Is there a special prayer that the Laws of Nature — Rich

I don't know. But its not me that believes in magic. That would be you.

I image that that laws are not fully deterministic or else that they apply over a limited scope. Is it even logically possible for full determinism to produce more than one outcome?

I can't see any point of disagreement here; other than the pedantic one concerning the idea of the sun rising.

Keep in touch then, because the Laws have me caught in this grip of non-believing, so if they happen to reveal something to you that might help, it would be much appreciated.

Is it even logically possible for full determinism to produce more than one outcome? — Perplexed

Nope. And such a point of view has no theory for variation in the universe. Quantum theory does.

The only way determinism works is if the Laws of Nature assume all of the authority and possibilities of gods (God). It is absolutely the silliest metaphysical theory I've ever come across and more correctly should be classified as a religion.

That the sun will rise tomorrow is something we can be sure of. Anything you add to that by way of philosophical or scientific theorising will not be as certainty as that the sun will rise. Indeed, saying that we know it will rise because we understand the rotation of the Earth is exactly wrong; we understand the rotation of the Earth because the sun rises each morning.

This is not correct. Prior to knowledge of the Sun being the center of the solar system, the Sun was understood to be a wandering God whose path like those of the other planets (gods) circumambulated the celestial sphere. Each night the Sun traversed the underworld and emerged victorious the following morning. It was possible (since the Greek Gods were not omnipotent) that the dark forces of the underworld could defeat the Sun; which would mean that it would fail to rise.

On a Christian perspective the Sun could fail to rise tomorrow if it turned out that Judgement Day had arrived or if God so willed it.

We believe that it could not fail to rise on account of our understanding of gravity and thermodynamics; our world is actually much more stable and certain in a way than the ancient world which was subject to the fate of the gods or the will or whim of God.

When you talk of certainty that the Sun will rise tomorrow you are referring to a feeling and arguing that that feeling is stronger than our feeling of certainty regarding celestial mechanics or physics. In a way this is true; but the modern feeling of certainty only exists on account of either mere habit or else our understanding of science. This understanding may not be possessed by many people but within our culture scientific understanding filters down to alter common feelings about the world.

And you still haven't addressed my point about the analogical nature of inductive and abductive thinking and the inappropriateness of applying the criterion of deductive validity where it doesn't belong, in order to dismiss the importance of its role in human inquiry into the nature of the world.

all the theories you list above are less certain than that the sun will come up. Each case is over-baking the cake.

Less certain to you? To me? To everybody? How can you be certain of that except perhaps in your own case? This is still a deflection in any case; so I give up.

And you still haven't addressed my point about the analogical nature of inductive and abductive thinking and the inappropriateness of applying the criterion of deductive validity where it doesn't belong, in order to dismiss the importance of its role in human inquiry into the nature of the world. — Janus

It's a matter of how he defines words. If he defines validity narrowly to mean truth-preserving validity, i.e. that an argument is valid if and only if its conclusion being false means some of its premises are false, then yes, induction is invalid because it can have a true premise and a false conclusion. But if you're like me and you define the concept of validity broadly to mean that an argument is valid if and only if it logically follows from the premises (i.e. if it does not violate the rules of reasoning) then induction is by definition valid.

Really, what he's saying is that induction, in the narrow way that he defines it, is not truth preserving. I think it's strange to say it's invalid because it suggests there is something wrong with it. If an argument is not trurh preserving that does not mean it's wrong. Sometimes, with some kinds of arguments, it does. But that does not apply to induction

then induction can be valid. — Magnus Anderson

Only if it is framed in deductive form, though and like you I have already presented an example of an inductive argument framed deductively. The inductive parts in that case form the assumptions in the premises which are obviously not themselves demonstrated by the argument itself; but which are also not subject to judgements of invalidity, as is the case with the premises of any deductive argument.

The premises of deductive arguments may be unsound, but unsoundness cannot be deduced, and is actually judged inductively (on the uncertain basis of experience and inference to the best explanation; in other words plausibility).

