I am trying to see whether or not HOL actually defeats Tarski Undefinability. — PL Olcott

One can formalize the semantics—define truth—of lower order logic in high-order logic. Under that fact, isn't it the case HOL defeats Tarsky Undefinability in the formalization, because TU only applies to the domain of Algebraic statements?

But that doesn't mean the door is closed on God. Only that God cannot be accessed by our Minds. Other means must be employed... — ENOAH

Sure, God could be an abstract object which is not perceivable via sense perception. Or it could be a manifestation in some mundane physical forms such as light (remember, God said, Let there be light, and there was light. in the Genesis?), or as ancient Egyptians believed God could be Sun. Without Sun, all life on earth will be extinguished within days.

As you suggested, God could be contacted in some other way than seeing or hearing him. It proves human reason and thinking is not really the 100% certain criteria for all the knowledge in the world.

What are the other means for employment you suggesting?

So, though I am yet to be a reader or student of Wittgenstein, I've come across enough to say, and I paraphrase, that of which we cannot speak, we must remain silent. — ENOAH

When W. said that of which we cannot speak, we must remain silent, was he not saying something already on something of which we cannot speak?, which implies that it is impossible for a language possessor to remain silent on things one feels inquisitive? Therefore he broke his own code as soon as he uttered the sentence?

I don't know the answers to your questions because I have never met any God or Goddess or Gods or Goddesses. It's possible that they are all fictitious. I am agnostic about it. — Truth Seeker

Fair enough. At least you are honest with you answer on the questions, which deserves respect. Not knowing can be start of new investigative discussions and analysis. Not knowing can be better position than knowing incorrectly.

Anyhow, I have asked the questions regarding Gods, because I believe that morality can have close connection with existence of God. For example, we can ask where does morality come from? Is morality based on human reasons? Or social customs and rules? Or on God?

If morality is based on human reason or social customs, then does it have absolute right or wrong in the judgements? In this case, would it be right to ask who is morally culpable?

For something to be absolute right in judgements, should it not be from something absolute in knowing and existing?

A knowledge ontology https://en.wikipedia.org/wiki/Ontology_(information_science) is essentially an inheritance hierarchy of types from type theory which is apparently the same thing as HOL. — PL Olcott

Great link with much useful info to learn. Thank you PL.

There seems to be a finite limit to the number of orders of logic needed. — PL Olcott

I was under impression that higher than 3rd-order logic would be for the multiple set theories and advanced calculus applications, therefore they wouldn't be used for describing the empirical world cases.

For formalizing the entire body of human knowledge that can be expressed using language we need this: — PL Olcott

High-Order Logic seems to be more flexible and powerful for the real world cases due to its expanded variables availability for the properties and relations.

If God or Goddess or Gods or Goddesses made me all-knowing and all-powerful, I would be convinced that it is possible to be all-knowing and all-powerful and I would then know that God or Goddess or Gods or Goddesses exist and what God or Goddess or Gods or Goddesses are actually like. — Truth Seeker

Would it be the only way that you could know the existence of Gods and Goddesses? No other ways?

Since you have studied the world religions extensively in the past, another questions would be, are Gods always in both sexes? Why are there so many Gods? Should it not be the only one God for the whole universe? If there are so many Gods, then which one is the real God?

I have studied most of the religions on Earth but not all of them. I have tried praying to many gods and goddesses. None of them answered my prayers. — Truth Seeker

Could it be the case you might have had prayed to the unreal or fake Gods, and there were no response for your prayer from them?

In Merlou-Ponty, the body itself is consciousness. According to his view, consciousness in the body would mean the body in the body, which sounds confusing. But the point seems clear. When the body dies, the consciousness also dies too.

Higher-order logic is the union of first-, second-, third-, ..., nth-order logic; i.e., higher-order logic admits quantification over sets that are nested arbitrarily deeply. — PL Olcott

Do we need more than first and second order logic in practical uses?

I don't know if any god or goddess exists. I have never met any. I don't know what they are like except for how they are portrayed in religious books. — Truth Seeker

So you studied all the religions in the world, and also the concepts of God extensively. You think about God much of your life. However, you are still agnostic until you actually meet God yourself face to face. Is it correct?

