Abstract mathematical objects such as numbers, functions, operational symbols are descriptive language for the existence in the real world. They are not the existence themselves. In that regard, I agree that Platonic math objects don't exist.

Do infinitesimals exist (in the platonic sense)? — Michael

They are convenient and useful descriptive tools to denote and express the small objects and motions in the real world such as the information or movements of particles and atoms.

And this, again, is just ignorance of the subject matter. It doesn't really merit much more engagement than that. — Darkneos

It is impossible to communicate with someone who doesn't understand the difference between the Big Bang theory, and a metaphor for accepting the theory blindly with no reasoning or evidence which is similar attitude of blindly accepting the creation of the world episode in Genesis of the Old Testament.

More ignorance on the Big Bang and what it means. To compare it to Genesis is the height of stupid. — Darkneos

Instead of trying to give out explanations or arguments, just keep saying it is stupid, is not philosophy.

My point was not a comparison between the BB and Genesis. It was a metaphor to describe your attitude of blindly accepting the BB as the absolute truth, which is not much different from believing Genesis creation of the world. You are not even understanding a simple English sentence.

Problem with the Big Bang theory is, inability for explaining the perfect position, and workings of the matter, space and time in the Solar system. — Corvus


That’s not a problem with it. The workings are pretty much standard for something with no design or intelligence. — Darkneos

Without solid explanation backed by evidence and reasoning, the BB is not much different from the creation of the world story in the Genesis of the Old Testament in terms of its coherence and cogency.

If you accept the BB blindly, you have committed yourself to being an esoteric shaman under the apparel of science.

Tell me you don’t understand the theory without telling me you don’t understand it. — Darkneos

What do you not understand on my understanding of the BB?

there is no need for a before the Big Bang being it's creater (motion) moves singularly at the moment of the universe's and time's first motion forward. — Gregory

Problem with the Big Bang theory is, inability for explaining the perfect position, and workings of the matter, space and time in the Solar system.

If the big bang was true as a form of gigantic explosion of some sort, then it wouldn't possibly have created the perfect ideal place for the existence of life such as the Earth in the solar system with all the intelligible physics and math working on the matter, ideas and life in the intelligent and harmonious way.

It would have been more like total chaos with debris of the rocks, minerals and burnt out matters scattered and floating around in the space even at this time. You see some of the old gignatic stars exploding when they are dying. It is nothing short of the massive nuclear explosion destroying and burning everything around them.

Therefore I am not quite into believing in the BB theory. If the BB had created the solar system as it is now, then it must be the most unbelievable magic ever created in the universe nothing short of the miracle act of some omnipotent being. But is it?

Still, I am EXCITED! I am all over the place, right now...835pm 12/18/25 Looking forward to sharing latest and greatest!, Thanks — Kizzy

Great post thanks!! When I say "3" out of the blue, I cannot even know what I was meaning apart from the fact that 3 is a number. One could say, well 3 is an odd, and prime number so on, but that doesn't add much more info than it is a number. Number is a concept in the mind.

Numbers are only meaningful when it is describing the objects and entities in the real world. Number can also describe the events, processes, motions and changes too. Numbers describe and denote things, motions and the other concepts.

When you had a shirt with number 3 on it, the 3 is a symbol of number 3. It is not 3 itself at all. 3 has not just the symbol, but also name too namely "Three".

Due to its ability to describe and count the physical objects in the world, numbers are also a property for existence. If something exists, then it can be counted. If something can be counted, then it exists in the physical form.

Kant thought numbers are psychological and the a priori concepts in the mind. This tradition has been ciriticised by the later philosophers such as Bolzano and Husserl. Numbers and truth must exist in the world objectively without mind. This new trend of thinking revolutionised development in the new Logic, Mathematics and Proof theories which gave foundations for the work of Cantor, Hilbert, Russell and Whitehead. But I still believe Kant was right in his idea of numbers and abstract ideas as the products of mind.

