And all of this is apples and oranges anyway because while there may be a limit to what inductive reasoning tells us about the actual world, deductive reasoning tells us nothing about the world. It tells us only about whether truth has been preserved from our premises, yet there is no suggestion (or requirement) that our premises be a truth about the world (e.g. all glurgs are gurps and all gurps are glomps, therefore all glurgs are glomps). So, you can talk about the limitations of inductive reasoning, but the limitations of deductive reasoning are more severe, as it tell us nothing at all other than whether we've correctly solved our Sudoku puzzle. — Hanover

Thank goodness for some commonsense.

The interesting thing was that a valid deductive syllogism could be defined in terms of the three elements, the three steps, of a rule, a case, and a result. Some general "truth" that ranges over a class, some particular instance of that class, and then a consequence that could be predicated of that instance as a necessary fact.

And then the question arises of what happens when you play around with those three elements and consider what they say in a different order.

Induction was hazily understood as a converse of deduction - a step from the particular back to the general. But Peirce pursued the idea that induction itself was distinguishable into abduction and inductive confirmation. That was the way we actually seemed to reason about things in pragmatic fashion. And it was the way that science was turning into an explicit epistemology. Now you could see that this triadic story was itself already revealed in the formal tripartide structure of a deductive syllogism.

Of course the two varieties of induction were both "invalid". To go from the particular back to the general must involve a probabilistic leap of faith. A willingness to believe rather than to doubt.

But the whole problem with deduction is that it can't itself ever derive new information. It is just a system of syntax. It can only rearrange whatever semantics you put into it in a way that makes that move from the general to the particular.

So the "problem" with induction was really a problem with deduction. It was the rationalist dream that deduction could yield certain knowledge about everything. And in fact, by itself, it can yield no new knowledge at all. You needed induction to get the game started and to pragmatically justify the results.

The puzzle for me is that Banno keeps contradicting himself on these issues. One minute he is attacking the sceptics who just refuse to be pragmatic and commit to a belief that works. The next he is attacking the inductive basis of that pragmatism on the grounds the truth is "out there" beyond any such probability-based understanding.

Either he just hasn't sorted out a basic incoherence in his own epistemic metaphysics or he has something further to say which he just can't seem to bring himself to say. It's all very curious.

My own thinking is informed by modern science and its efforts to build pattern recognising machines, as well as the efforts to understand the same in human brains. — apokrisis

I've read your posts and I am currently trying to make sense out of them. In the mean time, I want to ask you a very simple question in order to make sure that we are on the same page. The question is: do you agree that abductive reasoning is a specific type of inductive reasoning? Ultimately, I understand that this comes down to how we define the concept of inductive reasoning. I believe that if the concept of induction is defined sufficiently narrowly that the answer would be "no". I do not, however, define it that way and I believe that others do not either.

Here's an example of abductive reasoning:

1. The grass is wet.
2. If it rains, the grass gets wet.
3. Therefore, it rained.

It is quite apparent to me that abductive reasoning is a very narrow form of reasoning. By definition, it only forms conclusions regarding events that took place in the past. This means that abductive reasoning is restricted to making "predictions" about the past. In other words, it can only be used to create retrodictions. This is unlike induction which can be used to form beliefs of any kind. This suggests to me the possibility of you defining the concept of induction narrowly as pertaining to making assumptions about the future.

