are now in the future that acceptance of induction predicted, then that is inductive confirmation of a principle. We decided to use the principle and now we can see how well it has worked. So it would be matchingly unreasonable to now drop the principle. It’s converse lacks any empirical support and only has empirical falsification.

So sure, induction says we can’t know that the past predicts the future. But when we speak to the principle itself, it has got a track record that makes that a reasonable bet.

Quoting andrewk

We act according to our nature, which is to assume the principle of induction, without wasting time futilely seeking a warrant for the assumption.

It’s hardly futile if we have a history of evidence. Again, the issue is not whether things are certain but whether there are good reasons to continue to hold a principle. And the evidence weighs heavily here for the principle and not its contrary, or even a null hypothesis.

Gosh it's like someome here has never read Hume before.

Reply to apokrisis I haven't changed my position, and I certainly don't blame you if you feel confused. I feel confused most of the time, and I hope nobody blames me for it.
Quoting apokrisis

So it would be matchingly unreasonable to now drop the principle.

Nobody has suggested that we drop the principle. Look at the post eight up from here (for some reason I can't link to it), where I in fact suggest the opposite.

That one cannot find a non-circular, logical reason for holding a principle is not a reason not to adopt it.

Quoting andrewk

We act according to our nature, which is to assume the principle of induction, without wasting time futilely seeking a warrant for the assumption.

Why are we not rationally warranted to base our expectations on what we have observed and continue to observe to work; namely inductive reasoning? Particularly as we have no viable substitute at all, that seems to be a pretty good reason to accept induction.

Quoting andrewk

That one cannot find a non-circular, logical reason for holding a principle is not a reason not to adopt it.

I think that is the mistake you are making, and that Hume also made; is imagining that there could possibly be a logical reason. That just makes no sense at all! The reason that warrants acceptance of induction is not, and cannot be, purely deductive, it is simply practical.

Quoting Janus

I think that is the mistake you are making, and that Hume also made; is imagining that there could possibly be a logical reason

Hume imagined no such thing. On the contrary he pointed out that there couldn't be a logical reason, or at least (being a fairly humble fellow) that he had no hope of ever finding such a reason.Quoting Janus

as we have no viable substitute at all, that seems to be a pretty good reason to accept induction.

That is Reichenbach's response, and IMHO it's a good one. Note that it says nothing about how likely induction is to work, just that we have no alternatives that we expect to work any better. That, either alone, or together with my observation that we cannot help but use induction, is enough reason to use it when deciding on actions. But whether that's enough to call it a warrant depends on how strong your standard of warranty is.

Note also that the Reichenbach response relates to deciding on actions, whereas I think Hume was more focused on beliefs, and what warrant we have for them. He is quoted as saying 'I have no reason to believe my dinner will not poison me.' As far as that pure belief goes, Reichenbach's response doesn't help, because it's only about actions. But Reichenbach helps with what Hume is reputed to have said next, which is:

'But I shall eat it anyway'

Reply to andrewk

If a man's beliefs are identified with his non-verbal behaviour, then it is no longer clear to me when he [I]isn't[/I] making an induction. Which suggests that epistemological warrant for induction might not be needed simply because it is vacuous to even speak of consenting to 'ceremonies' of induction, for if all behaviour can be regarded as future-anticipating then induction is just another word for behaviour.

Quoting sime

If a man's beliefs are identified with his non-verbal behaviour

That is a very contentious proposition, and in any case, I don't see how it bears on warrant. No one denies that we do think - and behave - inductively (except maybe Popperians).

Quoting SophistiCat

That is a very contentious proposition, and in any case, I don't see how it bears on warrant. No one denies that we do think - and behave - inductively (except maybe Popperians).

Because if induction is a vacuous notion then to insist upon warrant is to insist upon nothing. I'm with popper, but feel he didn't quite go far enough to dissolve the issue of warrant into being a non-issue.

Suppose that someone described themselves to be a gambler, but that they always bet on the least frequent outcome without offering any justification and regularly lost. Is there any difference between describing them as a being bad gambler vs denying that they are in fact a gambler?

Is there a clear distinction between predicting badly vs not making a prediction?

Doesn't the difference entirely rest upon the normative and hence subjective context by which we judge behaviour to be future-anticipating?