That is my quick reflection on numbers. Maybe it has some logical flaws for sure, but I believe this is what philosophical debates are about. Pointing out the logical flaws and problems in the other folks arguments and ideas. Or coming to mutual agreement when they sound consistent and making sense. And learning the truths in dialectical and critical way.

What you're not seeing - I don't know why - is that you're making two different arguments.

If john is in Tokyo, then John is in Japan. John is not in Tokyo. Maybe he is in Osaka or Yokohama.

But you're argument really is, If John is in Tokyo then John is in Japan. John is in Paris, therefore he is not in Japan. In this argument is the extra premise.

You can conclude John is not in Japan not because he is not in Tokyo, but because he is in Paris. — tim wood

I thought you wanted to stop discussing on this topic from your last post. I am surprised to see you keep replying.

The point here is, that the proof is about whether John is in Japan or not. (Q or not Q). It is not about whether John is in Tokyo or Osaka or anywhere in Japan. If John is in Tokyo, then he is in Japan was an assumption for the proof (Q or not Q). But the assertion from the reality was John is in Paris, which proves John is not in Japan.

This is such a simple logic, but you are worrying about whether John is in any other part of Japan, which is irrelevant for the proof.

Anyhow, this was a sideline thought for proving the PSR is not valid. It is not related directly to the OP. Hence we better stop at here. If you feel that this is a worthy of a separate OP, please go and start one. I don't think it is worth for a new OP with this topic, because it is such a simple and basic stuff.
But if you feel so, do so. Thank you for your feedback. Good luck.

space and time within the universe can be motion, obviously.

The universe is in motion due to its own space and time. — Darkneos

When something is in motion, you have the information on the motion such as direction, speed, and the mode of the motion (straight, loop), acceleration, energy and time. Do you have these data from the motion of the universe? If you do, what are they?

If you don't understand the point from all the examples I have give out with the explanations, then I don't see any point carrying on. I shall not waste my time or yours. I suggest you do the same. Good luck.

The word "three" doesn't make sense alone. What does? That is, what does make sense alone? Is anything alone as a word without action or a place that is to be made sense of? — Kizzy

The point here is the OP was asking about the ontological status of ideas, hence 3 was used for a sample idea to consider. At this stage we are not considering any other objects for its ontological status, but a number which is a typical example of abstract ideas.

What do you know, when I say to you out of the blue "3"?

Maybe the millionaire example was not clear. Try with these example cases.

If X=0, then X+1 = 1
X = 2
Therefore X+1 = 3

The statement X=2, tells that
X=0 was not true.
Until the value of X is known, nothing is known in the premise.
X=2 decides the variable X and T or F of P and Q.

It also tells X+1=1 is false too.
X+1=3 is true.


If John is in Tokyo, then John is in Japan.
John is in Paris (not in Tokyo). <=== A fact from real life situation.
Therefore John is not in Japan.
P -> Q
~P
Therefore ~Q

You don't need more complication in the proof here.
You use axioms and facts in reality as the verification statements instead of the antique Truth table.

Yes i think there are infinite things we don't know about existence. We are connected by our bodies to the physical world and both are connected with God, — Gregory

Yes, I accept the fact the universe exists, but a large part of it is unknown. From that premise, I can further infer that there are entities which solidly exist, but unknown to us.

It logically and deductively validates the concept of infinity. However, I am not sure if it can validate the existence of God too.

Now I think it's time to stop. You've taken a turn from Mistaken Dr. onto Fool Ave., and that a wrong turn to make, a waste of time for everyone. Return as seems best to you, but if you insist on yours, I insist you provide a proof. — tim wood

You seem to keep writing contradictory posts. You suggest to stop, but at the same time you insist to provide a proof. Isn't it a real waste of time? I suggest you to read some First Order Logic books. If you cannot see from P -> Q, ~P, therefore ~Q, then you are not reasoning at all. Ok, I will leave you to it. All the best.