Now let's take a look at a simple example of inductive reasoning. We have a sequence of numbers such as 1 2 3 4. Inductive reasoning can be defined as the process of identifying the pattern that best matches some given data and then using that pattern to form beliefs regarding data that lies outside of this data. Note that there are several ways, perhaps infinitely many different ways, that data can be outside of data. For example, you can ask "what comes after the number 4?" We can all agree it is 5. And we do so intuitively without being aware of the underlying process. We are often unware of answers to questions such as 1) how do we identify the right pattern based on the data that we're given?, and 2) how do we use that pattern to calculate the best guess regarding the unknown we are interested in? (The question #2 less so than the question #1.) We can formalize the question "what comes after number 4?" as 1 2 3 4 ? where question mark denotes the unknown we are interested in. But we can also ask "what comes before the number 1?" This would be analogous to retrodiction. We can formalize this question as ? 1 2 3 4 and we can also immediately answer it by saying that the number that comes before 1 is 0. But we can go further than that and we can ask questions such as "what comes between the number 2 and 3?" We can formalize this question as 1 - 2 ? 3 - 4 where hyphen represents an unknown we are not interested in. The answer is, of course, 2.5. An example of an inductive question that is most similar to what is called abductive reasoning would be a question formalized like 1 2 3 ? 5. This would be analogous to an abductive argument such as:

1. Number 5 is observed.
2. Every number is equal to the sum of the number that precedes it and number 1.
3. Therefore, number 5 was preceded by number 4.

Note that the abductive argument does not specify how we arrived at the rule that constitutes the premise #2. We did so using induction on a number of observations the majority of which have been ommited from the argument (i.e. the sequence of values 1 2 3 ?.) What this indicates is that abductive arguments, like deductive arguments and pretty much all other arguments, are simplifications of reality. They are simplistic. Inductive arguments are also simplistic but they are LESS simplistic than these two types of arguments. Unless, of course, you define induction narrowly.

The interesting question then is how induction, or whatever you want to call it, works. The question is how do we find the pattern that best fits some given data. In fact, my thinking is that the very concept of pattern is unnecessary. We do not need to be aware of any patterns. When I guess that the next value in the sequence 1 2 3 4 is number 5 I do not necessarily do so because I am aware of the underlying pattern. Rather, in most cases, I do so because I know that the set {1, 2, 3, 4, 5} has the highest degree of similarity to the set {1, 2, 3, 4} among the sets that have the form {1, 2, 3, 4, *}. Thinking is fundamentally associative. So the interesting question then becomes the formalization of fluid concept of equality (a.k.a. similarity) between mathematical objects such as sets. The question becomes: how do we measure the degree of similarity between symbols?

Regarding AGI research, most of the research has been dedicated to modelling how the world works rather than to modelling how thinking works. I think that's the problem. Rather than having a programmer create a model of reality, an ontology, for the computer to think within, it is better for a programmer to create a model of thinking which will allow machines to create models of reality -- ontologies -- on their own based on the data that is given to them. This would make machine thinking much more adaptable.

Your observations about the syllogisms look right to me.

My objection is a small one. I would reserve the word "logic" for deductive reasoning. Talk of inductive logic gives an undeserved legitimacy to making a guess.



A graven image. It should have an all-seeing eye at its centre. Another odd example of the obsession with trinities that helped keep Pierce from mainstream approval.

None of which should be taken as disparaging Bayesian analysis and other legitimate and excellent work around this topic. Unlike the philosopher's notion of induction, and even worse, abduction, Bayesian approaches have a strong standing.

The question is how do we know when these patterns are inherent in nature as opposed to arbitrary artefacts of our mode of perceiving? — Perplexed

By layering patterns upon patterns seeking similarities within differences and differences within similarities. This process should provide practical knowledge of the nature of nature and life. It should be useful insights.

So, you can talk about the limitations of inductive reasoning, but the limitations of deductive reasoning are more severe, as it tell us nothing at all other than whether we've correctly solved our Sudoku puzzle. — Hanover

True. I prefer to think in terms of Zebra puzzle. When someone says "deduction" I imagine think of this puzzle (that noone can solve except for genuises.)

Talk of inductive logic gives an undeserved legitimacy to making a guess. — Banno

Surely though you recognize where induction ends and speculation begins. Rational thought, even when not limited to formal deduction, is relied upon not because it's our religion, but because it works. I open the door in the morning and the cat runs in, not because we both guessed we would show up there, but we both expect one another from past events. That is logic, reason, and understanding the world. It is the J of Knowledge. Why is Gumbo there? She's hungry. That's not a guess. That's a reason, the basis that forms the reasonable and rational.