Quoting sime

Doesn't the difference entirely rest upon the normative and hence subjective context by which we judge behaviour to be future-anticipating?

Of course warrant is normative. How can you say that it is both normative and vacuous? That seems contradictory.

Quoting andrewk

I think that is the mistake you are making, and that Hume also made; is imagining that there could possibly be a logical reason — Janus

Hume imagined no such thing. On the contrary he pointed out that there couldn't be a logical reason, or at least (being a fairly humble fellow) that he had no hope of ever finding such a reason.

I probably did not express that every well. What I meant to say is that Hume's mistake consists in imagining that it ever should have been thought that there could be purely logical reasons justifying inductive reasoning, and to claim it as an interesting insight that there are not such reasons. In other words it just seems silly to think that it could ever have turned out that not to believe in induction would involve a contradiction. How could it ever be thought, for example, that it would be self-contradictory to believe that it was possible the Sun would not rise tomorrow?

The point I find most inconsistent in Hume's position is that, although he claims we have no reason to believe in the regularities we observe constantly in nature, he seems to think there is good reason to believe that humans and other creatures habitually expect them. Such habitual expectation would itself be a regularity, so Hume's argument fails according to its own principles.

Returning to the example of the Sun's rising; it seems that there is actually a deductive principle at work, but that it relies on a premise which itself cannot be deductively proven (which is really quite trivial since such is the case for all deductive reasoning). Taking the Sun's rising as an exemplar of natural invariance, we can deduce that 'if nature is governed by necessary laws, then then the Sun will rise tomorrow unless some other unforeseen lawful event prevents it from doing so'. Or, taking Peirce's alternative, if we adopt the premise that "nature takes habits", we can deduce that it is most likely that the Sun will rise tomorrow, unless some greater unforeseen habit of nature intervenes.

If Hume's argument were taken to its logical conclusion then it would result in Meillassoux's radical contingency, and we could not even trust in our own memories of, or documents recording, what happened in the past, let alone our expectations of what is to come. All our discourse would then be thoroughly undermined and we would not be capable of saying anything sensible about anything at all.

Quoting Janus

Or, taking Peirce's alternative, if we adopt the premise that "nature takes habits", we can deduce that it is most likely that the Sun will rise tomorrow, unless some greater unforeseen habit of nature intervenes.

This is important as Peirce is giving an actual reason for why induction is something that strengthens with time. A constraints-based view of the world says induction should become ever more reliable because a reasonable habit will keep growing stronger in being reinforced by its own success.

That is how science works. Our conviction strengthens as a belief survives challenge to its applicability.

And that is how the solar system works. In its early days, the sun came up everyday on the earth in a more unreliable manner. It took a while for a ball of debris to even accumulate into a planet. The early solar system was fraught with broken up junk that could have smashed into and derailed the earth, ending any nascent habit of a daily dawning of the sun.

But over time, the solar system got cleared up of all the junk, all the chaos, and settled down into a long-term groove. The inductive grounds of a belief became ever firmer.

So while there is nothing absolute to warrant that the past predicts the future, a constraints-based view of causality makes it deductively reasonable that regularity develops over time. Habits want to emerge. Order predicts not just order, but increasing order. Constraints develop a weight that make it increasingly hard for individual accidents to derail.

So the principle of induction is - as Peirce put it - about the taking of habits.

The Humean view arises from imagining a reality without real interactions. It is a Newtonian paradigm where everything reduces to local accidents - random collisions. Of course, in a world imagined like that, you would expect there to be no gathering history, no developing state of generalised coherence. If everything is imagined as fundamentally random and memory-less, then of course the deductive consequence - Hume's argument - is that even the laws of nature might change for no reason at any time.

But once you have a metaphysics which can take account of interactions - see how that requires a generalised coherence to emerge just due to "randomness" - then you will deduce something quite different about nature. You will have a different model-theoretic view to test by observation.

So really Hume is advancing a metaphysics-based hypothesis - and one that is believed due to Newtonian science. That is what gives it any credence it might have.

However, the "shock" is that this Newtonian causality just isn't what we observe in nature - on the whole. Instead we see a world where interactions result in a generalised state of coherence. Constraints or habits inevitably - and logically! (we can do the maths of self-organisation!) - must emerge to bring predictable and increasing order to their "worlds".

