Air is beneficial to folks, but the polluted air also kills folks. So they have the contradictory cases, which makes them unfit for qualifying as acceptable premises which prove the PSR true. — Corvus

I could generalise.

If the PSR was not valid, one day, everything that had been beneficial to life could now be lethal to life, and vice versa.

Could life survive in such a world?

There is a reason for it happening, whether we know it happened or not. — Fooloso4

Philosophically, how is it possible to know something about something we don't know about?

In this particular case, that the something we don't know about has a reason.

Therefore the premises of the reasoning is incorrect or irrelevant, which proves the PSR is not sound. — Corvus

The PSR states that for every fact there is a reason.

If the PSR was not valid, and for every fact there was no reason, then there would be no reason why facts didn't change.

Suppose one day water was beneficial to life and the next day it was lethal, one day air was beneficial to life and the next day it was lethal, one day potatoes were beneficial to life and the next day they were lethal, etc.

Are you saying that life would be able to survive in such a world?

If the PSR is valid it should hold for all events whether known or unknown. — Fooloso4

The expression "all events whether known or unknown" is a contradiction in terms. It is not possible to know that there are unknown events as they are unknown. All that is known are known events.
===============================================================================

If PSR is restricted to what we know or observe then the reason for the star exploding is contingent upon our knowledge of it happening. — Fooloso4

The PSR is a contingent theory in the sense that it states that for every fact there must be an explanation. It doesn't state that every fact is a brute fact.

The PSR is a necessary theory in the sense that for every fact there must be an explanation.

As we don't know what we don't know, the PSR is contingent on what we know.

As regards what we know, the PSR is necessary.

What is the explanation for "for every fact there is an explanation"? — Corvus

Not everyone accepts the PSR, for example Hume. He challenged the PSR and argued that the ideas of cause and effect are distinct, and that we can conceive of an effect without a cause.

But suppose that for every fact there was no explanation. Then equally there would be no explanation why a fact couldn't change. For example, one day it could be a fact that "food is beneficial to humans" and the next day it could be the fact that "food is lethal to humans".

If the PSR was not valid, humans couldn't survive. But humans have survived, Therefore the PSR must be valid.

This sounds like a contradiction. Surely PSR doesn't allow contradictions for the conclusions. — Corvus

PSR - for every fact there is an explanation
Fact = light bends around sources with high mass
Explanation = gravity
There is no contradiction in the explanation.
===============================================================================

These are just repeating the same thing the first part of the sentence using because — Corvus

Yes. "Gravity" is an explanation, but what does it explain?
===============================================================================

Gravity is a scientific concept which must apply to every cases in the universe if it is true. — Corvus

Why does a scientific concept have to be true everywhere?

On Earth the acceleration due to gravity is $9.81\frac{m}{s^2}$ whilst on the Moon it is $1.62\frac{m}{s^2}$

But the light bends around sources with high mass due to gravity. — Corvus

On the one hand "light bends around sources with high mass due to gravity" and on the other hand "gravity causes light to bend around sources with high mass".

In the same way that "the reason he is ambitious is because he is driven" and "the reason the job was complex was because it was complicated."

"Gravity" is more a synonym than a reason why light bends around sources with high mass.

When the light is released into the space, why doesn't it fall to the ground? — Corvus

In a sense it does, as light bends around sources with high mass due to gravity.

From www.astronomy.com

While it is true that photons have no mass, it is also true that we see light bend around sources with high mass due to gravity.

Suppose a star explodes 10 light years from us. It will not be observable to us for 10 years. If the PSR only applies to observable,facts does that mean that with regard to that event the PSR is not valid and will not be valid for 10 years? — Fooloso4

The PSR states that for every event there is a reason

The PSR is valid within certain restrictions.

Prior to the light from the exploding star reaching us, we don't know that there is an exploding star. It is an unknown.

I can certainly imagine a star exploding, but the PSR doesn't apply to the imagination because I can imagine all kinds of impossible things. I can imagine a star exploding for no reason as I can imagine unicorns grazing in Central Park.

Therefore the PSR cannot apply to imagined events.

But what about events that we don't know about. Can I apply the PSR to something unknown. Does every unknown thing have a reason? I can never know because the unknown thing is unknown, and I don't know what to apply the PSR to.

Therefore the PSR cannot be applied to the unknown.

The PSR can be reformulated as "for every observed event there is a reason"

The reason we observed the rock falling is that it fell and we were there to see if fall. There may be various reasons why it fell and various reasons why we were there to see it fall. It does not follow from the fact that we can posit reasons for why we observed the rock fall, that there is a reason for everything. — Fooloso4

True, there are different events.

Let the PSR be that for each event there must be a reason

Situation One - The rock falls, and I see it. There is event A such that I see the rock falling and there is event B such that the rock falls.
Situation Two - The rock falls, but there is no one to see it. There is event C that the rock falls.

Event C
However, as there is no one to observe event C, event C is unknown. As event C is unknown, there can be no discussion as to whether it has a reason or not. Whether unknown event C has a reason or not we can never know, meaning that the PSR for unknown events is unknowable.