Whether or not a certain syllogism is "valid" is only relevant on graded tests.

What is relevant is knowledge is acquired by a combination of personal observations, group consensus, and periodic moments of intuition and inspiration. Such knowledge can be used in a formal manner using some symbolic logic, but the root of knowledge is in observational pattern recognition of various sorts.

then induction can be valid.
— Magnus Anderson

Only if it is framed in deductive form — Janus

Not really. If I define logical validity broadly to mean that an argument is valid if and only if it logically follows from the premises (i.e. if it does not violate the rules of reasoning) then induction is by definition valid. Note that I corrected myself? I initially said that it can be valid but then I realized that induction is defined so narrowly that it cannot be other than valid.

1. Some Ps are Qs
2. Therefore, all Ps are Qs

If there is a conditional rule between the premise (the independent variable) and the conclusion (the dependent variable) which states that the P and Q in the conclusion must be the same P and Q in the premise, then it is impossible for this sort of argument to be anything other than logically valid. It is not necessary for the argument to be truth preserving to be considered valid i.e. if its conclusion is false it's not necessary that some of its premises be false.

The problem is that logical validity is poorly defined. Look at this:

In logic, an argument is valid if and only if it takes a form that makes it impossible for the premises to be true and the conclusion nevertheless to be false. — Wikipedia

This suggests that logical validity and truth preservation are one and the same thing. They are not. Truth preservation is merely a symptom of logical validity and even then not always.

Here's an argument that is truth preserving but nonetheless invalid:

1. Donald Trump has an orange hair
2. Melania Trump is Donald Trump's wife
2. Therefore, 2+2=4

Truth preserving but not valid. The conclusion does not follow from the premises.

The reverse is also true. If an argument is not truth preserving that does not mean it's not valid. The following is perfectly valid:

1. All observed swans are white.
2. Therefore, all swans are white.

Logical validity simply means that the conclusion logically follows from the premises. It means that it does not violate the rules of reasoning. It means that the structure of the argument, the combination of the premises and conclusion, is legal.

The problem is that two distinct concepts have been confused: one broad (logical validity) and one narrow (truth preservation.) I believe the mistake stems from the initial observation that logical validity is always coupled with truth preservation. People will always make such mistakes so as long they focus on narrow concepts first and broad concepts second.

Whether or not a certain syllogism is "valid" is only relevant on graded tests.

What is relevant is knowledge is acquired by a combination of personal observations, group consensus, and periodic moments of intuition and inspiration. Such knowledge can be used in a formal manner using some symbolic logic, but the root of knowledge is in observational pattern recognition of v various sorts. — Rich

Reasoning isn't merely about making observations. A mass of observations will mean nothing to you if you cannot generalize from them. Logic is the study of this process of generalization. This process of generalization can take any of form but there is one form that we consider "rational" or "valid" and numerous other forms that we consider "irrational" or "invalid". Logic is the effort to discriminate between the two. More generally, it is the effort to discriminate between different patterns of reasoning and analyze their consequences, their pros and cons, under different circumstances.

Not really. If I define logical validity broadly to mean that an argument is valid if and only if it logically follows from the premises (i.e. if it does not violate the rules of reasoning) then induction is by definition valid. — Magnus Anderson

If an argument is such that its conclusion follows necessarily from its premises then it is an deductive argument, end of story. That is how a deductive argument is defined.

Induction and abduction really consist in inferences not.

Take the example I gave earlier of graviataional lensing. The abductive/inductive reasoning is analogical.

• Curved transparent materials are observed to refract light.

• Space is transparent

• Conclusion: It is likely that if space is curved by mass it will be observed to cause refraction of light.

The conclusion does not follow logically from the premises, the premises could be true and the conclusion false, but with additional premises involving laws of nature it could be framed in deductive form, and then the conclusion would follow logically from the premises.