Hume had the right argument for the wrong metaphysics. And physics has since moved on as well.

Quoting StreetlightX

Gosh it's like someome here has never read Hume before.

Ah. Hear the plaintiff squeak of someone who has never stopped to truly consider what Humean doubt is about. Such a big difference between reading about something and thinking about something.

Reply to apokrisis

That's a nice elaboration of what is entailed by the Treatise of Humean Nature. In his ambition to do for human nature what he thought Newton had done for Nature in general he seems to have fallen into a deeply contradictory position given that, without accepting the very regularities his position denied, no such ambition could be fulfilled. Hume seems to have both rejected, and yet put his faith in, the determining power of regularity. :)

Quoting Janus

Hume's mistake consists in imagining that it ever should have been thought that there could be purely logical reasons justifying inductive reasoning, and to claim it as an interesting insight that there are not such reasons

My recollection is that Hume was not imagining this himself, but rather writing in response to Rationalists who not only imagined it but believed it possible. It sounds like you are agreeing with Hume that it was not.
Quoting Janus

he seems to think there is good reason to believe that humans and other creatures habitually expect them

Are you sure he wasn't observing that humans always have habitually expected them, which is past tense, and doesn't need to use induction.

If Hume's argument were taken to its logical conclusion .... All our discourse would then be thoroughly undermined and we would not be capable of saying anything sensible about anything at all.

No, because we can make the discourse perfectly well just by accepting the principle of induction without insisting on a warrant for it. Remember, Hume didn't say we shouldn't use induction, but rather that it seemed to him to be futile to search for a warrant for it.

We can draw a parallel between Hume and Godel.

In the early 20th century mathematicians, led by Hilbert, were engaged in a program of proving the soundness of mathematics. Godel proved that that was impossible. Did that mean that Godel claimed we shouldn't use mathematics? Of course not! He thought we should, but just that we should not waste our time trying to prove its foundations were sound.

Similarly, the Rationalists in the 16-18th century were trying to prove the soundness of reason and scientific methods. Hume showed that that was impossible. Did that mean that Hume claimed we shouldn't use reason? Of course not! He thought we should, but just that we should not waste our time trying to prove its foundations were sound.

Quoting SophistiCat

Of course warrant is normative. How can you say that it is both normative and vacuous? That seems contradictory.

Sorry, i meant warrant being epistemologically vacuous.

Quoting andrewk

My recollection is that Hume was not imagining this himself, but rather writing in response to Rationalists who not only imagined it but believed it possible. It sounds like you are agreeing with Hume that it was not.

Can you cite a statement by any rationalist that says it would be logically contradictory for things not to be as they are, or not to be in the future as they have in the past?

It's true that rationalist philosophers such as Spinoza and Leibniz believed that things are necessarily as they are; but this is not a logical necessity, but rather in accordance with what they thought of as the necessity of the Divine Nature. It is a complicated story but it has nothing to do with pure logical necessity as in the law of non-contradiction.

Quoting andrewk

Are you sure he wasn't observing that humans always have habitually expected them, which is past tense, and doesn't need to use induction.

What so his argument only applied to the past then? Basing his account of human nature on past observations of regularity is no different, in principle, than basing an account of non-human nature on past observations of regularity. In any case if there is really no regularity in nature then memory itself could not be counted as reliable, which would render even his account of the past untenable.

Quoting andrewk

No, because we can make the discourse perfectly well just by accepting the principle of induction without insisting on a warrant for it. Remember, Hume didn't say we shouldn't use induction, but rather that it seemed to him to be futile to search for a warrant for it.

The argument is only over whether induction is rationally warranted. Hume says it isn't at all, and this entails that his own arguments are not rationally warranted either.

Quoting andrewk

We can draw a parallel between Hume and Godel.

That axioms are not proveable does not entail that they are not rationally warranted. They are rationally warranted because without them there can be no discourse. The irrational demand for absolute proof is the whole source of these kinds of humean errors of thought.

Reply to Janus

The argument is only over whether induction is rationally warranted. Hume says it isn't at all, and this entails that his own arguments are not rationally warranted either.

which, being a pragmatist, doesn't bother him. He just assumes the principle of induction as an axiom, and then any arguments he makes are conditionally warranted based on acceptance of that axiom, which is all he, or any sensible pragmatist, wants.