Therefore, the PSR is only applicable to observable events.

Event A
The PSR states that there must be a reason why I observe the rock falling.
Assume the PSR is not valid, such that there is no reason why I observe the rock falling.
Then, if I observe a rock falling there would be no reason why I hadn't observed the rock not falling.
But if I had observed the rock not falling, there is no reason why I hadn't observed the rock falling.
But if I had observed the rock falling, there is no reason why I hadn't observed the rock not falling.
If the PSR was not valid, this would lead into an infinite regress.
Therefore, the PSR is valid, ie, there must be a reason why I observe the rock falling.

Event B
The PSR states that there must be a reason why the rock I observe falls.
Assume the PSR is not valid, such that there is no reason why the rock I observe falls.
Then, if the rock I observe falls, then there would be no reason why the rock I observe didn't fall
But if the rock I observe didn't fall, there is no reason why the rock I observe hadn't fallen.
But if I the rock I observe hadn't fallen, there is no reason why the rock I observe didn't fall.
If the PSR was not valid, this would lead into an infinite regress.
Therefore, the PSR is valid, ie, there must be a reason why the rock I observe falls.

In conclusion, the PSR is valid, but only applies to observable facts, events and truths.

Note that "reason" may include a prior explanation, such as "I order a pizza because I was hungry", or contemporaneous ground such as "I order a pizza being hungry".

You did not address the problem. Observing that a rock falls is not a reason for why the rock falls. — Fooloso4

Assume the PSR is not valid

Then, if we observe a rock falling there would be no reason why we hadn't observed the rock not falling.

But if we had observed the rock not falling, there is no reason why we hadn't observed the rock falling.

But if we had observed the rock falling, there is no reason why we hadn't observed the rock not falling.

If the PSR was not valid, this would lead into an infinite regress.

Therefore, the PSR is valid.

What does this mean in terms of PSR? The observation that a rock falls is not a reason for or explanation for it falling. If explanation reaches a dead end then either we have failed to find the reason or there is no reason. — Fooloso4

Using Emilie du Chatelet's argument (SEP - PSR):

P1 - The PSR in the OP states that for any thing that exists or is true, there is a sufficient reason for it to exist or to be true.

P2 - Consider bread. If there was no reason why bread was beneficial to life, there would also be no reason why bread wasn't lethal to life. One day bread could be beneficial and the next day bread could be lethal.

C1 - If the PSR was not valid, humans would be unable to survive in the world.

C2 - As humans do survive in the world, then the PSR must be valid.

But gravity means more than that. — Fooloso4

True, but if a rock never fell to the ground when released, no one would ever have known about gravity.

General relativity remains the framework for the understanding of gravity. The Einstein field equations form the basis of general relativity. The Einstein field equation are based on the cosmological constant. The cosmological constant represents the energy density of space. Nobody really knows what the cosmological constant is exactly, but it is required in cosmological equations in order to reconcile theory with our observations of the universe. (Wikipedia-gravity)

Sooner or later explanations reach a dead end, and we just have to accept our observation that gravity causes a rock to fall to the ground when released, where gravity is something that causes a rock to fall to the ground when released.

This is a false dilemma: either everything has a reason or nothing has a reason. Deniers of the PSR do not claim that nothing has a reason; only that not everything has a reason. Most people accept the laws of logic, and accept logical inferences as valid reasons. But they might still also believe that some brute facts exist without reason. — A Christian Philosophy

1) Some people believe that for any thing that exists or is true, there is always a sufficient reason for it to exist or to be true. These people support the PSR.

2) Some people believe that some things that exist or is true have a sufficient reason for it to exist or to be true, and that some things that exist or is true there is no sufficient reason for it to exist or to be true. These people are ambiguous towards the PSR.

3) Some people believe that for any thing that exists or is true, there is never a sufficient reason for it to exist or to be true. These people deny the PSR.

If 3) is true, and there is no sufficient reason why a lamp turns on, and there is no sufficient reason why a lamp turns off, then there is no sufficient reason for the lamp not turning on and off contemporaneously, other than the Law of Non-Contradiction.

Are you claiming that there are reasons that do not involve explanations? — Fooloso4

Suppose someone said that the reason a rock falls to the ground when released is because of gravity. Is "gravity" an explanation as to why the rock falls to the ground when released when "gravity" means no more than a rock falls to the ground when released.

Similarly:
The reason he is ambitious is because he is driven
The reason it is chilly this evening is because it is cool.
The reason the job was complex was because it was complicated.
The reason she is an advocate for three-yearly driving tests is because that is something she supports.
The reason the tree is in a state of decay is because it is rotten.

From the OP — Fooloso4

What are you saying?

In accord with the OP it means that there is an explanation. Did you mean 'petitio principii', begging the question? — Fooloso4

The OP describes the PSR as "For any thing that exists or is true, there is a sufficient reason for it to exist or to be true."

There are different definitions of "reason"

The Merriam Webster gives one definition of reason as "a statement offered in explanation or justification" and another definition of reason as "a rational ground or motive".