None of which should be taken as disparaging Bayesian analysis and other legitimate and excellent work around this topic. Unlike the philosopher's notion of induction, and even worse, abduction, Bayesian approaches have a strong standing. — Banno

You'll have to distiguish for me the distinction you're resting upon between induction and Bayesian analysis. Bayesian analysis is simply rigorous induction isn't it? Is your objection just that you find people sloppily drawing conclusions with incomplete information and you demand greater rigor? You're simply the juror who demands more proof because you see too many other possible explanations, but you're not the juror (as perhaps you suggest) who rejects the whole enterprise of induction and refuses to draw any conclusions from it regardless of the extent of supportive evidence, right?

The question is: do you agree that abductive reasoning is a specific type of inductive reasoning? — Magnus Anderson

I'm not getting too hung up on the divisions. There is the more familiar dichotomy of deductive vs inductive argument - necessary inferences vs probable inferences. That kind of works in the sense that deduction proceeds from the general to the particular with syntactic certainty while induction does the reverse of going from the particular to the general with provisional hopefulness.

But then a triadic view - one where a dichotomistic separation resolves itself into a hierarchical structure - is the special twist that Peirce brings to everything. It is the next step which completes the metaphysics.

So that is why it is a neat result - one that hierarchical structuralism predicts - that the actual process of human reasoning splits itself so cleanly into a trichotomistic process. It makes reasoning not an arbitrary business but one that works in the same basic way as the nature it wants to describe.

This is obviously a huge metaphysical deal - for those who still have faith in metaphysics as a grand unifying project.

So is abduction a specific form of induction? The Peircean question is instead where does abduction fit in the basic semiotic triad.

And it slots in as Firstness. A hypothesis is the first free and spontaneous act, which then leads to the "deductive" secondness that is mechanically determined reaction, and followed then by the thirdness which is the generalisation of such individual reactions to the form of some regular and enduring global habit.

Here's an example of abductive reasoning:

1. The grass is wet.
2. If it rains, the grass gets wet.
3. Therefore, it rained. — Magnus Anderson

But is it?

The classical deductive syllogism is:
Major premise (or the general rule: All M are P.
Minor premise (or the particular case): All S are M.
Conclusion (or result): All S are P.

Abduction then rearranges the order so that the argument is: All Ms are Ps (rule); all Ss are Ps (result); therefore, all Ss are Ms (case).

So you would have to say something like:
- Rain makes things wet.
- This grass is wet.
- Therefore, the grass was (probably) left out in the rain last night.

It is quite apparent to me that abductive reasoning is a very narrow form of reasoning. By definition, it only forms conclusions regarding events that took place in the past. This means that abductive reasoning is restricted to making "predictions" about the past. In other words, it can only be used to create retrodictions. This is unlike induction which can be used to form beliefs of any kind. This suggests to me the possibility of you defining the concept of induction narrowly as pertaining only to making assumptions about the future. — Magnus Anderson

I'm not sure why it seems a problem that abduction is retroductive - that the past is being assumed to hold the key to the future. To the degree the world has actually developed some stable intelligible being, it will have developed those general constraints which serve to restrict freedom and spontaneity to give the world its predictable shape.

This is the point concerning the metaphysics. Rather than going with the classical metaphysics which thinks reality is some God-given realm of law and deterministic material action, Peirce is up-ending that view to build a logic that arises out of a completely probabilistic model of existence.

So again, induction is not a problem as it sits on the side of probability. Deduction is now the problem as the shallowness of a deterministic or mechanical metaphysics stands exposed. The issue is really why would deduction function at all? And clearly - just as we find with computers and other machines - they can't stand alone. They are helpless if it weren't for us to bookend them and makes sense of their furious syntactical whirrings.

