What exactly do you say metaphysics is? — tim wood
The study of the fundamental nature of things. — Bartricks

Then metaphysics is best left to the physicists and not the incoherent ramblings of philosophers who have no understanding of physics.

Or perhaps the more sensible thing to do would be to abandon any attempt to define 'truth' or even to use it in any formal system. — A Seagull
I personally think that Tarski's convention T is an elegant and adequate workaround for the undefinability of truth. The video below explains convention T in approximately 10 minutes and in a surprisingly simple way: — alcontali

Well I watched your video. It seems that the main aim of the T convention was to avoid the so called 'liar paradox'.

But as mentioned/discussed in another thread (Statements are true?), there is no paradox if the assumption that statements are 'true' or 'false' is not made.

Without the requirement for statements to be 'true' or 'false' but that instead 'true' or 'false' are merely labels that can be appended to a statement, there is no paradox nor problem. It would not even be paradoxical for a statement to be labelled as both 'true' and 'false'.

↪A SeagullThis is the classic 'god of the gaps' argument. — A Seagull
No it isn't. I don't think you know what you're talking about.

Do you have any formal qualifications in philosophy? — Bartricks

This from Wikipedia: "God of the gaps" is a theological perspective in which gaps in scientific knowledge are taken to be evidence or proof of God's existence.

BTW I hope you realise that ad hominems are a disappointing tactic used by people who cannot put forward any rational argument.

1. Prescriptions of Reason exist
2. All prescriptions have a mind that issues them.
3. Therefore, the prescriptions of Reason have a mind that issues them.
4. None of the prescriptions of Reason are issued by my mind (and that applies to you too, of course)
5. Therefore, the prescriptions of Reason have a mind that issues them, and the mind in question is not my mind, or your mind.

That mind - Reason's mind - is a god, and with a few more steps it becomes more reasonable than not to suppose that the mind in question is 'God' (where 'God' is taken to be a mind who is omnipotent, omniscient and omnibenevolent). — Bartricks

This is the classic 'god of the gaps' argument.

Does ignorance = god?

Given Tarski's undefinability of truth, any system has no other choice but to receive its fundamental truths from a higher meta-system. — alcontali

Or perhaps the more sensible thing to do would be to abandon any attempt to define 'truth' or even to use it in any formal system.

Almost recently the late Stephen Hawking declared:“Philosophy is dead” — David Jones

Philosophy is not so much dead as it is stuck at the end of a blind canyon.

There is no way forward except to retrace one's steps and re-examine the assumptions that have been made, particularly the implicit one's that are not even realised are assumptions. And then proceed from there.

So replace god with ? — Pantagruel
1. A newt.
2. A two-headed snake.
3. Medusa.
4. Me. Me, me, me!!!!
5. Peter Goddard. (Not much adjustment in spelling is required.)
6. A piano.
7. Sticky glue.
8. Air.
9. Many people who believe in him.
10, Another god. — god must be atheist

11. The manifestation of an illusion.

A lot of philosophy is systems-thinking and you can make right or wrong moves within systems. — BitconnectCarlos

Yes I agree, but do those systems have a direct connection to the real world? My answer is that no they don't.

↪A Seagull Is your username "A Seagull" because you're just here to shit on everything? — Pfhorrest

No it isn't.

Is your username Pfhorrest because you are an idiot?

There are no experts in philosophy, only specialists; just as there are no experts in phrenology, only specialists.

This is because there are no objective or provable truths in philosophy; it is all opinion.

Who is 'feeding a logic sentence to a theory'? — A Seagull
The user of the theory.

What is a 'logic sentence'? - as opposed to a 'non-logic sentence'? — A Seagull
A logic sentence evaluates to true or false. A non-logic sentence may evaluate to something else or to nothing at all. Example:

5+3 --> non-logic sentence, because it evaluates to a number.
It is raining now --> logic sentence, because it evaluates to a boolean value. — alcontali

Since we have agreed that the truth of a statement is a label and not a property, how can a statement be 'evaluated' to a truth or falsity?

Just because one can apply a statement to a formal system, this does not mean that it is expedient or useful to do so. It seems to me to be a pointless exercise.

The PC brigade are scared of free-speech because they do not have the intellectual capacity to refute comments or opinions that they do not like. Instead they take the cowardly course of merely labelling such comments as 'racism', 'homophobia', 'hate-speech' and the like.

I prefer to deal with the real world rather than hypotheticals.