Using the SEP article on PSR:

As regards "reason", i) Archimedes attributed the fact that equal weights at equal distance remain in equilibrium because there is no reason why either side of the balance should move up or down and ii) Leibniz wrote: “This is rightly observed, and agrees with what I am accustomed to saying that nothing exists but that for whose existence a sufficient reason can be provided”.

As regards "ground", i) Hegel argued for the Principle of Sufficient Ground, and ii) Dasgupta proposed that the PSR can be reformulated in terms of grounds.

There are different type of PSR.

In the Unrestricted PSR, every fact requires an explanation.

In the Restricted PSR, various restrictions can be placed on the PSR, such as i) requiring a sufficient reason for every true proposition or ii) requiring a reason only for the existence or non-existence of entities.

Example One
Why does a rock fall to the ground when released. The reason is gravity. What is gravity. Gravity is something that causes a rock fall to the ground when released. An example of petito principii.

Example Two
A stone hits a window and the glass shatters. As I see it:

As regards cause, a cause is something in the world that is prior to an event, such that the cause of the glass shattering was a stone hitting the glass.

As regards reason, a reason is something in language that describes an event in the world, such that the reason the glass shattered was that it was hit by a stone

As regards ground, which is not cause, ground is contemporaneous with the event, in that there is an event with constituent parts. For example, glass of a certain thickness and a stone of a certain kinetic energy. According to Dasgupta, this avoids the Agrippan Trilemma of circularity, infinite regress and dogmatism because the event is autonomous and independent of anything prior to the event.

Example Three
4 = 2 + 2.

As 4 is contemporaneous with 2 + 2, the 4 was not caused by the 2 + 2, no more than the 2 + 2 was caused by 4.

The reason 2 + 2 = 4 is linguistic, as numbers don't exist in the world.

4 is grounded in 2 + 2, which is neither cause nor reason, because autonomous and independent of anything prior.

And (C1) - our inability to conceive how something can come from nothing marks a limit of our thinking, but should we assume that our limits are the measure of reality or possibility? — Fooloso4

Yes, it would be unrealistic to assume that our limits are the measure of reality.

As a cat may never understand the symbolism within The Old Man and The Sea, humans may never understand the nature of reality. But then again, as a cat doesn't need to understand the symbolism within The Old Man and The Sea, humans don't necessarily need to understand the nature of reality.

I may believe that everything has a reason, even though I have no concept of what these reasons are. For example, I believe that a stone when released falls to the ground for a reason, even though I have little concept of the nature of gravity.

It depends on the meaning of "reason" (Using SEP - Principle of Sufficient Reason)

Does "reason" mean 1) "an explanation of why a stone falls to the ground when released", an Unrestricted PSR and a rejection of brute or unexplainable facts.

Or does "reason" mean 2) that "when released a stone falls to the ground" in the sense of Petito Principii, doing no more than duplicating the fact.

It is more likely the case that "reason" is being used in sense 2, where "gravity" means no more than "when released a stone falls to the ground".

There are several conclusions that might follow from not being able to answer a question. They include the possibility that: C1 - Reason and our capacity to understand is limited. C2 - The question itself is the problem. C3 - Any conclusion that follows is questionable. — Fooloso4

All those things are true:
C1 - I could try to explain Hemingway's novel The old man and the sea to my pet cat until "the cows come home" without any glimmer of understanding on the cat's part. In the same way, a super-knowledgeable alien could try to explain the nature of the universe to a human, also without any glimmer of understanding on the humans' part
C2 - As Dr Lanning's Hologram in the film I, Robot says "I'm sorry, my responses are limited. You must ask the right questions"
C3 - As with a dictionary definition, even if a question is answered, the answer in its turn may be questioned, ad infinitum.

However
C1 - The fact that my cat cannot understand The Old Man and the Sea does not mean that the book isn't understandable
C2 - The fact that a question is the wrong question doesn't mean that there isn't a right question
C3 - The fact that every answer can be questioned doesn't mean that there isn't an answer.

I still hold that the relevant propositions must have "at the same time" added to them — A Christian Philosophy

It could be that the phrase "at the same time" is crucial to the argument defending the Principle of Sufficient Reason.

Parmenides pointed out that if the world had come into existence from nothing, there is no answer to the question as to why the world didn't come into existence earlier or later than it did. From this he concluded that the world has always existed (Edit - From this he concluded that the world did not come from nothing) (SEP - Principle of Sufficient Reason)

P1 - Let event 1 be a lamp on the table turning on and event 2 be the same lamp turning off.
P2 - The Law of Non-Contradiction states that the lamp cannot turn on and off "at the same time"
P3 - Assume that the Principle of Sufficient Reason is not valid, and the lamp turns on and off for no reason.

C1 - If there is no reason why the lamp turns on, then there is no reason why the lamp turns on earlier or later than the lamp turning off.
C2 - However, if there is no reason why the lamp turns on, then there is no reason why the lamp cannot turn on "at the same time " as the lamp turning off, other than the Law of Non-Contradiction.
C3 - Therefore, it cannot be the case that the Principle of Sufficient Reason is not valid, as there is a reason limiting when the lamp turns on and off, and that reason is the Law of Non-Contradiction.