So if you sit on the side of a probabilistic ontology, now the whole picture can snap into place properly. Abduction seeks out the constraints that must underly any observable regularity in the world. A classical/deductive/mechanical/deterministic/atomistic world is merely the emergent limit on this probabilistic description. So the task is to guess at the rules that stabilise things sufficiently that the probability of causal certainty approaches arbitrarily near 1 (or 0) for the things we might care about as fundamental facts of the world.

Will we always fall down rather than up when stepping off that cliff? Well thermodynamics says all our atoms could fluctuate upwards at that precise moment and give us a surprise. Yet also, that is almost surely never going to happen - even given a really vast number of lifetimes for our Universe.

Thus abduction does seek to recover rules already formed. And inductive confirmation seeks to show our guesses are correct. And it is all couched in probabilistic language. We no longer believe in a classical Cosmos - the one of Newton and Hume. We are presciently already into a quantum reality where concrete classicality is an emergent and inherently probabilistic limit state.

When I guess that the next value in the sequence 1 2 3 4 is number 5 I do not necessarily do so because I am aware of the underlying pattern. Rather, in most cases, we do so because we know that the superset {1, 2, 3, 4, 5} has the highest degree of similarity to the superset {1, 2, 3, 4} among the supersets that have the form {1, 2, 3, 4, *}. — Magnus Anderson

I'm sure the rule you abduce is the simper one - 1+1=2. And so on, ad infinitum.

So you abduce a deductive rule, an algorithm that blindly constructs. You are recovering the set theoretic approach that is already the axiomatic basis for number theory.

A cherry-picked example which is a textbook case of deductive thought is hardly a good way to illustrate an argument about the true nature of induction. :-}

Regarding AGI research, most of the research has been dedicated to modelling how the world works rather than to modelling how thinking works. I think that's the problem. Rather than having a programmer create a model of reality, an ontology, for the computer to think within, it is better for a programmer to create a model of thinking which will allow machines to create models of reality -- ontologies -- on their own from the data that is given to them. — Magnus Anderson

Well that is why I always say forget Turing Machines and symbolic logic. It is neural networkers who have been thinking about how to properly mimic the Bayesian principles by which a brain actually makes inductive predictions.

A graven image. It should have an all-seeing eye at its centre. Another odd example of the obsession with trinities that helped kept Pierce from mainstream approval.

None of which should be taken as disparaging Bayesian analysis and other legitimate and excellent work around this topic. Unlike the philosopher's notion of induction, and even worse, abduction, Bayesian approaches have a strong standing. — Banno

Rock it like it's still the 1970s!

I'm not getting too hung up on the divisions. There is the more familiar dichotomy of deductive vs inductive argument - necessary inferences vs probable inferences. That kind of works in the sense that deduction proceeds from the general to the particular with syntactic certainty while induction does the reverse of going from the particular to the general with provisional hopefulness. — apokrisis

Syntactic certainty, or logical validity, isn't unique to deduction. Here's an example of inductive argument that is logically invalid:

1. Every swan in the past has been white.
2. Every swan in the future will be black.

That's invalid because it violates the rules of inductive reasoning according to which the future must mimic the past.

Similarly, probability isn't unique to induction. Deductive conclusions aren't certain. They can turn out to be wrong.

The special thing about deduction is merely the fact that if its conclusion turns out to be wrong then some or all of its premises will also turn out to be wrong. This is not the case with induction.

But then a triadic view - one where a dichotomistic separation resolves itself into a hierarchical structure - is the special twist that Peirce brings to everything. It is the next step which completes the metaphysics. — apokrisis

I have yet to see the relevance of placing so much emphasis on the concept of trinity.

But is it?

The classical deductive syllogism is:
Major premise (or the general rule: All M are P.
Minor premise (or the particular case): All S are M.
Conclusion (or result): All S are P.