The point is that one has to adopt that principle as an unfounded axiom, and arguments that one can somehow 'prove' the axiom are unneeded and unsound..

Reply to andrewk

My real complaint, though, is that Hume paints our acceptance of induction as being merely a matter of habit, and not in any way rationally justified. Also, I would not agree with classing Hume as a pragmatist. Perhaps you just meant that he was a pragmatic thinker? Otherwise we seem to be in agreement.

Quoting andrewk

which, being a pragmatist, doesn't bother him.

But Hume represents the nominalist turn of thought. He was not a pragmatist in the sense of arguing for the reality of the general or universal. He was an atomist in regards to empirical sense data. So his epistemology reflects a particular brand of metaphysics.

Reply to Janus

That axioms are not proveable does not entail that they are not rationally warranted. They are rationally warranted because without them there can be no discourse. The irrational demand for absolute proof is the whole source of these kinds of humean errors of thought.

I think I was mostly with you until you said this (depending on what you meant). If by this you meant a particular set of axioms are rationally warranted because without them discourse is impossible, I would find that dubious (people disagree about what axioms should be adopted in math and logic, and they do so intelligibly). But if you meant there needed to be some set of axioms to get thing s rolling, then I would agree.

Reply to andrewk

We can draw a parallel between Hume and Godel.

In the early 20th century mathematicians, led by Hilbert, were engaged in a program of proving the soundness of mathematics. Godel proved that that was impossible. Did that mean that Godel claimed we shouldn't use mathematics? Of course not! He thought we should, but just that we should not waste our time trying to prove its foundations were sound.

Ehh, that's not it. Early 20th century mathematicians weren't trying to prove the soundness of mathematics, they were trying to prove its completeness and consistency of it. But as it turned out, you could only have incompleteness or inconsistency. I don't think the analogy holds since the Incompleteness of formalisms capable of expressing number theory doesn't make mathematics rationally unjustifiable. It just means you have to accept that, unless you go with Paraconsistent Mathematics, your mathematical enterprise will be incomplete.

Quoting SophistiCat

That is a very contentious proposition, and in any case, I don't see how it bears on warrant. No one denies that we do think - and behave - inductively (except maybe Popperians).

Umm, no. Popperians wouldn't claim so either:

[hide="Block of text"]"[i]I had become interested in the problem of induction in 1923. Although this problem is very closely connected with the problem of demarcation, I did not fully appreciate the connection for about five years.

I approached the problem of induction through Hume. Hume, I felt, was perfectly right in pointing out that induction cannot be logically justified. He held that there can be no valid logical arguments allowing us to establish 'that those instances, of which we have had no experience, resemble those, of which we have had experience'. Consequently 'even after the observation of the frequent or constant conjunction of objects, we have no reason to draw any inference concerning any object beyond those of which we have had experience'. For 'shou'd it be said that we have experience' --experience teaching us that objects constantly conjoined with certain other objects continue to be so conjoined--then, Hume says, 'I wou'd renew my question, why from this experience we form any conclusion beyond those past instances, of which we have had experience'. In other words, an attempt to justify the practice of induction by an appeal to experience must lead to an infinite regress. As a result we can say that theories can never be inferred from observation statements, or rationally justified by them.

I found Hume's refutation of inductive inference clear and conclusive. But I felt completely dissatisfied with his psychological explanation of induction in terms of custom or habit.

It has often been noticed that this explanation of Hume's is philosophically not very satisfactory. It is, however, without doubt intended as a psychological rather than a philosophical theory; for it tries to give a causal explanation of a psychological fact--the fact that we believe in laws, in statements asserting regularities or constantly conjoined kinds of events--by asserting that this fact is due to (i.e. constantly conjoined with) custom or habit. But even this reformulation of Hume's theory is still unsatisfactory; for what I have just called a 'psychological fact' may itself be described as a custom or habit -- the custom or habit of believing in laws or regularities; and it is neither very surprising nor very enlightening to hear that such a custom or habit must be explained as due to, or conjoined with, a custom or habit (even though a different one). Only when we remember that the words 'custom' and 'habit' are used by Hume, as they are in ordinary language, not merely to describe regular behaviour, but rather to theorize about its origin (ascribed to frequent repetition), can we reformulate his psychological theory in a more satisfactory way. We can then say that, like other habits, our habit of believing in laws is the product of frequent repetition--of the repeated observation that things of a certain kind are constantly conjoined with things of another kind.This genetico-psychological theory is, as indicated, incorporated in ordinary language, and it is therefore hardly as revolutionary as Hume thought. It is no doubt an extremely popular psychological theory--part of 'common sense', one might say. But in spite of my love of both common sense and Hume, I felt convinced that this psychological theory was mistaken; and that it was in fact refutable on purely logical grounds. Hume's psychology, which is the popular psychology, was mistaken, I felt, about at least three different things: (a) the typical result of repetition; (b) the genesis of habits; and especially (c) the character of those experiences or modes of behaviour which may be described as 'believing in a law' or 'expecting a law-like succession of events'.