By the Law of Non-Contradiction, a fact/event cannot be other than it is at the same time.
Suppose true randomness exists such that event 1 occurs without reason. Still, by the law of non-contradiction, event 1 cannot be something else at the same time. But it still occurred without reason. — A Christian Philosophy

I agree that by the Law of Contradiction, a fact/event cannot be other than it is at the same time. For a fact to be other than it is at the same time is a contradiction in terms. For example, the fact that apple A is on the table is a different fact to the fact that apple A is on the floor.

P1 - Let there be an event which could be either event 1 or event 2, where event 1 and event 2 are different.
P2 - The Principle of Sufficient Reason states that if event 1 occurs there must be a reason.
P3 - By the Law of Non-Contradiction, if event 1 occurs then event 2 could not have occurred.
P4- Suppose event 1 occurs without reason.

C1 - From P4, if event 1 occurs then event 2 could have occurred.
C2 - C1 and P3 are contradictory.
C3 - Therefore, if the Law of Non-Contradiction is valid (P3), then events occurring without reason is invalid (P4).

Thus, while the uniformity of nature is not known with certainty, it is still known beyond reasonable doubt. — A Christian Philosophy

From the SEP article Principle of Sufficient Reason: the PSR may be formulated as "For every fact F, there must be a sufficient reason why F is the case."

I agree that although the uniformity of nature is not known with certainty, it is still known beyond reasonable doubt.

Does this mean that the PSR should be re-formulated as "For every fact F, there is probably a sufficient reason why F is the case."
===============================================================================

one can imagine an event without a cause...............This is expected because the test of imagination is associated with logic, and the PSR (which includes causality) is not derived from logic. — A Christian Philosophy

In other words:
P1 - We can imagine a fact/event
P2 - The test of imagination is associated with logic
P3 - The PSR states that given a fact/event there must be a reason/cause
P4 - The PSR is not derived from logic
C1 - We can imagine a fact/event that doesn't have a reason/cause

In particular:
P1 - We can imagine a unicorn
P2 - We can test that the unicorn we imagine is true or not using logic.

P1 - I imagine a unicorn in my mind
P2 - I have never seen a unicorn in the world
C1 - Therefore, it is possible that unicorns only exist in my mind
C2 - Therefore, it is possible that unicorns may or may not exist in the world.

P3 - True
P4 - Depends what is meant by "derived"
In logic, conclusions follow from premises based on the structure of arguments alone, independent of their topic and content. (Wikipedia - Logic).
An attempt may be made to prove the PSR using logic

P1 - If there can be a fact/event without a reason/cause, then the fact/event could have been other than it is.
P2 - By the Law of Non-Contradiction, a fact/event cannot be other than it is
C1 - Therefore, a fact/event must have a reason/cause

The PSR may possibly be proved using logic, even though there is no logical necessity that a fact/event has a reason/cause.
C1 - We can imagine a unicorn in our mind even if unicorns don't exist in the world.

We can imagine a unicorn in our mind even though there is no unicorn in the world. Does this mean that there is nothing that has caused us to imagine a unicorn in our mind?

For any thing that exists or is true, there is a sufficient reason for it to exist or to be true.............................We observe that our reasoning works in 2 ways: deduction and induction — A Christian Philosophy

The Principle of Sufficient Reason (PSR) proposes that for every fact F, there must be a sufficient reason why F is the case (SEP - Principle of Sufficient Reason)

We use deduction and induction when reasoning.

Hume's critique of causation challenges PSR. In his Treatise of Human Nature, Hume considers the idea that whatever begins to exist must have a cause, but he finds this open to doubt. Since cause and effect are distinct, one can imagine an event without a cause. Hume said that induction gives truth only if nature is uniform, and if we do use induction, we are presupposing the uniformity of nature, which may or may not be the case (SEP - Principle of Sufficient Reason).

However, this introduces an inevitable circularity as induction and deduction presuppose a uniformity in nature, which may or may not be the case. Therefore any reason we come up with for a fact based on induction and deduction may or may not be the case.

It follows that given a fact, as we can never know whether any particular reason is or is not the case, we can never know whether for any fact there is a reason or not.

We could only say that for every fact there must be a sufficient reason why F is the case if we knew that nature was uniform. But we don't know that nature is uniform. We know that many aspects of nature are contingently uniform, but we don't know that they are necessarily uniform.

Counter-Argument against the PSR: Quantum Physics — A Christian Philosophy

In addition, something that nobody understands cannot properly be used as a counter-argument against anything.

As Feynman said "I think I can safely say that nobody understands quantum mechanics"

You pour out your soul here and you're met with blank stares — Dominic Osborn

Welcome to the Forum !!!

While a functioning brain is undeniably necessary for reasoning, it doesn't follow that reasoning is reducible to or explainable as neurophysiological processes — Wayfarer

Useful post.

But think of the brain as a computer.