Abduction then rearranges the order so that the argument is: All Ms are Ps (rule); all Ss are Ps (result); therefore, all Ss are Ms (case).

So you would have to say something like:
- Rain makes things wet.
- This grass is wet.
- Therefore, the grass was (probably) left out in the rain last night. — apokrisis

What's the difference? You changed the order of the premises. You put the rule in front of the observation. Charles Sanders Peirce, according to Wikipedia (1902 and after), had no problem with placing the observation before the rule.

1. The surprising fact, C, is observed. (The grass is wet.)
2. But if A were true, C would be a matter of course. (If it rains, the grass gets wet.)
3. Hence, there is reason to suspect that A is true. (Therefore, it rained.)

You also emphasize that the conclusion is merely probable. I think that such an emphasis is unnecessary since it is a given. All conclusions can turn out to be wrong. No conclusion is certain in the sense that it cannot turn out to be wrong.

I'm not sure why it seems a problem that abduction is retroductive - that the past is being assumed to hold the key to the future. — apokrisis

It is not a problem. The problem is that abduction is a narrowly defined concept. Specific concepts have specific needs. What are these specific needs? This is what I am trying to understand. I want to understand its relevance.

Abduction seeks out the constraints that must underly any observable regularity in the world. — apokrisis

But that's what induction does. Its job is to identify regularities in data. But instead of talking about induction, or more generally intelligence or thinking, you talk about abduction. And instead of speaking in terms of regularities or patterns, you speak in terms of constraints. I don't understand why. There must be a reason. What kind of reason is it? Is it a good or a bad one?

I'm sure the rule you abduce is the simper one - 1+1=2. And so on, ad infinitum. — apokrisis

What does that mean?

But instead of talking about induction, or more generally intelligence or thinking, you talk about abduction. — Magnus Anderson

I'm not following you. I've talked about all those things. You seem to want to make some campaign against abduction as a concept. And I am interested in how abduction fits into a holistic and naturalistic scheme of reasoning.

You will have to explain why I should be concerned by your problems with seeing a relevance in abduction. I've already explained why it would be relevant to a metaphysics that is irreducibly triadic (rather than dyadic or monadic).

And instead of speaking in terms of regularities or patterns, you speak in terms of constraints. — Magnus Anderson

Constraints generate regular patterns in a probabilistic fashion. So that is how science understands physical systems. And it is how we would speak of nature if we take a systems view where we grant generality a reality as a species of cause.

So again, it is simply a reflection that I am arguing from a consistent metaphysical basis. It is how reality would be understood if you believe in an Aristotelean four causes analysis of substantial being.

Notice that the syllogisms under Inductive and Abductive are invalid?

Giving them a name does not alter their invalidity. — Banno

They are deductively invalid; but that's no surprise since they are not purported to be deductive syllogisms.

I'm not following you. I've talked about all those things. You seem to want to make some campaign against abduction as a concept. And I am interested in how abduction fits into a holistic and naturalistic scheme of reasoning. — apokrisis

I have nothing against the concept. I am just trying to understand why you place so much emphasis on it. I don't see why such a concept is relevant. That's all. And if what I say appears to be an attack then it's merely due to the possibility that some of the things you say are no more than smokes and mirrors. I have to entertain such a possibility.

You will have to explain why I should be concerned by your problems with seeing a relevance in abduction. I've already explained why it would be relevant to a metaphysics that is irreducibly triadic (rather than dyadic or monadic). — apokrisis

You don't have to if you don't want to. I take it to be a matter of good will on your part.

Of course. As I said, they pretend to be a different sort of logic. It's the pretence that is problematic.

"Science works by induction"

"Ah! well, that's an end to that problem, then!"

Hume, Popper, Feyerabend, Quine, Kuhn - all show that it's questionable.

I am just trying to understand why you place so much emphasis on it. — Magnus Anderson

So did I make a big thing of it, or have I just replied to your continuing questions about it?

