It is a proof process based on the inference and reasoning. — Corvus

What this means in the context of this logic, I have no idea. — tim wood

You have explained the case of truth table application very succinctly in your previous post.  I understand exactly what you mean on all your points.

However, you seem to be in confusion for this particular case of the proof I have shown in my post.
What you are saying is totally based on truth table cases dealing with purely symbolic logic i.e. you don't know or care what the content of the antecedent or conclusion in the -> statement.  Of course in that case, you must take account of all the cases of Q, which could be T or F.  You don't know what the status of Q is.  You have explained that, and I agree with that.

In this case, we know the content of the antecedent and conclusion of the -> statement.P -> Q was introduced for an assumption.   We don't need to be worried about the case where Q is T or F.  Because Q will be totally dependent on P being T or F.

Think of an example.  If I was told to prove if I am a millionaire, I would start with an assumption If I won the lottery jackpot tonight, I am a millionaire. It is just an assumption introduced for the proof process.

If I won the lottery jackpot tonight, then I am a millionaire .I am a millionaire totally and solely dependent on the fact of the antecedent "If I win the lottery jackpot".  In this case, I don't need to worry about whether I am a millionaire is T or F.  Because it would totally depend on the antecedent "If I won the lottery jackpot".

So I introduce (discharge) a factual statement, I have not won the lottery jackpot, which proves (based on the antecedent which is found not true), I am not a millionaire (which is True), which proves the original statement Q (I am a millionaire) was False. Remember this is not a denial of the antecedent. It is a fact from the real world case.

Therefore your points are correct under the book and truth table application method.  But you are totally under the confusion in insisting that you don't know what the content of Q was, blindly thinking Q is just Q, not thinking at all about the fact the we know the content of Q. The content of Q was given out at the very first, prove that "I am a millionaire."

P ->Q is based on the assumption P (If I won lottery jackpot), which we also know the details of the content, and was found as F from the real world case.  In this case, you don't need to think about the case where Q is T or F.

You apply truth table when all you have are the symbols bereft of any content of the symbols like in the textbooks. Because you cannot verify the symbols with the real world cases you are trying to prove. However, when you know the content of the symbols, you don't apply all the cases in truth table. Because you can verify the P or Q from the real world observations, deductions or inferences.

Remember textbook truth table tells you how the symbols in the propositions gets T F value in all cases. They are not telling you anything about the the proof processes in the real life which you must take into account prior to examining the symbols.

If the world wasn't in motion there could not be life. — Gregory

I am not so sure if the world is in motion. Because when you say something is in motion, it is moving from and towards a direction i.e. from a to b, or b to a. The world doesn't seem to be moving in that way or physically in motion.

However, there are changes in the world. The physical objects and life go through changes, and some are in motion. Both change and motion require space and time for their operations. We can see the changes and motions happening in front of us all the time. We can notice also the changes and motions taken place in the past by looking at the history of the world and life.

The universe seems to be just a container for all the objects, life and events taking place, and then vanishing into the void. We don't know how large the universe is, how old it is, and even how it began. It has a few theories, but none seem to be the definite truth. The universe will always remain as the deepest mystery in which we are born, live and perish into. Is it real? What is real?

No, no, no. From the assumption that P>Q, and given ~P, you know that P is F. and with P being F, P>Q is always true, and that Q can be either T or F. — tim wood

Whenever, then, P is F, the assumption is always T. And when Q is T, the assumption is always T. All this is clearer and less effort with truth tables. — tim wood

Great explanation! :up: I appreciate that. Thank you.

If you have P>Q and ~P, you got nothing about Q. Q can be either T or F. — tim wood

That was what I was pointing out to you. You seem to be totally relying on truth table for the value of Q. This is not a truth table case. It is a proof process based on the inference and reasoning.

From the introduction of P -> Q, we know ~P, hence the assumption P -> Q was not true.
Therefore we can make a logical inference ~Q.

This problem had been in discussion before a few times.
If you say, prove the ground is wet. You would bringing an assumption, If it rains, ground is wet.
But you find out, it doesn't rain. Therefore (from the assumption) you can prove the ground wet is not true. Why is it still true, the assumption is true? (when the antecedent is false?) This is what you are saying, and it is a rule. But if the rule doesn't make sense in real life, do you still have to go by the rule?

Since your book is misleading/confusing you, or itself wrong - which happens - I suggest you get another book. In any case it's usually good to have more than one book, one elucidating what another leaves dark. — tim wood

I am trying to do some reading on Logic this holiday period, and try to brush up the practical side of Logic. I thought the Cauman book was quite good. It reads quite well. But perhaps I could get another 1 - 2 books to compare on these fuzzy points. Any recommendations?