There needs be no vicious regress between reason and neurology if reason is the purpose of the neurology. In the same way, there is no vicious regress between the truth that 1+1=2 and a logic gate that calculates the sum of 1+1 if the purpose of the logic gate is to calculate the sum of 1+1.

The brain is required for reason, as the logic gate is required for the truth of its calculations.

The computer is indifferent to the truth of its calculations, yet the purpose of the computer is to arrive at the truth.

The logic gates have an intentionality, which is to arrive at one consistent output when given two inputs

Edward Feyser wrote that brain processes are devoid of meaning, yet our thoughts have meaning , concluding that thoughts cannot be identified with brain processes. Yet his argument is circular, in that he starts by assuming that the brain is separate to meaning and concludes that the brain is separate to meaning. As the meaning of a logic gate is the process it undertakes, the meaning of a neurological process is the very process itself.

Thomas Nagel wrote that one can only understand reason from within reason, meaning that one cannot understand reason from outside reason, ie from neurology. Yet again his argument is circular, in that he starts by assuming that one can only understand reason from within reason and concludes that one cannot understand reason from outside reason, ie neurology. As the reason for a logic gate is the process it undertakes, the reason for a neurological process is the very process itself.

As the logic gate is necessary for logic, logic is a product of the logic gate. Similarly, as the brain is necessary for reason, reason is the product of the brain.

(Leaving whether transcendental or not for another day)

3. Thus, according to Berkeley, a mind had to exist before or come to existence simultaneously with ideas. — Brenner T

It depends on the relationships between mind, perceiving, sensing, ideas and thoughts.

For example, for Berkeley, what exactly is the relationship between mind and ideas.

Is it the case that the mind has ideas or is it the case that the mind is ideas. For example, is it the case that an object has extension in space or is it the case that an object is an extension in space.

As an object having no extension in space would be a contradiction in terms, for a mind not to have ideas would perhaps also be a contradiction in terms.

Does the mind have intentionality about ideas, or is the mind intentionality of ideas?

In philosophy, intentionality is the power of minds and mental states to be about, to represent, or to stand for, things, properties and states of affairs. To say of an individual’s mental states that they have intentionality is to say that they are mental representations or that they have contents. (SEP - Intentionality)

For Berkeley, what is the relation between the mind and ideas.

It does not follow from the fact all sciences of reason contain synthetic a priori judgements as principles, that instances of particular relations of particular conceptions, are all principles in themselves................................If you wish to stipulate that Kant’s synthetic a priori is the principle that….that’s fine, but I doubt it’s what Kant intended for it. — Mww

Kant writes that the term "principle" is ambiguous.

B356 The term "a principle" is ambiguous, and commonly signifies only a cognition that can be used as a principle even if in itself and as to its own origin it is not a principle.

Kant writes that on the one hand there are "principles absolutely" as used in the a priori concepts of the Categories, and on the other hand there are "principles comparatively" as used in the theoretical sciences.

B358 Thus the understanding cannot yield synthetic cognitions from concepts at all, and it is properly these that I call principles absolutely; nevertheless, all universal propositions in general can be called principles comparatively.

Paul Guyer and Allen Wood in the Introduction to the CPR talk about "synthetic a priori principles", presumably as "principles comparatively".

page 13 - At this point in the Critique Kant has completed the largest part of his constructive project, showing how synthetic a priori principles of theoretical cognition are the necessary conditions of the application of the categories to sensible data structured by the pure forms of intuition.

page 85 - Synthetic a priori judgments are contained as principles' in all theoretical sciences of reason.

I agree that the Categories are "principles absolutely"

I could change the wording of my belief to "Kant's synthetic a priori is the universal principle that we can discover a priori necessity from a posteriori contingency".

Synthetic a priori is not itself a principle; it is the condition of principles, unities, conceptions and anything else to which it applies, in which representations relate to each other in a certain manner, re: synthetically, and, representations are of a certain origin, re: a priori................If you want to say certain forms of representations adhere to the synthetic a priori principle, you haven’t in the least said anything about those forms, other than give them a name, without anything about what it means to be so. — Mww

The relation between thought (a priori) and being (synthetic)

Paul Guyer and Allen Wood in the Introduction to CPR explicitly say that synthetic a priori principles can be established, meaning that there can exist synthetic a priori principles.

The "Transcendental Analytic" has prepared the way for this critique of traditional metaphysics and its foundations by its argument that synthetic a priori principles can be established only within the limited domain of sensible experience.

Yes, "synthetic a priori" is the name of a principle, not a description, in the same way that "the conservation of energy" and "the conservation of momentum" are names of principles.

Kant's "synthetic a priori" is the name of a principle that relates the synthetic to the a priori.

My original point is that B276 can be read as a transcendental argument, not in the sense of transcendental used by Kant in CPR A2, but in the sense as used by the Britannica.

CPR A2: "I call all cognition transcendental that is occupied not so much with objects but rather with our a priori concepts of objects in general. A system of such concepts would be called transcendental philosophy."
Britannica transcendental argument: "a form of argument that is supposed to proceed from a fact to the necessary conditions of its possibility."