I don't see why such a concept is relevant. — Magnus Anderson

Fine. And yet you kept asking anyway. And I kept explaining why I do find it relevant. And so far you haven't rebutted my reasons for finding it relevant. And importantly so. Yet you want to keep telling me you don't find it relevant - despite offering no supporting reasons.

And if what I say appears to be an attack then it's merely due to the possibility that some of the things you say are no more than smokes and mirrors. I have to entertain such a possibility. — Magnus Anderson

I'm not bothered by your attack. I'm more disappointed at its lack of bite.

You don't have to if you don't want to. — Magnus Anderson

It's not a case of not wanting to. You have simply failed to supply an argument that could be evaluated.

Fine. And yet you kept asking anyway. And I kept explaining why I do find it relevant. And so far you haven't rebutted my reasons for finding it relevant. And importantly so. Yet you want to keep telling me you don't find it relevant - despite offering no supporting reasons. — apokrisis

Can you prove a negative? If so, how do you do it? By showing that there is no evidence supporting the claim, right?

Negatives are problematic. They could be caused by personal deficiency (subjective lack such as ignorance) or they might be real (objective lack.) You can never be sure.

The best I can do in this case is to ask further questions for the purpose of clarification. Maybe my post was deficient in this regard? Could be.

Hume merely showed that induction is not deduction as far as I can tell. Popper championed the role of abduction in science; conjectures just are abductions. Feyerabend, Quine and Kuhn I cannot comment on, since I haven't read them. Can you explain how the latter three showed induction has no role to play in science?

It seems obvious to me that induction and abduction both have their own logics; logics which clearly are not the same as the logic of deduction. All three have their own roles to play in human inquiry.

The best I can do in this case is to ask further questions for the purpose of clarification. — Magnus Anderson

But I asked you for clarification about this "relevance" of yours. For me, there is a background metaphysics that explains the specific relevance. For you, there must be likewise some background metaphysics - given that it seems you must have some good reason to reject my metaphysics as a relevant grounding.

So what is this metaphysics exactly? Put it on the table.

Popper championed the role of abduction in science; conjectures just are abductions. — Janus

Popper tried his best to dispose of induction and replace it with deduction in the form of falsification. He understood its illegitimacy. Abduction is not a term he much used. He did write formidably about statistical method, yet in the end held that we can never justify a theory.

Bah. No point in trying to sum up these guys in ten words or less.

I'm just going to be hard-nosed and say that what is called induction only has a legitimacy in science insofar as they are supported by deductive reasoning. There is only one sort of validity, deductive validity. Further the very idea of a single scientific method that when applied solves problems of science is fraught. Science is not algorithmic; it is a human activity with twists and turns and little accidents and big surprises.

And finish with a question: if there is a legitimate inductive logic, someone ought be able to set it out. What we have seen is some handwaving towards statistical analysis, but of course that is not induction. It has a base firmly in deductive mathematical logic.

I haven't read Popper in years, but I do seem to remember that he was greatly influenced by Peirce. What he saw as the conjectural moment of scientific inquiry; the creative imagining of explanatory scenarios, is the same as abduction as far as I can tell. I do agree with you that deductive reasoning is involved in both induction and abduction.

For example: take the well-worn example of whether the sun will rise tomorrow. On a purely deductive analysis the fact that the sun rose today and all the past days we know of provides no guarantee that it will rise tomorrow. This is just to say that there is no purely logical reason why the sun should rise tomorrow. But we can put this in deductive terms:

P1: The sun has always been observed to rise each day
P2: The rising of the sun is one of the countless invariances governed by the immutable laws of nature
P3: All lawful invariances must obtain unless some other lawful event intervenes
C: Therefore, the Sun must rise tomorrow unless some other lawful event causes it not to rise.

Is that a "legitimate inductive logic"?