The argument in its inductive form is neither valid nor invalid, though; because the "likely" makes that indeterminable. If it had said instead "therefore refraction of light will be observed", then it would be purporting to be a deductive argument, but would be invalid.

mass of observations will mean nothing — Magnus Anderson

Observations together with pattern recognition combined with inspiration/intuition that gives new meaning to these recognized patterns.

A child builds a sandcastle.
Every time the ocean waves come in, it destroys the castle. (observation and pattern recognition).
Something must be done to avoid or redirect the water. (inspiration).

This is how knowledge is acquired.

If an argument is such that its conclusion follows necessarily from its premises then it is an deductive argument, end of story. That is how a deductive argument is defined. — Janus

Not true.

Here's an inductive argument:

1. Some Ps are Qs
2. Therefore, all Ps are Qs

The conclusion necessarily follows from the premise. You cannot conclude something like "Therefore, no P is Q". It is necessary that you conclude "Therefore, all Ps are Qs". Note that we're talking about logical necessity and not objective necessity.

Observations together with pattern recognition combined with inspiration/intuition that gives new meaning to these recognized patterns. — Rich

That's my point: observations together with the process of generalization which you call "pattern recognition combined with inspiration/intuition". That process is not arbitrary. It unfolds according to some set of rules. Logic studies the rules of that process.

If we are agreeing, then great. However, I don't know where intuition/inspiration falls within the rules of logic. Also, pattern recognition is not simply generalization. Frequently it is a process of observing differences and similarities among many patterns and then intuitively combining these intuitively conceived newer patterns into an entirely new greater pattern that allows one to acquire an entirely new way of understanding something. Most breakthroughs in metaphysics and science happen this way though the poor metaphysician is often ignored because the insights are entirely his/her own.

↪Magnus Anderson If we are agreeing, then great. However, I don't know where intuition/inspiration falls within the rules of logic. Also, pattern recognition is not simply generalization. Frequently it is a process of observing differences and similarities among many patterns and then intuitively combining these intuitively conceived newer patterns into an entirely new greater pattern that allows one to acquire an entirely new way of understanding something. Most breakthroughs in science happen this way. — Rich

I think that inspiration is irrelevant to understanding how reasoning works. Intuition, on the other hand, is a poorly defined term that for the most part means nothing other than "knowing something without being able to explain how". That's not very useful.

What is important is how the set of known particulars (i.e. experience, past observations, etc) is mapped to the set of unknown particulars (i.e. predictions and retrodictions.) It might not be appropriate to call this process "generalization" since high-level concepts (i.e. laws, rules, patterns, models, universals, etc) are ignored. Instead, we map directly from known particulars to unknown particulars. We go directly from observations to predictions. In some cases, we go straight to actions.

Logic is the study of this mapping. This mapping is initially intuitive in the sense that we cannot explain how it works. But through time, with careful introspection, we gradually become aware of its inner workings. The intuition, in part or in whole, becomes formalized. It acquires a memetic existence which allows us to employ it mechanically i.e. by simply following its written instructions.

I think that inspiration is irrelevant to understanding how reasoning works. — Magnus Anderson

I'm actually talking about knowledge acquisition. I believe this is what Hume was also interested in.

Intuition is not only poorly defined, it is impossible to define because it pops out of the experience of living. It just happens. However, the more one practices observation and pattern recognition, the more one is likely to have moments of inspiration because it is sharp observation skills that is the mother of inspiration. With such a process, one is merely traveling on the same path of knowledge forever. I guess one can rely on the inspiration of others

I'm actually talking about knowledge acquisition. I believe this is what Hume was also interested in.