You can carry on with the other interlocuters and I am sure you will have good discussions. cheers.

Good question. It depends on the case you are trying to prove. Some cases will work ok with MP or MT. But the cases like Cogito is awkward with the formalisation. You try different inferences and reasonings, and whatever looks most reasonable should be used, I believe.

The classic syllogism cannot handle more complicated cases well, and it would be better to use Modal, Epistemic or Descriptive Logics. But if you convert the complex sentences into more atomic ones, and formalise them, then it works ok too. I am not a Logic expert, and I will be rereading my old logic books to brush up my knowledge on it.

I am now really bowing out from this thread. I have spoken enough, and learnt a lot myself. Thank you for your engagement with me. Although there were some rough times between us, I respect your strong interest in the subject. I hope to meet you in the other threads for the other discussions later hopefully. All the best.

It has to be one or the other. Either (a -> b) leads to (~a -> ~b) as a general rule, or it's not a general rule. I would like clarity on this. — flannel jesus

Thats an inference.

A→B ↔ ¬A∨B
¬A∨B ↔ B∨¬A
B∨¬A ↔ ¬B→¬A = ¬A -> ¬B ? — Corvus

This is inference from the rule.

If this proof were valid, A→B would always imply ¬A → ¬B - that's what I call a "general rule". — flannel jesus

Yes, that was the general rule. It was to show the logical inference processes in detail from the rule to Lion because he seems having difficulties understanding it.

Dumb troll. — Lionino

It is not. You are wrong again.
¬(a→b) = It is not the case (a→b) = negation. It is not contradiction.
You never admit the truth as truth. That is part of your problem.

The contradiction to a→b is ¬(a→b), it is not ¬a→¬b. — Lionino

This seems to be your problem. ¬(a→b) is negation, not contradiction.
You don't know the difference between negation and contradiction.

It is not, these two are not mutually contradictory. One translates to (a∨¬b) and the other to (¬a∨b). Both are true if a and b are true. — Lionino

A→B ↔ ¬A∨B
¬A∨B ↔ B∨¬A
B∨¬A ↔ ¬B→¬A = ¬A -> ¬B ?

I await to hear your contradiction of "I think therefore I am" in plain English, and will take it from there.

The contradiction to "I think therefore I am" is not "I don't think therefore I am not".

More BS — Lionino

What is the contradiction of it? Tell us exactly what is the contraction of "I think therefore I am" in plain English.

The contradiction to a→b is ¬(a→b), it is not ¬a→¬b. — Lionino

You must reason the contradiction, and check it over with the real events or existence for the truth or falsehood. You don't keep on going on with the set truth table on this cogito case.

~~

a -> b) -> (~a -> ~b) is not modus ponens, we can both agree on that now. Fantastic progress. — flannel jesus

OK fine. That's rather quick and easy solution to us all. We have agreement. Thanks.

t's a shock to me that you call it modus ponens, which is a general rule, and then say now that it's not a general rule, without ever explicitly acknowledging that the thing your'e doing is in fact not modus ponens. — flannel jesus

It is a reasoning by contradiction in proof. It is so obvious just by looking at it, both premises and conclusions are contradicted and checked out.

So you don't think it's a general rule, meaning you think there are scenarios where you can have an implication, a implies b, and yet not have the implication of (not a implies not b), is that right? — flannel jesus

I am quite surprised to hear you all the way thought it was MP. MP is the most basic form, and was implemented by the Stoics. If it doesn't suit for the statement you are trying to prove, then you must move on to another type of reasoning.

Oh, fascinating. That's not what it sounded like when you called it Modus Ponens, because Modus Ponens is indeed a general rule. — flannel jesus

There are many different ways proofs can be done. MP is one way to do it, but it was not good for proving cogito, so I tried different arguments to suit it. Is it such a shock? :rofl:

I would love to know who he can make see the light. One person who thinks (a -> b) leads to (~a -> ~b) as a general rule. I'd love to have a conversation with that person. — flannel jesus

Sure, if you keep your control and just concentrate on the topics under the discussion, we can give another try. It is not because I am against using bad languages and swearing. I do swear in real life as much as anyone. Perhaps even much worse than you do. But in the forum, we must keep in control and respect the other party we are talking to. You cannot discuss anything rationally with someone who is not in control of their emotions.