In B276, The Refutation of Idealism, are the two statements which come under the Britannica definition of transcendental rather than the A2 definition.
1) The mere, but empirically determined, consciousness of my own existence proves the existence of objects in space outside me.
2) Consequently, the determination of my existence in time is possible only by means of the existence of actual things that I perceive outside myself.

This is why I originally proposed that “Kant's synthetic a priori is the principle that we can discover a priori necessity from a posteriori contingency".

Since then we have been discussing my expression "Kant's synthetic a priori is the principle that....."

You have been making the case that "synthetic a priori isn’t a principle", whilst I have been making the case that ""Kant's synthetic a priori is the principle that....."

This needs to be resolved before continuing with the remainder of my statement that "we can discover a priori necessity from a posteriori contingency".

.synthetic a priori isn’t a principle, it’s a relation of the content of certain kinds of conceptions to each other — Mww

You said synthetic a priori is a principle; Kant says synthetic a priori judgements are principles. — Mww

Kant writes about synthetic a priori unity (B264), synthetic a priori concepts (A220), synthetic a priori about appearances (B217), synthetic a priori cognitions (B19) and synthetic a priori judgements (B19).

Paul Guyer and Allen Wood in the Introduction talk about synthetic a priori principles.

The "Transcendental Analytic" has prepared the way for this critique of traditional metaphysics and its foundations by its argument that synthetic a priori principles can be established only within the limited domain of sensible experience.

At this point in the Critique Kant has completed the largest part of his constructive project, showing how synthetic a priori principles of theoretical cognition are the necessary conditions of the application of the categories to sensible data structured by the pure forms of intuition.

Of course the synthetic a priori is a principle.

synthetic a priori isn’t a principle, it’s a relation of the content of certain kinds of conceptions to each other; — Mww

Just taking your first point.

Kant writes in CPR B14 section V that a synthetic a priori judgement is a principle of reason.

"Synthetic a priori judgments are contained as principles in all theoretical sciences of reason."

The Merriam Webster Dictionary includes "a comprehensive and fundamental law, doctrine, or assumption" as part of its definition of "principle".

It is true that "synthetic a priori judgements" relate the synthetic with the a priori, but it is also true that a synthetic a priori judgement is a principle that may be used, for example in mathematics (B14)

Kant's synthetic a priori is the principle that relates the synthetic to the a priori.

Kant also refers to other principles, such as the principle of contradiction (B14), principle that all things as appearances are in time (B52), principle of the ideality of our sensible intuitions (B70), principle of the unity of manifold of representations (A117), principle of the unity of apperception (A112), etc.

Over the course of seven days, you’ve included B276 in every single one of seven consecutive responses to my posts to you, but never say any more than the text itself. — Mww

Apart from my ongoing justification, based on the text, that "Kant's synthetic a priori is the principle that we can discover a priori necessity from a posteriori contingency".

One must not overlook the significance embedded in propositions such as, consciousness of determinations of existence in time. — Mww

Kant starts his proof in CPR B276 with "I am conscious of my existence as determined in time", and continues with his proof that "The mere, but empirically determined, consciousness of my own existence proves the existence of objects in space outside me."

I agree with the significance of the passage of time as central to Kant's refutation of Problematic and Dogmatic Idealism.

While that is the case, it is merely beside the point. It needs be shown why external objects as considered by the established idealisms of the day were conceived without proper regard for what came to be posited as transcendental conditions, the foremost being, of course, time. — Mww

In what way is Kant's proof in CPR B276 besides the point, ie "The mere, but empirically determined, consciousness of my own existence proves the existence of objects in space outside me".

Berkeley's Dogmatic Idealism declares that space and all the things in it are impossible and things in space are imaginary (CPR B275)

Kant wanted to show that his idealism is a formal idealism rather than Berkeley's subjective realism, and therefore included in the second edition his Refutation of Idealism (Introduction to CPR).

In the Refutation of Idealism (CPR B276), Kant attempts to prove not only the existence of things outside me, but also that our inner experience of these things outside me is immediate, and we are only conscious of our own existence in time because of the existence of things outside me.

In Practice, it would be difficult fr Berkeleyan Idealism to prove the non-existence of things outside me.

Kant isn’t proving the existence of things as much as he’s proving the material idealist’s denial or doubt of things, is improperly justified. — Mww

In B276, Kant starts with the theorem: "The mere, but empirically determined, consciousness of my own existence proves the existence of objects in space outside me."

He then follows this by his proof: "Therefore it is also necessarily combined with the existence of the things outside me, as the condition of time-determination; i.e., the consciousness of my own existence is at the same time an immediate consciousness of the existence of other things outside me."

In B276, Kant seems to be proving that objects in space and time exist independently of our experience of them, regardless of any belief of the Transcendental Idealist.

But naturalism then presumes that the mind which knows it, is the product of that process it only knows metaphorically. — Wayfarer

That's my question. Are scientific explanations literally true or metaphorically true? Is F = ma literal or metaphorical?