If someone has said that they have proven something, but the proof is couched in jargon and convoluted arguments rather than plain and explicit logic and I disagree with the conclusion then I am not going to waste my time finding the flaw(s) in their 'proof'. — A Seagull
I thought you don't like to deal with hypotheticals.... (Tse-hee-hee) (-: — god must be atheist

It is not so much hypothetical as it is my experience. :)

When you feed a logic sentence to a theory, you need to provide the two-tuple (┌s┐ ⌜s⌝\ulcorner s\urcorner,s) to the formal system. Example:


("Socrates is mortal",true) — alcontali

Who is 'feeding a logic sentence to a theory'?

What is a 'logic sentence'? - as opposed to a 'non-logic sentence'?

What theory are you referring to?

And why does it 'need' a two-tuple?

The thing about formal systems, which are necessarily abstract, is that any proof or truth they generate is only applicable within that particular formal system.

In order to apply the theorems of a formal system to some other system, a mapping is required between the elements or symbols of one system with those of the other. This mapping process is not a logical deductive process and so when the mapping is complete the deductive proof and certainty provided by the formal system cannot be carried over onto the other system.

All too often formal systems and semantic systems are conflated, this is unjustifiable.

What does it mean to say that a statement is true? — A SeagullThat if people believe that statement and use it to inform their actions, they will be more likely to make useful decisions related to what the statement refers to. — Coben

Yes, this is exactly right. Without this link words, statements and even philosophy are meaningless.

↪A Seagull That's just refusing to pose an answer to the question. Which is your choice to do, but... it's not really an answer, obviously. — Pfhorrest

I prefer to deal with the real world rather than hypotheticals.

If someone has said that they have proven something, but the proof is couched in jargon and convoluted arguments rather than plain and explicit logic and I disagree with the conclusion then I am not going to waste my time finding the flaw(s) in their 'proof'.

Do you dismiss Russell's incomprehensible argument as obscurantist nonsense, or accept the conclusion of his complex technical argument you're not smart enough to follow just on his word? — Pfhorrest

No, I just dismiss your hypothetical.

B = Some propositions are true. It is absolutely certain that B is true. — TheMadFool

What does 'true' mean in this context? What makes you so certain that the statement is 'true'?

At best the statement is not self-contradictory, but that doesn't make it 'true' in any significant way.

Ok so 4>3. What is your point?

Without happiness and misery there is no life. Peace is non-life, ie death.

for me to believe that I know something but not objectively causes great dissonance.

What makes you think you know anything at all 'objectively'?

Isn't it just your ego coming to the fore to think that you do?

In any case, why does it cause you 'dissonance'? Isn't it just a part of the human condition?

The problem is that there is no well-defined or logical process for determining whether a statement is 'true' or 'false'. — A Seagull
Truth tables can be used to explore all possibilities. — TheMadFool

Sure, but that doesn't mean that they are 'true'.

The sentence can be either true or false.

If it's false then it's antecedent is false and that means the entire sentence evaluates to true.

If it is true, well, then it's true — TheMadFool

The problem is that there is no well-defined or logical process for determining whether a statement is 'true' or 'false'. And without such a process one has to resort to some arbitrary or even random process; with the result that one ends up in some meaningless la la land.

I would prefer you to admit that you can't answer my questions nor respond sensibly to my comments. — A Seagull
Perhaps you'd like to hear it straight from the horse's mouth...Curry's paradox — TheMadFool

It is nonsense for the reasons cited above.

This is what happens when you play with words without meaning or logic...you end up with nonsense. — A Seagull
Would you like to read the above replies. — TheMadFool

I would prefer you to admit that you can't answer my questions nor respond sensibly to my comments.

Where is the contradiction? — TheMadFool
"This sentence is false."

If P1 is "not P1", assuming P1 assumes a contradiction.

So if P1 is "not-P1 or P2", assuming P1 assumes either a contradiction or P2.

And "If P1 then P2" is logically equivalent to "not-P1 or P2", so if P1 is "if P1 then P2", same situation.

P1 is equivalent to “this sentence is false or P2”, so I think assuming P1 is to assume P2, not to prove it. — Michael
:100:

A loose more idiomatic way of phrasing P1 would be "If I'm right, P2" or "Unless I'm wrong, P2." That's basically just a way of asserting P2. — Pfhorrest

This is what happens when you play with words without meaning or logic...you end up with nonsense.

Formal proof:

The main statement is: If this sentence is true, then P2

Let P1 = if this sentence is true then P2

Further translation yields P1 = P1 > P2

1. P1 = (P1 > P2)....assume
2. P1 > P1......Id
3. P1 > (P1 > P2)....1 Id
4. (P1 & P1) > P2....3 Exp
5. P1 > P2............4 Taut
6.P1....from 1, 5
7. P2....5, 6 MP

Informal proof:

The statement P1 = If P1 then P2. Assuming P1 means both P1 and if P1 then P2 are true. Apply modus ponens and P2 is true which means if P1 then P2 is true. We know then that P1 is true because P1 = P1 > P2. Use modus ponens one more time and we get P2.