A. The typical result of repetition--say, of repeating a difficult passage on the piano--is that movements which at first needed attention are in the end executed without attention. We might say that the process becomes radically abbreviated, and ceases to be conscious: it becomes 'physiological'. Such a process, far from creating a conscious expectation of law-like succession, or a belief in a law, may on the contrary begin with a conscious belief and destroy it by making it superfluous. In learning to ride a bicycle we may start with the belief that we can avoid falling if we steer in the direction in which we threaten to fall, and this belief may be useful for guiding our movements. After sufficient practice we may forget the rule; in any case, we do not need it any longer. On the other hand, even if it is true that repetition may create unconscious expectations, these become conscious only if something goes wrong (we may not have heard the clock tick, but we may hear that it has stopped).
B. Habits or customs do not, as a rule, originate in repetition. Even the habit of walking, or of speaking, or of feeding at certain hours, begins before repetition can play any part whatever. We may say, if we like, that they deserve to be called 'habits' or 'customs' only after repetition has played its typical part; but we must not say that the practices in question originated as the result of many repetitions.
C. Belief in a law is not quite the same thing as behaviour which betrays an expectation of a law-like succession of events; but these two are sufficiently closely connected to be treated together. They may, perhaps, in exceptional cases, result from a mere repetition of sense impressions (as in the case of the stopping clock). I was prepared to concede this, but I contended that normally, and in most cases of any interest, they cannot be so explained. As Hume admits, even a single striking observation may be sufficient to create a belief or an expectation--a fact which he tries to explain as due to an inductive habit, formed as the result of a vast number of long repetitive sequences which had been experienced at an earlier period of life. But this, I contended, was merely his attempt to explain away unfavourable facts which threatened his theory; an unsuccessful attempt, since these unfavourable facts could be observed in very young animals and babies-- as early, indeed, as we like. 'A lighted cigarette was held near the noses of the young puppies', reports F. Bäge. 'They sniffed at it once, turned tail, and nothing would induce them to come back to the source of the smell and to sniff again. A few days later, they reacted to the mere sight of a cigarette or even of a rolled piece of white paper, by bounding away, and sneezing.' If we try to explain cases like this by postulating a vast number of long repetitive sequences at a still earlier age we are not only romancing, but forgetting that in the clever puppies' short lives there must be room not only for repetition but also for a great deal of novelty, and consequently of non-repetition.

But it is not only that certain empirical facts do not support Hume; there are decisive arguments of a purely logical nature against his psychological theory.

The central idea of Hume's theory is that of repetition, based upon similarity (or 'resemblance'). This idea is used in a very uncritical way. We are led to think of the water-drop that hollows the stone: of sequences of unquestionably like events slowly forcing themselves upon us, as does the tick of the clock. But we ought to realize that in a psychological theory such as Hume's, only repetition-for-us, based upon similarity-for-us, can be allowed to have any effect upon us. We must respond to situations as if they were equivalent; take them as similar; interpret them as repetitions. The clever puppies, we may assume, showed by their response, their way of acting or of reacting, that they recognized or interpreted the second situation as a repetition of the first: that they expected its main element, the objectionable smell, to be present. The situation was a repetition-for-them because they responded to it by anticipating its similarity to the previous one.