You are judged by only on what you write here. So, check out if you are writing the facts, not the distortions or untruths and dishonest claims before posting. If you are ok with that, then I can give another try for clarifying (a -> b) leads to (~a -> ~b).

By the way, it is not a general rule. (~a -> ~b) is an assertion or inference against (a -> b).
You are trying prove (a -> b) is true or false.
One of the ways it can be done is applying the contradictions to (a -> b), and check if it is true or false with the reality.

So here already, it is clear that you have mistaken the very start of the point (a -> b) leads to (~a -> ~b) as a general rule. It is not a general rule at all. It is a reasoning by introducing contradiction case.

Because it is obvious. — Lionino

It is the most mysterious answer I have heard in the forum, I am afraid. :D

No. Go post that picture of a logic book you were talking about. And also translate my phrase to propositional logic. — Lionino

No Lion. Posting picture of a logic book is not a philosophical process. It is unnecessary. Our linguistic discussions and reasonings should be able to lead us to some sort of conclusion. I was going to explain everything again in detail, if you only let us know what you meant by you said thousands of times, but you were again telling untruths there.

You keep demanding to translate your phrase to PL. It is also unnecessary bizarre act in philosophical discussions. I have never heard such a ludicrous demand. If you read the good logic books, they would tell you with the reasonable inference and introducing assertions for the premises, one can build a logical argument on every event in the world. Obviously you aren't aware of that.

OK, I can only conclude that your motive was not philosophical in this discussion. So, I will leave you to it. I have learnt my lesson that I cannot make the folks to see the light, who are determined not to see it. So I will not keep trying wasting my time. All the best.

Because your bio says something other than what you meant. If anything, it means something funny. — Lionino

I still cannot see any relevance of my Bio to this thread and what we have been discussing. Something other than what I meant? How do you know what I meant? :)

Another case of selective amensia in this thread. — Lionino

I did discuss the argument case with Banno, but never with yourself.
Are you not mistaking me for someone else?
Please tell us what you said about it in summaries and points.

I don't think it means anything. I know what it means. And it is not what you were thinking. — Lionino

But why do you talk about the Bio, in the middle of talking about order and logic? It would help in understanding, if you let us know what you think it means.

I have tried that a thousand times already with "If it rains, the floor is wet". Banno also. It is pointless. — Lionino

Mentioning about Banno or the other folks in the discussion won't help for clarification on the point.
What did you say about "If it rains, the floor is wet."? What is your point? This is the first time I am reading you talking about it.

We can't change all determinants and constraints but we can change some determinants and constraints. It varies from person to person depending on their genes, environments from conception to the present, nutrients from conception to the present, and experiences from the womb to the present. I have not assessed how efficiently we deal with our determinants and constraints.

I don't know if Gods exist and if they are all-knowing and all-powerful. I am agnostic about the existence and nature of all Gods. Humans have believed in and still believe in many Gods. That does not mean that they exist. — Truth Seeker

I agree with you that some people make good efforts for improving and bettering the human living conditions which are under the negative inherent determinants and constraints. I do hope they will make good progress, and suppose that is actually what most of the public works are about.

You also mentioned the existence of God, and your agnostic attitude on the existence.
I think it is an interesting comment. It tells me that you think you know what God is, but you are not convinced it exists. Because one cannot be agnostic without having reasons for being agnostic, and it follows that one cannot have reasons for being agnostic without knowing the concept of God.

Therefore it follows that your thinking and knowing God's existence doesn't necessarily warrant the existence of God to yourself.

What would give you 100% certainly of the knowledge for the existence of God? What do you need for you to believe in God's existence with 100% certainty?

Some of the determinants and constraints can be changed.

For example:
1. Gene therapy.
2. Changing the environment by moving to a different part of the Earth.
3. Giving aid to famine victims who are dying from not having enough nutrients.
4. Rescuing people from modern slavery and giving them treatment for PTSD if necessary.