Ok. Prove it. — tim wood

I thought it was proved and explained already in the previous posts, but you seem to disagree, or haven't read it at all. That's fair enough. Maybe you still have points on the issue, or missed what I was saying. I am not saying that you are totally wrong here.

I am saying your point seem to be coming from the Classic Logic theory which is mainly based on utilizing Truth Table ignoring the fact that the modern logical proofs are done using the Axioms and real life events.

I am reading some Logic books now, and trying to expand my knowledge on the subject. If I find anything relevant and interesting to our topic in discussion, I will get back to you. Thank you for your feedback.

The diagram should make clear that denying P leaves plenty of Q, and says nothing about Q other than if there is a Q, then it is not also a P. — tim wood

You are still totally dismissing the fact P was verified as ~P from a real life event. When P is ~P, then it can be inferred ~P -> ~Q proving ~Q. It is not a groundless denial of the antecedent, but an assertion verified from the fact.

I have agreed that your points makes sense too, but only from the Classic Logic point of view. You seem not applying the proof methods using the Axioms, inference, implications and real world events in the proof process.

Galileo started saying things like dropping something on the moon should follow the same physics as here on earth. — Gregory

We are not denying the existence of the universe, but saying the end point of the universe is not known. It could be the proof or ground for the existence and validity of the concept of infinity i.e infinity exists, but the end of infinity is unknown.

Therefore we could deduce The Principle of Unknowability in existence i.e. there are entities which do exist for certain, but the details of the existence is unknown.

You could already be a millionaire prior to the lottery drawing. — EricH

In which case, Q would have been proved without the proof process.

(P>Q) ^ (~P) ^ (~P>~Q) => ~Q.

And without which, you have left the logic behind, not having proved ~Q, but simply having asserted it. — tim wood

Why make it more complicated? When you can

P -> Q
~P
Therefore ~Q

Truth table is for the classical logic, and has serious limitations. If you read some First Order Logic books, you would see they use axioms and real life case verifications in the proof rather than Truth tables.

The universe is in motion. It’s more like you have a limiting notion of movement. — Darkneos

If something is in motion, it requires space and time. If the universe is in motion, then which space and time is it in motion? Space and time within the universe cannot be motion in itself. They require space and time which is external and separate to themselves in order to be in motion.

You're the one questioning the world.. I'm saying that to doubt the sky is blue and the suns shines is a pointless exercise unless you get to a higher philosophical stage from the doubt. We all know what it MEANS to say your body is real — Gregory

My body is real of course, but my body is not the world. Here again, you are confusing body and the world.

It is not the case I am denying the world as not real. The case is that whether you could say the world is real or not, without knowing what the world is.

The world is not an abstract concept like moral good or numbers. The world is physical entity, but we don't know its boundaries to outside of it. How did it start, when, and where does it end, and does it have an outer world, which this world is contained, or is it the only world existing?

The world doesn't seem to be moving in that way or physically in motion. — Corvus


Except it is. — Darkneos

There are some objects in the universe in motion, but the universe itself is not. You seem to be in confusion in telling between the objects in the universe, and the universe itself.

We don't know how large the universe is, how old it is, and even how it began. — Corvus


Yes we do, yes we do, and we have some solid ideas. — Darkneos

The religious folks say the same thing about their Gods.

Not really. Some parts of it are mysteries but we know quite a bit about it. It's real for sure, as for asking what is real...that's often a useless and dumb question. — Darkneos

Instead of thinking about it, and trying to find the answer, just saying that it is a useless and dumb question is a real dumb and useless statement.

What a silly notion it is to say nothing is real. — Gregory

I didn't say nothing is real. You said it. Read your own post. :D

I asked what do you mean by real, when you say X is real. Is all that you see real? Is all that you know real? You think something is real, but later it turns out to be something else, or it disappears from your sight.

Is the universe real? What is the universe? Where does it start and end? If you don't know what universe is, then how do you know it is real?

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?