According to Britannica articles:
" naturalism, in philosophy, a theory that relates scientific method to philosophy by affirming that all beings and events in the universe (whatever their inherent character may be) are natural."

"scientific method, mathematical and experimental technique employed in the sciences. More specifically, it is the technique used in the construction and testing of a scientific hypothesis."

"scientific hypothesis, an idea that proposes a tentative explanation about a phenomenon or a narrow set of phenomena observed in the natural world."

Certainly we can imagine the early universe, devoid of organic life, but that imagined universe still contains a perspective and a sense of scale provided by the observing mind. — Wayfarer

It depends on the viewpoint.

We can imagine a sense of scale in an early universe devoid of life from our viewpoint, but we can't imagine a sense of scale in an early universe devoid of life from the viewpoint of an early universe devoid of life.
===============================================================================

Nothing will ever lead me to understand what a nebula, which could not be seen by anyone, might be. Maurice Merleau-Ponty — Wayfarer

It's a question of logic.

Something can be only be named if an observer knows what that something is.

If there is no observer to know what a something is, then it cannot be named.

Therefore, for something to be named "nebula" when there is no one to know what that something is is a logical contradiction.
===============================================================================

We cannot step outside the life-world, because we carry it with us wherever we go. — The Blind Spot - Adam Frank, Marcelo Gleiser, Evan Thompson

The Direct Realist would disagree. I would estimate that 50% of those on the PF believe in Direct Realism.

For the Direct Realist, the world they see around them is the real world itself. Things in the world are perceived immediately or directly rather than inferred on the basis of perceptual evidence.

If a Direct Realist sees an apple on a table, for the Direct Realist, the apple and table exist in the world exactly as they perceive it independently of being perceived.

The Direct Realist does believe that they can step outside the life-world.
===============================================================================

Whereas, I think you're taking what you understand as the scientific picture of the world as being real independently of any observer, attributing with a kind of absolute or taken-for-granted reality. But then you can't see where 'mind' fits in, because that picture is purportedly 'mind-independent'! — Wayfarer

As an Indirect Realist, I agree that I cannot know the early universe independently of my mind, as I can only know the early universe using my mind.

I cannot literally know the early universe, but I can metaphorically know it.

The book Metaphors We Live By 1980 by George Lakoff and Mark Johnson suggests that metaphor is a tool that enables people to use what they know about their direct physical and social experiences to understand more abstract things like work, time, mental activity and feelings.

It can be argued that language, including the language of science, is more metaphorical rather than literal.

Metaphors are commonly used in science, such as: evolution by natural selection, F = ma, the wave theory of light, DNA is the code of life, the genome is the book of life, gravity, dendritic branches, Maxwell's Demon, Schrödinger’s cat, Einstein’s twins, greenhouse gas, the battle against cancer, faith in a hypothesis, the miracle of consciousness, the gift of understanding, the laws of physics, the language of mathematics, deserving an effective mathematics, etc.

For example, Andrew May in Metaphors in Science 2000 makes the point that even Newton's second law is a metaphor, in that it is difficult to see how it could be argued that F = ma "is" the motion of an object in any literal sense.

As I understand gravity using the metaphor of a heavy ball on a sheet of rubber, I understand an early universe metaphorically rather than literally.
===============================================================================

Also see How Time Began with the First Eye Opening — Wayfarer

Those who like mythological interpretations may take the birth of Kronos, the youngest of the Titans, as a symbol of the moment here referred to at which time appears, though, indeed it has no beginning; for with him, since he ate his father, the crude productions of heaven and earth cease, and the races of gods and men appear upon the scene - Schopenhauer

Our understanding is more metaphorical than literal, whether figure of speech, myth as noted by Schopenhauer, analogy or symbolism. After all, language is a symbolic system.

The quoted section is only a synthetic judgement based on a pure a priori intuition. — Mww

CPR B276
Theorem = The mere, but empirically determined, consciousness of my own existence proves the existence of objects in space outside me.
Proof = I am conscious of my existence as determined in time.
All time-determination presupposes something persistent in perception.
This persistent thing, however, cannot be something in me, since my own existence in time can first be determined only through this persistent thing.
Thus the perception of this persistent thing is possible only through a thing outside me and not through the mere representation of a thing outside me.
Consequently, the determination of my existence in time is possible only by means of the existenceb of actual things that I perceive outside myself.
Now consciousness in time is necessarily combined with the consciousness of the possibility of this time-determination:
Therefore it is also necessarily combined with the existence of the things outside me, as the condition of time-determination;
i.e., the consciousness of my own existence is at the same time an immediate consciousness of the existence of other things outside me.

Being conscious of my existence must be prior to any perception of persistence
Kant wrote "I am conscious of my existence as determined in time"

For Kant, we have a priori pure intuitions of time and space. These intuitions are non-empirical, singular, immediate, objective and conscious representations.

The unity of consciousness is central to Kant's transcendental deduction of the Categories, which are a priori pure concepts.

Consciousness of my existence cannot be a consequence of perceiving something persistent, but must be prior to perceiving something persistent.