This is elementary stuff; it doesn't do to be mistaken on it. On line or in many books is instruction on very basic logic, which MP and MT are. Consult them; you will be glad you did. — tim wood

The proof is inspired by the Cauman's book "First Order Logic". MP MT and also chain-rule are all in use in the proof.

~P, ~R was from chain rule, but ~R therefore ~Q is MT.
Q -> R
~R
Therefore ~Q

They are all there. It is just the chain-rule derivation was adopted in introducing the premises.

In any P>Q, however simple or complicated looking, if P is false (F), then P>Q is true. And from F>Q, nothing may be concluded about the status of Q. Them's the rules. — tim wood

Are you not just talking from Truth table, that nothing may be concluded about the status of Q?
Remember, we were to prove whether Q is true or not. P -> Q is an assumption introduced to embark on the proof.

From the proof process, we came to know that the assumption P -> Q is not true, which infers Q not true. This is a proof process, not Truth table.

If either the unicorn or flying pig didn't exist somewhere, then you couldn't have written your post. — RussellA

I know them in my thoughts, and that's how I could write about them. I knew them as non-existence ideas, but they don't prevent me from writing about them. They don't exist. They are known as ideas.

The expression "exists somewhere" does not mean "exists nowhere". — RussellA

It means it doesn't mean anywhere. In other words, it is a meaningless assertion.

From Q>R and ~R, you can conclude ~Q. That's just modus tollens. — tim wood

According to L. S. Cauman (First-order Logic: An Introduction 1998, pp.29), introducing more premises and inducing the chain-rule derivation in arguments gives us more logically tight proof rather than just relying on the simplest MT or MP.

P1 - Numbers and colours exist somewhere otherwise we couldn't be discussing them. — RussellA

The fact that we are discussing something is not the evidence for existence of something. We can discuss about the unicorn or a flying pig. Does it mean the unicorn or flying pig exist?

"Numbers and colours exist somewhere"? Somewhere is like saying nowhere.
No one would know where the somewhere is. In which country, and which city, an what street, at which number of the property does it exist? It has to be a specific location that can be verified by possibility of visiting the site in person in giving out the location of the existence to be meaningful.

I could go on pointing out the logical problems in your list, but I will just stop at the first one (to save time).

In brief, from P>Q, all that can be known about Q from the argument is that if P>Q and P, then Q is true. Period. — tim wood

Could you not do following?
P -> Q
~P
Therefore ~Q

There is a biology of humanity since the laws wouldn't exist without that level of intelligence. — Gregory

Agree. :up:

Without consciousness itself the universe would be a world of a single thing just being, and moving, — Gregory

But this is not clear. What do you mean by a world of a single thing just being?

and moving, and being. — Gregory

How do you know it is moving?

R -> P was an assumption too. — Corvus

However, R (apparently) is not true, therefore ~R, therefore R is F.
R>P, then, is F>P, which is itself always true, but that says nothing about P. — tim wood

This is still not clear to me. What is R is F? Is it a misspelling? Or F for False?

From the assumption R -> P, but we know ~R is true. So we introduce ~R, which makes ~R <-> ~P
It says about the P, that P must be ~P.
It proves ~Q.

P -> Q
~P
~Q

So your comment,

R>P, then, is F>P, which is itself always true, but that says nothing about P. — tim wood

is unclear. Could you please confirm the point? Thanks.

However, R (apparently) is not true, therefore ~R, therefore R is F.
R>P, then, is F>P, which is itself always true, but that says nothing about P.
In brief, from P>Q, all that can be known about Q from the argument is that if P>Q and P, then Q is true. Period. Btw, you infer, everyone/thing else implies. — tim wood

OK, good point. How about this?

P -> Q
Q -> R

~P
~R
~(P -> R)
~R

Therefore ~Q (Contranegative MT)

Yours is neither, not a proof. I think it is called the fallacy of denying the antecedent. And I'm pretty sure you know this, but just got crossed up. — tim wood

The argument was to prove Q is untrue.
P -> Q was an assumption.
R -> P was an assumption too.
But we know that by the fact, R is not true (~R), which infers P is not true too (~P). It wasn't a denial of the antecedent. The antecedent which was assumed true was proved untrue. Therefore by MP, Q is untrue. Does this make sense?

Ideas are in the head, but ideas can change the world. — RussellA

I had an idea to cut down the tree in the back garden for 10 years, but it was just an idea. The tree is still standing tall. Can ideas themselves change the world?