Intuition is not only poorly defined, it is impossible to define because it pops out of the experience of living. It just happens. However, the more one practices observation and pattern recognition, the more one is likely to have moments of inspiration because it is sharp observation skills that is the mother of inspiration. With such a process, one is merely traveling on the same path of knowledge forever. I guess one can rely on the inspiration of others — Rich

It makes sense to me to say that objects that are defined to be infinite in scope are impossible to be described in entirety. It makes sense because it is true by definition. You defined the object under your scrutiny to be infinite in size, so it's impossible to fully exhaust it. If you define a human body to be infinite in complexity, you cannot hope to describe it completely. No matter how much of it you include in your description, there is always something about it you have yet to describe. Though you cannot describe such phenomena in entirely, you can nonetheless describe it in part. Your descriptions can be more or less exhaustive. The same thing about intuition. Regardless of whether you define it to be finite or infinite in complexity, you can always describe it to a higher or lower degree.

What I am trying to understand is why do you think that intuition is impossible to describe. I can describe my intuition no problem. All I have to do is make an effort to do so. Again, intuition is merely defined as a process of decision making that is outside of our awareness.

Again, intuition is merely defined as a process of decision making that is outside of our awareness. — Magnus Anderson

My intuition moments just happen. Something may trigger the moment of epiphany. Something some someone says. Maybe a passing scene. Maybe a dream. It just happens for unknown reasons. It springs out and things all of a sudden makes sense. I've had situations where everything didn't make sense and all of a sudden the mist clears and every piece of the puzzle becomes clear. That moment of inspiration is write undefinable for me. It is as did the deeper soul is speaking.

I think I will take your advice and look at the literature since I am rather new to all this. However, if you can elaborate some of the conceptual issues with regard to determinism that might be helpful. — Perplexed

I am myself in a (leisurely) process of reading up on such issues, although at the moment I am more focused on causation.

SEP provides an overview of the topic in Causal Determinism.

An accessible introduction to determinism (or lack thereof) in physics can be found in the works of John Earman (he has written a number of articles, as well as a book). Here is his article in a book Freedom and Determinism (Topics in Contemporary Philosophy):

One might have hoped that this survey would provide an answer to the question: If we believe modern physics, is the world deterministic or not? But there is no simple and clean answer. The theories of modern physics paint many different and seemingly incommensurable pictures of the world; not only is there no unified theory of physics, there is not even agreement on the best route to getting one. And even within a particular theory— say, QM or GTR—there is no clear verdict. This is a reflection of the fact that determinism is bound up with some of the most important unresolved foundations problems for these theories. While this linkage makes for frustration if one is in search of a quick and neat answer to the above question, it also makes determinism an exciting topic for the philosophy of science. — Determinism: What We Have Learned and What We Still Don’t Know

Determinism is bound up with other topics. Philosophers find issues with the concept of the laws of nature. Reductionism is also a very controversial issue. The failure of either of these concepts threatens the very cogency of the question "Is the universe deterministic?"

I'm not familiar with Goodman's grue scenario. In any case I was referring to the past, not the future. I don't see why, if it is based on an understanding of evolution, it would not rely on the assumption that the invariances of nature were in the past as they are today. And that assumption is as much irrationally inductive as the assumption that the invariances of nature will be in the future as they appear to be today. — Janus

The theory of evolution, like any theory, is based on what we already know. Induction is a way of inferring what we don't know, whether it occurs in the past or in the future. Having evolved in a regular environment (regular enough for practical purposes), we are conditioned to trust in induction, because those who in the past could best exploit those regularities had a fitness advantage. But all that was in the (known) past. Our shared inductive instincts owe everything to the past and nothing to the future, which is why it is not right to appeal to those instincts for validating inferences of future observations.

By the way, to return to the topic of the thread, one can read Hume as mounting a similar argument, only he believed that our causal and inductive beliefs are shaped by observing "constant conjunctions" of similar events. Hume's psychological explanations may be too simplistic for our age, but the idea here is basically the same: induction's seeming self-evidence is not enough to justify it when you consider why it seems to be self-evident.