This apparently psychological criticism has a purely logical basis which may be summed up in the following simple argument. (It happens to be the one from which I originally started my criticism.) The kind of repetition envisaged by Hume can never be perfect; the cases he has in mind cannot be cases of perfect sameness; they can only be cases of similarity. Thus they are repetitions only from a certain point of view. (What has the effect upon me of a repetition may not have this effect upon a spider.) But this means that, for logical reasons, there must always be a point of view--such as a system of expectations, anticipations, assumptions, or interests--before there can be any repetition; which point of view, consequently, cannot be merely the result of repetition. (See now also appendix *X, (1), to my L.Sc.D.)

We must thus replace, for the purposes of a psychological theory of the origin of our beliefs, the naïve idea of events which are similar by the idea of events to which we react by interpreting them as being similar. But if this is so (and I can see no escape from it) then Hume's psychological theory of induction leads to an infinite regress, precisely analogous to that other infinite regress which was discovered by Hume himself, and used by him to explode the logical theory of induction. For what do we wish to explain? In the example of the puppies we wish to explain behaviour which may be described as recognizing or interpreting a situation as a repetition of another. Clearly, we cannot hope to explain this by an appeal to earlier repetitions, once we realize that the earlier repetitions must also have been repetitions-for-them, so that precisely the same problem arises again: that of recognizing or interpreting a situation as a repetition of another.

To put it more concisely, similarity-for-us is the product of a response involving interpretations (which may be inadequate) and anticipations or expectations (which may never be fulfilled). It is therefore impossible to explain anticipations, or expectations, as resulting from many repetitions, as suggested by Hume. For even the first repetitionfor-us must be based upon similarity-for-us, and therefore upon expectations--precisely the kind of thing we wished to explain.

This shows that there is an infinite regress involved in Hume's psychological theory.

"Hume, I felt, had never accepted the full force of his own logical analysis. Having refuted the logical idea of induction he was faced with the following problem: how do we actually obtain our knowledge, as a matter of psychological fact, if induction is a procedure which is logically invalid and rationally unjustifiable? There are two possible answers: (1) We obtain our knowledge by a non-inductive procedure. This answer would have allowed Hume to retain a form of rationalism. (2) We obtain our knowledge by repetition and induction, and therefore by a logically invalid and rationally unjustifiable procedure, so that all apparent knowledge is merely a kind of belief--belief based on habit. This answer would imply that even scientific knowledge is irrational, so that rationalism is absurd, and must be given up. (I shall not discuss here the age-old attempts, now again fashionable, to get out of the difficulty by asserting that though induction is of course logically invalid if we mean by 'logic' the same as 'deductive logic', it is not irrational by its own standards, as may be seen from the fact that every reasonable man applies it as a matter of fact: it was Hume's great achievement to break this uncritical identification of the question of fact--quid facti--and the question of justification or validity--quid juris. (See below, point (13) of the appendix to the present chapter.)

It seems that Hume never seriously considered the first alternative. Having cast out the logical theory of induction by repetition he struck a bargain with common sense, meekly allowing the reentry of induction by repetition, in the guise of a psychological theory. I proposed to turn the tables upon this theory of Hume's. Instead of explaining our propensity to expect regularities as the result of repetition, I proposed to explain repetition-for-us as the result of our propensity to expect regularities and to search for them.

Thus I was led by purely logical considerations to replace the psychological theory of induction by the following view. Without waiting, passively, for repetitions to impress or impose regularities upon us, we actively try to impose regularities upon the world. We try to discover similarities in it, and to interpret it in terms of laws invented by us. Without waiting for premises we jump to conclusions. These may have to be discarded later, should observation show that they are wrong.

This was a theory of trial and error--of conjectures and refutations. It made it possible to understand why our attempts to force interpretations upon the world were logically prior to the observation of similarities. Since there were logical reasons behind this procedure, I thought that it would apply in the field of science also; that scientific theories were not the digest of observations, but that they were inventions--conjectures boldly put forward for trial, to be eliminated if they clashed with observations; with observations which were rarely accidental but as a rule undertaken with the definite intention of testing a theory by obtaining, if possible, a decisive refutation.[/i]"
-Karl Popper, "Conjectures and Refutations", p. 55-61[/hide]

Reply to MindForged

Early 20th century mathematicians weren't trying to prove the soundness of mathematics, they were trying to prove its completeness and consistency of it. But as it turned out, you could only have incompleteness or inconsistency

I know. I just didn't want to use technical terms like completeness and consistency in a discussion that has not been heavily technical thus far.