Re Popper and Peirce: www.nmwt.org/nmwt/?r=article/download&id=124

Good stuff.

Here's how I would phrase the same solution, in a somewhat simpler fashion.

1. The number of my beliefs that would have to be wrong for the sun not to come up tomorrow is extraordinarily large.
2. Therefore, the sun will rise tomorrow.

It's just as invalid as your argument, with the benefit of being briefer. :P

It's interesting to think about why this is the example of choice. The truth is, that the sun will come up tomorrow is something of which we are certain. Hence it's usefulness as an example.

I had a quick look and Peirce hardly gets a mention in Popper's Logic of Scientific Discovery. Pragmatism is only mentioned in passing.

But I asked you for clarification about this "relevance" of yours. For me, there is a background metaphysics that explains the specific relevance. For you, there must be likewise some background metaphysics - given that it seems you must have some good reason to reject my metaphysics as a relevant grounding.

So what is this metaphysics exactly? Put it on the table. — apokrisis

I would more than like to. The problem is I have no clue what metaphysics is. What is it? I've heard stories about it but they never made any sense and in those rare cases when they did it was a combination of epistemology, logic and conceptual analysis. Maybe ask a specific question? or describe to me what metaphysics is so that I can give you an answer? I might be too demanding, I know.

Or we could discuss some of the things we have already touched upon such as how thinking works. We can discuss "the thinking algorithm" if you want. What rules do we follow when we make assumptions? How do we proceed from a set of particular knowns (i.e. past observations) to a set of ranked candidates for particular unknowns (i.e. predictions and retrodictions)? I already gave you the basic idea behind my approach but you rejected it on the ground that it was a textbook of something you call "deductive thought". I have no idea what "deductive thought" is. You appear to be fond of ANN's but you find something wrong with my approach? I have no idea what's the problem.

It's already difficult to agree on what deductive and inductive reasoning are. Most people have trouble ADMITTING that the key difference between the two is NOT that one is certain and the other is uncertain. Every conclusion is uncertain in the sense that it can turn out to be wrong. The idea of a conclusion that is not uncertan -- that is certain -- in the sense that it cannot possible turn out to be wrong is NON-SENSICAL. It is possible that there are conclusions that WILL NEVER turn out to be wrong but it makes no sense to say that there are conclusions that cannot POSSIBLY turn out to be wrong. A subtle but crucial distinction. Thus, both induction and deduction produce conclusions that are UNCERTAIN. I am not going to say PROBABLE even though I can. It should be a given that every truth-claim is probable since for a claim to be probable simply means that it has a probability value assigned to it. And every truth-claim has a probability value assigned to it. True/false is a measure of probability. And a measure of probability is simply how we subjectively rank possibilities in terms of their likelihood. True/false is two-valued probability measure. It makes no sense to call it something other than probability simply because it is not one-hundred-valued (0% to 100%) or infinite-valued (such as 0.000~ to 1.000~.) Furthermore, both induction and deduction can either be logically valid (or syntactically certain) or logically invalid (or syntactically uncertain.) I gave an example of logically invalid induction in one of my previous posts.

Almost none of our beliefs are justified (in our mind) by science. So if you only accept reductive explanations as justification for beliefs, then you would have to conclude that almost all of our beliefs lack any justification whatsoever - and that cannot be true, because it is part of our usual understanding of the notion of "justified belief" that a large proportion of our beliefs is fairly justified. — SophistiCat

That's exactly the point I'm making. I'm not saying that our beliefs can either be justified or not (that's an entire epistemological position) I'm disputing that there is any good grounds for specify that science cannot justify the passions, as if there were some other group of things that it could justify. If there's nothing that science can justify (in that way) then the comment is entirely specious, claiming to provide some in formation about 'the passions', when in fact it is merely reporting the limits of science in general.