Therefore being conscious of my existence must be prior to any perception of persistence.
===============================================================================

The quoted part is a pretty good definition of sensation. The assertion as a whole is false, insofar as experience is not of things perceived, but representations of them. — Mww

Kant is trying to prove the validity of Realism
Kant wrote "Consequently, the determination of my existence in time is possible only by means of the existence of actual things that I perceive outside myself."

Kant wrote "actual things that I perceive outside me".

This is the purpose of Kant's Refutation of Idealism, an attempt to prove the existence of objects in space outside a representation of them.
===============================================================================

Maybe YOUR a priori pure intuitions according to your transcendental argument, but if Kant with his means for humanity in general the only two are space and time, and they are the necessary conditions for possible experience, it is the other way around from yours. — Mww

Kant seems to be using a Transcendental Argument
Kant writes
a) I am conscious of my existence as determined in time.
b) All time-determination presupposes something persistent in perception.
c) Thus the perception of this persistent thing is possible only through a thing outside me and not through the mere representation of a thing outside me.
d) Consequently, the determination of my existence in time is possible only by means of the existence of actual things that I perceive outside myself.

In other words
1) My consciousness of existence must be prior to being able to perceive a persistence
2) My perception of a persistence is only possible because of things outside me
3) It is the things outside me that determine the consciousness of my existence

This seems to be a transcendental argument.

What things do we not know through their effects/acts? How could we know anything immanent if not through its effects/acts? — Count Timothy von Icarus

I agree, so let's take this as a starting position.
===============================================================================

The dividing line is at the eye because the mind/brain is assumed to be the dividing line between the world and the observer. Yet one could make the same sort of case for any dividing line one wants to defend. — Count Timothy von Icarus

I agree, in that there have been many different carriers of the information we have in our consciousness about the Andromeda Galaxy. Each change in carrier may be called a dividing line.

One question is, does the change in the carrier of information of necessity require a change in the information carried?

For example, the information about a red star is carried as an electromagnetic wavelength of 700nm through space and an electric current up the optic nerve.

Is it logically possible to maintain exactly the same information when changing from a carrier of oscillating electric and magnetic fields to a carrier of charged particles moving along an electrical conductor?

If it is, the Direct Realists have a persuasive argument that the world we see around us is the real world itself, where things in the world are perceived immediately or directly rather than inferred on the basis of perceptual evidence.

If not, then the Indirect Realists have a persuasive argument that things in the world are perceived indirectly.
===============================================================================

How unknown is it if you know what it causes and that it is red? — Count Timothy von Icarus

I agree when you say: "What things do we not know through their effects/acts? How could we know anything immanent if not through its effects/acts?"

We perceive as a sensory experience the phenomenon that we understand as a red postbox.

We believe that something has caused our sensory experience, in that we don't believe our sensory experience has generated itself.

Regardless of whether we do or don't know the cause of our sensory experiences, we can name the cause "a red postbox".

The name "red postbox" is not the name of a thing-in-itself in a world outside our mind, but rather is the name of the cause of a known sensory experience

In the same way, i) we name the cause of an acrid smell something that is "acrid", as in "acrid smoke from a bonfire", ii) we name the cause of a bitter taste something that is bitter, as in "angostine bitters", iii) we name the cause of a sweet taste as something that is sweet, as in "a sweet apple", we name the cause of a silky feel as something that is silky, as in "silk" and finally v) we name the cause of crackling sound as something that crackles, as in "a cracking fire".

IE, we can name the cause of our sensory experiences after the known sensory experience, meaning that we can even talk about an unknown cause as "the cracking fire giving off acrid smoke".
===============================================================================

This seems to be equivocating between different sorts of mind-independence. — Count Timothy von Icarus

In one sense, in philosophy-speak, "the early universe" is not mind-independent, in that "the early universe" are words which only exist in language, and language only exists in the mind. As "the early universe" only exists in the mind, by definition, it cannot be mind-independent.

In another sense, in ordinary language, "the early universe" was clearly mind-independent, and can be affirmed by every non-philosopher, by every person going to the supermarket or waiting at a bus stop,

For those philosophers that do believe that "the early universe" is not mind-independent, then logically no referent of any expression can be mind-independent, including expressions such as "tables and chairs". This which would be a problem for Direct Realists, as they do believe that things like tables and chairs do exist independently of the mind, that they are perceived immediately or directly rather than inferred on the basis of perceptual evidence.

That appearances are the necessary antecedent occasions for their employment, it does not follow they are derived from them, and in accordance with the theory, they are indeed, not, nor can they be. — Mww

Kant writes in CPR B276 on the Refutation of Idealism: "I am conscious of my existence as determined in time............................Consequently, the determination of my existence in time is possible only by means of the existence of actual things that I perceive outside myself."

"I am conscious of my existence as determined in time" is an a priori pure intuition.

"The existence of actual things that I perceive outside myself" is a posteriori empirical experience.

Therefore "Consequently, the determination of my existence in time is possible only by means of the existence of actual things that I perceive outside myself" can be read to mean that my a priori pure intuition is possible only by means of a posteriori empirical experience.

This is a transcendental argument.