Reply to Janus

I would not agree with classing Hume as a pragmatist. Perhaps you just meant that he was a pragmatic thinker?

Yes that's what I mean, which is why I carefully avoided using a capital P that would imply similarity to Peirce, James and Dewey. I happen to think there are some similarities but it doesn't matter to this discussion whether there are, or how deep they go, and I think it would be a distraction to get into that.

Reply to andrewk Ah, my mistake then.

Quoting MindForged

Ehh, that's not it. Early 20th century mathematicians weren't trying to prove the soundness of mathematics, they were trying to prove its completeness and consistency of it. But as it turned out, you could only have incompleteness or inconsistency. I don't think the analogy holds since the Incompleteness of formalisms capable of expressing number theory doesn't make mathematics rationally unjustifiable. It just means you have to accept that, unless you go with Paraconsistent Mathematics, your mathematical enterprise will be incomplete.

Gödel shows how limited is our ability to give direct proofs. (Just like, well, Turing did also.) Gödel's theorems simply show how tricky self-reference (which with Gödel doesn't end up in a Paradox) is and thus the idea of there being a way to prove everything that is true to be so is simply false. That doesn't at all make Mathematics unlogical.

Some sciences do have the problem of self reference or subjectivity. Just think about the social sciences: if the findings in social sciences like economics or sociology themselves have an effect on how we behave, how we understand ourselves and how we make decisions, then it has a "problem" of self reference. This is totally evident in things like economics where there allways is a normative side to the subject along with the descriptive.

Yet this doesn't at all mean that the study of societies wouldn't be a scientific endeavour.

Quoting sime

Sorry, i meant warrant being epistemologically vacuous.

I still have no idea what you mean by this. Warrant is what makes epistemology normative. To say that such and such belief is warranted is to say that you can and should believe such and such. What is vacuous about this?

Quoting apokrisis

But Hume represents the nominalist turn of thought. He was not a pragmatist in the sense of arguing for the reality of the general or universal. He was an atomist in regards to empirical sense data. So his epistemology reflects a particular brand of metaphysics.

Whether or not Hume was an atomist is irrelevant, as Goodman's new riddle of induction illustrates.

If today one person sees an object as green, and another person sees it as grue (i.e. currently green up until some future time t, then blue afterwards), then their principles of the uniformity of nature are different.

As this illustrates, the so called 'principle' of the uniformity of nature is relative to one's ontology, and hence so is one's principle of induction. And regardless of whatever this ontology is, the infallibility of induction relative to this ontology cannot be non-circularly justified, nor empirically defended.

In my opinion a better way to understand Hume, is to say that whatever one uses as a principle of induction it is impossible to distinguish good from bad inductions without pain of circularity.

Quoting SophistiCat

I still have no idea what you mean by this. Warrant is what makes epistemology normative. To say that such and such belief is warranted is to say that you can and should believe such and such. What is vacuous about this?

I'm saying that if there are no objective criteria, i.e. physical criteria, for ascribing to agents propositional-attitudes pertaining to prediction-making, then it makes no objective sense to discuss agents as needing epistemological warranty for induction, since applications of rules of induction is then in the eye of the beholder, for example the community the agent belongs to who selectively interprets his behaviour as prediction-making for their own concerns.

In other words, I am suggesting that to follow a rule of induction is no different to following any other rule; it is a normative principle pertaining to language-games, but not in any way that is significant to metaphysics or epistemology.

Reply to ssu

Gödel shows how limited is our ability to give direct proofs. (Just like, well, Turing did also.) Gödel's theorems simply show how tricky self-reference (which with Gödel doesn't end up in a Paradox) is and thus the idea of there being a way to prove everything that is true to be so is simply false. That doesn't at all make Mathematics unlogical.

...yea? I didn't say Godel's results made math "unlogical", I said his Incompleteness theorems entail that any sufficiently expressive formal system (i.e. one capable of arithmetic) must be either incomplete or inconsistent. In other words, there's a limitation of what sorts of desirable properties such an enterprise can have. Paraconsistent Mathematics allows one to (non-trivially) maintain Completeness, but it's inconsistent (this is too far for some people). Standard mathematics retains consistency (well, no known inconsistencies anyway), and as such is necessarily incomplete. That's all I said, so I don't think we disagree.