In the same way that an idea physically exists within the brain, numbers, being ideas, would also only exist within the brain in physical form. — RussellA

Where about in the brain do you see numbers existing in physical form?

If we know everything in the universe, then the PSR makes sense.
If we can verify everything in the universe, then we know everything in the universe.
We cannot verify everything in the universe.
Therefore we don't know everything in the universe.
==========================================
"Therefore the PSR is makes sense." is not true.

Prove Q
P -> Q
R -> P
~R
~P
=======
~Q

What do you think of this proof?

If thoughts didn't exist, then how can a thought affect the physical world, — RussellA

You apply the thoughts onto the physical world i.e. typing, measuring, hammering, drilling, and driving ... etc. You have ideas how to use and manipulate the physical objects. But the ideas are in your head, not in the world.

the thought of pressing the "t" key on the keyboard turns into actually pressing the "t" key on the keyboard. — RussellA

Folks learn to type from the early age, and typing becomes their 2nd nature.

Thoughts exist, otherwise you couldn't have written your post. — RussellA

I had thoughts, but I wouldn't say the thought existed. You cannot use "exist" on the abstract concepts. Well you could, just like you have done, but it doesn't quite make sense, and could be classed as "unintelligible".

You have ideas and know the concepts, but ideas and concepts don't exist in the external world like the physical objects do.

Is a thought in the mind any less real than something in a world outside any mind? — RussellA

That sounds like a categorical mistake. It is not matter of real or unreal. It is matter of knowing or not knowing.

In the beginning there was nothing. Then something came into existence. — alleybear

How did something come into existence from nothing?

But you are writing about the first even prime greater than 100, so it must exist. — RussellA

So what do you think it means to you when someone said "100", or when you saw a writing on the wall "100" apart from the fact that it is a even number?

??? I"d say 3 makes perfect sense on its own. It's an integer, prime, odd, etc. — Art48

So are, 5, 7, 11, 13, 17 .... etc etc? Surely you would have been looking for something more than the textbook definitions of 3?

We know, have them in our mind, and use numbers to describe the physical objects in the world.
Numbers don't exist like the physical objects. Numbers are concepts.

3 doesn't make sense on its own, but 3 kings do, 4 apples do as well.
It took me 2 days to read the book. 2 itself is meaningless, but 2 days makes sense.

Same with good and bad. They don't exist. We know them have them in mind, and use them to describe things, actions and situations, and people ... etc.

Good itself doesn't make sense. Whatever definition you give to good, it would be a tautology.
Good person, good deed, good food, good books, and good feeling do. Diito with bad.

Nihilism is rejected as a false view in Buddhism. It is one of the 'two extremes', the other extreme being eternalism, although that is a difficult concept to explain in few words.

Although that essay you quote is indeed pessimistic, perhaps I have been too easily impressed by the idealist aspects of his philosophy. His dour pessimism is alienating at times. — Wayfarer

Buddha was a royal dude in his country where he was born. He had everything i.e. money, power, luxury of life and thousands around him to do things for him. But he knew all that good things in life won't last. He will get old, and eventually die giving up everything he had just like any other ordinary folks.

So after much thought about it, he decided to abandon everything he had, and went up to the mountain penniless and hungry. He sat down under the tree, and meditated for the knowledge and meaning of life until his death.

That is a typical scenario of nihilism. All the good things and luxury of life one has at present will not last, because everything changes, and his life too. Getting old and dying is the fate of man. Therefore everything in life is meaningless. But if life is meaningless, then dying is also meaningless. Because whether one likes it or not, it will come to him anyway. Isn't it nihilism?

Schopenhauer says in his essays, because all above and more, life is bad, and not worth living. After reading his pessimistic essays, many German young folks killed themselves at the time when Schopenhauer was living. One of the famous philosophers who followed the path was Mainlander, I believe. But ironically Schopenhauer didn't kill himself. He lived a long life, and had a natural death.

The way I compare Schopenhauer's philosophy to Buddhism is that he has an acute sense of the 'first noble truth' of Buddhism, that existence is dukkha, suffering or sorrowful or unsatisfying. But not so much of the remaining three 'noble truths' - that suffering has a cause, that it has an end, and that there is a way to that end. So it's not unreservedly pessmistic, although it is not very compatible with what modern culture regards as normality. — Wayfarer

Suffering will only end after one's death. That's not a good ending. Death is unknown and eternal, forcing life to give up even the minimum existence and freedom of thinking. Life is a pinnacle of tragedy from Schopenhauer's view in his essays.