Whether or not I know of some scientific explanation for my feeling of hunger or my perception of the color of the sky is completely irrelevant to my warrant for holding the respective beliefs. — SophistiCat

This rather presumes a position on conciousness which is far from agreed upon. If you take the view that conciousness is some kind of causal force than you might be right, or even if it is an epiphenomenon caused by the actual brain states it 'watches', but if it is either a brain state itself, or an epiphenomenon caused by a brain state specifically responsible for causing it, then it is perfectly possible for you to be wrong about your belief that you are hungry. 'Hungry' would be typically held as being that disposition which (in the absence of competing forces) would cause a person to eat. It is perfectly possible that your brain could be in that state, but the part of your brain responsible for generating the epiphenomenon of concious awareness erroneously reports that you are not. In that sense you would be incorrect about your assertion 'I'm hungry'.

It is perfectly possible that your brain could be in that state, but the part of your brain responsible for generating the epiphenomenon of concious awareness erroneously reports that you are not. In that sense you would be incorrect about your assertion 'I'm hungry'. — Pseudonym

This is where pattern recognition in the form of finding differences in similarities and similarities within differences becomes the most helpful tool to a philosophy.

1) All life forms are organizing in some form to maintain life.

2) Some have brains and some do not.

3) There is no theory that explains why some particles try to survive and others do not.

4) Therefore there is some life force that acts in somewhat the same fashion (with differences and similarities) that is trying to survive and creating the feeling of hunger so that the total life entity gathers itself to survive.

This is how one forms a metaphysical point of view that is instructive and useful about one's own life and nature in general.

If one were to follow Hume's position that we have no rational basis for believing that induction from experience is a valid form of knowledge, then how can we claim that these invariances are objectively true?

logicians agree that deduction offers no new information, only clarify that which is know — charleton

Could clarification not provide new information? After all, if it is already known then why clarify in the first place?

Only if you accept that free will is defined as not compelled to act from external forces — charleton

So do you say that to be free is to act only from internal forces? How does one begin the process of disassociating from external forces in order to follow internal ones? Would this change not violate determinism?

I suppose 18th century science could be said to "assert determinism". The question is, does our modern science allow for non-deterministic events to take place?

It sounds like you are advocating a kind of statistical analysis to find correlations between the patterns in nature. This still doesn't get us over the "correlation is not causation" problem though.

It appears to be quite different from statistical analysis. The mind is creating recognizing and observing new patterns and then from memory overlaying one upon the other upon the other (not necessarily consciously) and attempting to find differences within the similarities and similarities within the differences (a creative process) and then intuiting something new about nature. It is entirely a creative/intuitive process.

There is not a strict method. It is more like detective work, experimenting with new ideas and observing effects. Creativity and intuition is the path to new understanding, however it cannot be taught, it is as skill that can only be learned through practice of various creative efforts.

This sounds like a psychological process, perhaps similar to what they call "prediction error" in neuroscience and learning theory. How can we tell the extend to which a pattern is created by the brain rather than inherent in world?

This sounds like a psychological process — Perplexed

100%. Totally psychological.

How can we tell the extend to which a pattern is created by the brain rather than inherent in world? — Perplexed

Nothing is "created" by the brain? The brain (actually the total nervous system) is merely a transmitter/receiver. Look at it. It looks like a transmitting/receiving antenna.

The mind is observing the patterns, whether it be football plays it an artist's reference model. The more we practice this amount various fields of endeavor the better we get. From this we develop the ability to create new patterns from the source patterns which yields new insights that we test. I do not this all the time when I practice Tai Chi, play piano, draw, play table tennis, sing, etc. Sometimes I find small new patterns and sometimes major new patterns. I've been doing this my whole life and with practice I get better at it. Then I experiment with it to see if it provides useful and practical applications in my life. I am always experimenting. This is true evolution of life.

This is not a guaranteed process. It is one of trial and error. Learning to adjust is also part of life and evolution. We are navigators not robots, that is the process of creating.