Quoting sime

objective criteria, i.e. physical criteria

What exactly do you mean by "physical criteria"? What is your warrant for equating objective criteria with physical criteria?

Quoting MindForged

...yea? I didn't say Godel's results made math "unlogical", I said his Incompleteness theorems entail that any sufficiently expressive formal system (i.e. one capable of arithmetic) must be either incomplete or inconsistent. In other words, there's a limitation of what sorts of desirable properties such an enterprise can have. Paraconsistent Mathematics allows one to (non-trivially) maintain Completeness, but it's inconsistent (this is too far for some people). Standard mathematics retains consistency (well, no known inconsistencies anyway), and as such is necessarily incomplete. That's all I said, so I don't think we disagree.

No, we don't.

As typical with Mathematics, you can say something differently from just another point of view and still both are correct.

Reply to ssu Well I missed where the disagreement was then, we both said that Godel showed a limitation on the ability to give proofs in mathematics. Sooo, eh, whatever.

Couldn't we just abandon the idea of internal consistence, like Tarski did, and then keep on doing logic in whatever other meta-language provides external consistency to maths? :-|

Quoting SophistiCat

No one denies that we do think - and behave - inductively (except maybe Popperians).

Quoting Ying

Umm, no. Popperians wouldn't claim so either:

I am not sure why you posted this lengthy excerpt in response to my off-hand remark. In it Popper criticizes Hume's psychological account of induction, ending up endorsing the view that "We obtain our knowledge by a non-inductive procedure."

First of all, I wasn't referring to Hume specifically. By "inductive thinking" I meant our tendency to identify patterns of occurrences and extrapolate them beyond the available concrete facts, both as a way of explaining what we know and of predicting what we don't know.

You might instead argue that Popper rather overstates his opposition to induction, and that his own view is distinguished only in some particulars from the common-sense take that I outlined above. But this is not all too obvious from your quote.

Anyway, this is all very dated stuff, of interest mainly to historians.

Quoting sime

In other words, I am suggesting that to follow a rule of induction is no different to following any other rule; it is a normative principle pertaining to language-games, but not in any way that is significant to metaphysics or epistemology.

Of course induction is normative - I don't understand why you keep saying this as if this is something controversial. And your last remark makes me wonder what you think metaphysics and epistemology are about.

Quoting MindForged

That axioms are not proveable does not entail that they are not rationally warranted. They are rationally warranted because without them there can be no discourse. The irrational demand for absolute proof is the whole source of these kinds of humean errors of thought.


I think I was mostly with you until you said this (depending on what you meant). If by this you meant a particular set of axioms are rationally warranted because without them discourse is impossible, I would find that dubious (people disagree about what axioms should be adopted in math and logic, and they do so intelligibly). But if you meant there needed to be some set of axioms to get thing s rolling, then I would agree.

I was not referring to any "particular set of axioms" as being indispensable, although it is arguable that there are some axioms that seem to be fundamental to human experience; and that consequently seem self-evident, and anyone can intuitively 'get' them. The axioms of Euclidean geometry would seem to fall into this category. Of course, non-Euclidean geometries exist, but they are not intuitive in the 'direct' way that Euclidean geometry is.

Reply to Janus

I was not referring to any "particular set of axioms" as being indispensable, although it is arguable that there are some axioms that seem to be fundamental to human experience; and that consequently seem self-evident, and anyone can intuitively 'get' them. The axioms of Euclidean geometry would seem to fall into this category. Of course, non-Euclidean geometries exist, but they are not intuitive in the 'direct' way that Euclidean geometry is.

But doesn't that show the weakness of this view (relying on intuition to settle the matter)? Intuition doesn't really seem to lend much justification to accept what we are "getting" via it, and worse, intuition can cause us to dismiss truths which conflict with them. You mention Euclidean Geometry as being direct and intuitive, but some of our best scientific theories suggest we have to understand the space of the universe as being Non-Euclidean (Relativity comes to mind).

That's not to say intuitions aren't important, but I'd probably not hold them in too high a regard when discussing "deeper" issues.

Reply to MindForged

I agree it is arguable that non-intuitive scientific models and theories may show us a "deeper" structure of reality (whatever we might think that means) but when it comes to rational justification, in the sense of the logical structures, of our everyday discourse about the world the foundational axioms that make that discourse possible are mostly intuitively given, I would say.