It seems clear that Schopenhauer was strongly influenced by Kant's idealism and transcendental philosophy as well as Buddhism. I gather he had written substantial critical commentary on Kant's TI, but seems to had adopted part of the TI into his epistemology and the idea of the World.

But if you read his original essays called "On the Suffering of the World", it seems to be unmistakably nihilism writing. Isn't Buddhism after all based on the nihilism?

I asked Clearbury that same question and s/he got all huffy and claimed I didn't understand their version of solipsism. It seems that Clearbury is not at all clear on that point, so s/he wants to bury it so that others won't notice the central problem with the OP, namely the lack os a clear account of how s/he understands solipsism. — Janus

I too, have been trying to get some clarification on the OP, which has some unclear parts. But it seems clear, that the author of the OP, @clearbury keeps avoiding to give out his clear answers to the questions.

P -> Q
~Q
=======
~P (MT)

If the PSR is true, then we know about everything in the universe.
We don't know about everything in the universe.
Therefore the PSR is not true.

. He says Schopenhauer was the ‘godfather of nihilism’ which I don’t necessarily agree with. — Wayfarer

What are the reasons for you don't agree with the claim?

I am not trying to make you follow me.   I am just saying there are some questions rising from the OP, and further your assertions, which are getting more mysterious and even spooky.

You claim that you posited a single mind for a single instance.  But is mind something which can be posited?  Is it your own mind, or someone else's mind which you posited?  How did you do that, if that operation had been done?

Because from my understanding, one can only be conscious of one's own mind, and no one else's.
If it were your mind, then how does your body function without the mind, which is posited to the OP or to some other location or storage? 

As your staunch claim, if your body doesn't exist, because it is disembodied from the mind, then how were you able to read my posts without the sights, and replied to them with no hands and fingers to type up?

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

This can happen in real life all the time, and is just a fact of life and reality. All things has positive sides, but also negative sides. It depends on what angle you are looking at the things.

For example, cars are beneficial to human life. It is fast, convenient, and essential to the business. But cars pollute the earth, contributing to major global weather changes. They can also cause people to die from the accidents ... etc. Nothing is 100% beneficial. Nothing is 100% lethal depending on how you look at them.

Could life survive in such a world? — RussellA

Of course, it can. Some life dies, but some survives. It is just a matter of the survival of the fittest.
The survival of life has nothing to do with the PSR.

And comes the notion that asking what is good, was never the right question to ask. — Mww

Fully agree with you. That was my whole point. Plus the sense of moral good changes from / to different cultures, and different historical times. The practical reason will always remind the above facts to the thinker in his / her moral reasoning.

An ethics where "moral good" is some sort of distinct property unrelated to these other uses of good and which primarily applies only to human acts seems doomed to failure IMHO, because it cannot explain what this "good" has to do with anything else that is desirable and choice-worthy. — Count Timothy von Icarus

Good point. This is where Kant's practical reason comes in. Kant says that you know by human nature what morally good acts are in your heart and mind. He said something like this in his writings,
"In the sky, you see the stars shinning. In your mind, you know what the moral good actions are."

You don't need a thick tome of ethic book with the abstract definitions of what moral Good is, or what things or who are morally good. You know what morally good actions are by reflecting the situations and actions you must take out of the moral duty, which you understand by the practical 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. — RussellA

The more you try to prove the PSR is valid, the more it seems to be the case it is invalid, unsound and false due to the false premises being used in the arguments.

I thought it was an extremely barmy attempt trying to define the undefinable spewing out loads of meaningless gibberish. :)
Great to have an agreement here. Thanks.

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? — RussellA

I am not sure if these reasoning prove the PSR is valid. Because there are cases, water can kill folks. Think of the cases such as flood, drowning or contaminated water which kill folks too.

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.

I might expand to say that a word represents a property of actions, good is a word that represents a property of actions, quality is a property of actions, therefore good is a word that represents the quality of actions. — Mww

We have agreement there.

Does that expansion diminish your point? Hopefully not too much anyway, cuz I agree with your major point. — Mww

It seems to supplement my point with more accuracy.

wasn’t ever a proper question anyway but oh well, right?….. it becomes clear, under certain theoretical conditions, why there isn’t going to be one, and furthermore, why there’s no need for it. — Mww

:up:

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. — RussellA

a fact that "food is beneficial to humans" and the next day it could be the fact that "food is lethal to humans" — RussellA

I am not sure if humans survived because food is beneficial. There are some food which is lethal to some humans due to its allergic reactions causing deaths. Some humans didn't survive because of the food in that case. Therefore the premises of the reasoning is incorrect or irrelevant, which proves the PSR is a nonsense.