Of course, many of the determinants and constraints can't be changed by the subjects and they need external help from others e.g. doctors, aid workers, police officers, paramedics, etc. — Truth Seeker

But do you think that humans with the restricted abilities are able to deal with the inherent determinants and constraints efficiently, even if they tried?

Would you not agree that the inherent determinants and constraints are rather in the domain of God, who are omniscient and omnipotent?

It means Google translate does not work properly. — Lionino

Why suddenly talk about the bio written in Latin? What do you think it means?

By the way, your bio does not mean what you think it means. — Lionino

What do you mean? Could you please explain on that point?

I did not run away all the times you posted nonsense, in fact I refuted you several times. And I refuted you again, your rendition of Descartes is wrong. Make some effort to actually read what he wrote. — Lionino

Even if a sentence is order form, it can be formalised and executed in the logic.
If you read anything about mathematical logic, then you would have known that many of the computer programming languages operate on the instructions executed under the Boolean logic in the order form.

For example, if total order >= 10$, then offer FREE shipping.

Therefore, your claim that sentences in order form are not Logic is not correct.

Yes, "drive away if there is a red light" is an order (drive away) with a conditional (if there is), it has nothing to do with statements of the type p→q. It is a bad example. Choose another one. — Lionino

You have changed my original example back to front to make it sound like order. Please read my original example given to you again, and confirm.

The example sentence in the logical form is not order at all. It can be expressed different way for the same meaning, if you have linguistic problem understanding the sentence. For example,

If it is red light, then it is safe to drive.
If it is red light, then it is legal to drive.
If it is red light, then it is ok to drive. ... etc.

The argument is made up into the formal sentence form in the argument.

It is only an order, if some one tells you to your face, "When it is is red light, drive", or as you have changed it "Drive away, if there is a red light."

You see, the number in the bottom left corner shows whether a message came up after or before. — Lionino

I have been away all day, and just returned to see your message to me. I have no clue what you were talking about on how time works. But I will catch them up when I have some spare time.
You see I don't read any other posts apart from which are directed to me.

I did not run away all the times you posted nonsense, in fact I refuted you several times. And I refuted you again, your rendition of Descartes is wrong. Make some effort to actually read what he wrote. — Lionino

When I asked you about the If Red Light then Drive logic for your agree or disagreement on it, you said it was order, not Logic. It is a logic. It gave the impression that you were trying to avoid the answer.
That logic is a critical one. We will examine that tomorrow. I will try to read what you sent me in full in due course.

For some reason unknown to us, he is not able to take on new information. — Banno

Banno, we all know that you keep scanning other folks messages for sussing out the irrelevant grounds for your attacks. If you are honest, you will see and admit that I have never spoken to anyone with out of context vulgarities under any circumstances. I always kept my control in respecting others in the discussions.

There are a few of your cliques who have been throwing irrelevant out of context insults with the vulgar languages umpteen times. It just shows that they don't have basic respect for others, and disregard the manner of the discussions. But you never point out the problems of these folks because they are in your cliques.

With just this one evidence, your bizarre post is an unfair and untrue criticism of yours based on your psychological bias. I hope that you could realise the reality and be able to see the true situation.

woof, woof, growl. — Banno

Calm down Banno. This is The Philosophy Forum. :nerd:

Further conversation becomes like a child hitting the dog's cage with a stick. It will bark and growl back at you; fun, but progress will not be made. — Banno

Seriously this is your problem Banno. You think you are a teacher, and the rest of the members are the students. But you have no knowledge of the field that you claim to be knowledgeable at. Your claims are full of misunderstandings. When it is pointed out, you get upset, and then you put out unfair and untrue ad hominem.

I tried to treat you with my best fairness and friendliness this time. But it is over the limit. Your insincerity, dishonest and pretensions are too obvious in your post. It is a regrettable affair to be honest.

Wow, so on top of not having ever read Descartes and feeling the gaul to comment on it, on top of not knowing how to use logic, you also don't know how time works? If you scroll up, you will see I requested that you translate my phrase before you deflected with that "question" of yours. — Lionino

Well, you keep running away from the question with smoky gibberish. How time works? Why do you suddenly want to know how time works? Please elaborate further.