I can't see any point of disagreement here; other than the pedantic one concerning the idea of the sun rising. — Janus

Sometimes posts are designed to agree.
Surely it does not always have to be confrontational.
Since we are discussing induction it is worth pointing out that the common sense perception that the sun rises was thought to be true for thousands of years, yet clever application of skepticism and induction has given us the heliocentric hypothesis.
So far from being flawed, it is worth pointing out the value of the scientific method.

↪charleton I image that that laws are not fully deterministic or else that they apply over a limited scope. Is it even logically possible for full determinism to produce more than one outcome? — Perplexed

Perplexed by name; perplexed by nature. Seems you want to keep your deterministic cake but want to eat the free will topping too.
Who or what decides when determinism leaves the room?

induction's seeming self-evidence is not enough to justify it when you consider why it seems to be self-evident. — SophistiCat

The problem is that everything is constantly changing. Induction is only approximated. There is no evidence of the unchanging nature of the universe and there is plenty of evidence to the contrary. Determinists are determined but have no evidence to support its preferences. And Hume was quite on target with his analysis of the psychological effect on induction. There are not only biases galore in all human activity, but in addition fundamental to quantum theory is the notion that the observer cannot be divorced from the measurement of the system.

As I have written elsewhere, the mathematics of General Relativity does not support either of these notions:

1) the Earth moves around the sun or

2) the ontology of space-time.

Any such stance is purely metaphysical in nature and an unwarranted one at that.

https://www.physicsforums.com/threads/general-relativity-the-sun-revolves-around-the-earth.245334/page-2

"Cleonis, you seem to also be confused on the purpose of the theory. Is Heliocentric system more convenient, and therefore, more useful? Absolutely. Does it give you any predictions you could not acquire in Geocentric system? Absolutely not. And when I map coordinates on Earth, is it more convenient to keep inertial frame of reference, or one that is fixed to rotating Earth. The later, of course. But does that mean that the Earth suddenly stopped rotating? No. Convenience of one model over the other does not imply any sort of physical truth. It's just that, a convenience. In order for one thing to be true and for another to be false, the two models must provide disagreement in predictions. Are there any disagreements in predictions? No. Then it is no more wrong to say that Earth is the center of the universe around which all else rotates, than it is to say that Earth rotates around the Sun.

https://www.physicsforums.com/threads/general-relativity-the-sun-revolves-around-the-earth.245334/page-3

"The purpose of GR, as you put it, is to consolidate SR with newtonian gravitation, from what I've read. It's achievement is being a good physical theory with accurate predictions. In newtonian gravitation, you have mass acting on mass. I can't recall ever reading or hearing that there is any significant mass-space coupling in newtonian gravitation. You seem to be discussing the philosophy of GR rather than its physics. Whether you choose to beleive that there exists a curved 4-D entity called spacetime which couples to matter, or whether you believe spacetime is a convenient mathematical tool for GR is completely up to the individual phycisist."

There are scientists who are completely reworking the theory of gravity based upon the notion of quantum entanglement and a holographic universe which will yield a mathematics that will be in approximate concordance with GR but with a completely new way of viewing gravity. One such scientist, Erik Verlinde, spoke at a symposium where he stated that he began looking at this new approach because he wasn't at all philosophical comfortable with the Big Bang Theory of the universe.

Here's an inductive argument:

1. Some Ps are Qs
2. Therefore, all Ps are Qs

The conclusion necessarily follows from the premise. — Magnus Anderson

I don't know of any logic where this would be the case. Induction is, generally speaking, plausible reasoning. So normally you would conclude that any P is probably Q, with the strength of this inference depending on how many Ps have been observed and perhaps other considerations.

By deductive reasoning we usually understand the application of something like Aristotelian or Classical logic. The rules of inference are fixed; even when we reason informally, if the reasoning is deductive, it can be straightforwardly translated into a formal logic without the loss of accuracy.

Strictly speaking, there is no such thing as the inductive logic. There is informal plausible reasoning, which can only be loosely approximated by some of the formal statistics, such as Bayesian inference.