The paradox is that P2 can be any imaginable proposition.

As another way of proving anything, distinct from the more familiar ex falso quodlibet, I'd like some opinions on this paradox. — TheMadFool

Why do you claim that this is a 'proof'?

What are the axioms and processes of inference for the logical system in which this 'proof' takes place?

You seem to be assuming that 'truth' has a significance outside of the logical system of the proof.

Whereas in fact 'truth' for a logical system is merely a label to indicate that the deduced theorem is consistent with the axioms and rules of inference of the system.

Even if we did live in a simulated world, the data relating to the simulated world would have to be stored somewhere, and this storage would have to be in something that was 'real'.

So something has to be 'real', but quite what it is, is unknown. Even if we live in a non-simulated world, we don't really know what is 'real' and I am thinking of the ephemeral string theories here.

Starting mathematics from the natural numbers is pretty natural. If you begin with nothing but the empty set and the sole sufficient operator of joint denial, the simplest new operator you can build is disjunction, and the simplest thing you can disjoin with the empty set is the set containing itself, and hey look that’s the first iteration of the successor function and if you keep doing that you end up with the natural numbers. — Pfhorrest

It is a lot simpler just to start with the natural numbers as axioms. Introducing set theory just complicates things and achieves nothing.

my feeling is that you can't really do pure maths without set theory, — boethius

Why set theory? Set theory is pretty uninteresting really, apart from Venn diagrams which are fun and useful. I presume that you are referring to the idea that set theory provides the 'foundation' to mathematics. But pure mathematics is abstract and doesn't need any foundations apart from its axioms which introduce the symbols and define the rules. (And admittedly these axioms are more implicit than explicit).

And as for the real numbers, they become necessary when one looks to divide (for example) 10 by 4. (10/4). although the task is in the domain of integers the answer is outside. It could be written as a fraction 2 1/2 and that is what ancient mathematicians did. They considered that all numbers could be written as integers or fractions or a composite of the two. It was quite a shock to them when they came to realise that the square root of two could not be expressed as a fraction! There was no alternative except to introduce real numbers.

In teaching maths, I think it is important to make a clear distinction between pure (abstract) maths and applied (to the real world) maths. It is the conflation of the two that causes problems.

Of course children first learn maths with the conflated maths; counting sheep etc. But perhaps around the time they enter secondary school ( around age 13) the distinction needs to be emphasised.

In pure maths one is dealing entirely with the manipulation of symbols following particular rules. Here the symbols used whether for integers, reals or imaginary numbers have no more connection to the 'real world' than any other; they are all abstract.

Then for the application to the 'real world' (applied maths) one takes a particular part of mathematics and applies a mapping between the abstract symbols and concepts that apply to the 'real world'.

With this clear distinction the complications of maths fade away.

"an apple is an apple", but why? I do not get why any certain thing called 'x', should be 'x'. — Monist

One needs first to clarify what 'x=x' means.

What the claim that x=x means is that in a strictly logical system the symbol 'x' can be 'replaced with the symbol 'x' without altering the truth value of the system ( ie whether the sequence of steps is 'true' within the system or 'false' within the system.)

Since the two symbols are in fact the same, it is unlikely, if not impossible for the truth value if the system to be altered.

In the same way, the claim that 'x=y' is the claim that the symbol 'x' can be replaced with the symbol 'y' in a particular logical system without altering the truth value of the sequence of logical steps.

Hope this helps.

If you were to start from scratch to study the fields of philosophy like epistemology, logic, metaphysics, ethics, philosophy of religion/science/mind etc., not to just know them, but being able to establish knowledge on any ground, to establish a ground you can build your beliefs on, how would your ultimate planning look like?

(If you could include details like, what subject you would start with and/or what materials and platforms you would make use of, I would appreciate that)

I welcome well-thought and, strategically smart answers. — Monist

If you really want to "establish a ground you can build your beliefs on", you need to avoid reading ancient philosophers, and indeed most modern ones too. All they do, in the most part, is set up possibilities with hand-waving arguments that amount to little more than religions beliefs; which is fine if you like the religion and can buy into its tenets, but otherwise not.

For example Aristotle's claim that things fall to the ground 'because that is where they want to be' is really quite useless for understanding the physics of gravity. The early philosophers were just scratching at the surface, like an early botanist might start by classifying plants according to the colour of their flowers.

Later philosophers ask questions about whether something 'exists' or is 'right' or 'moral' or 'art'; but they are just playing with words like children play with toy bricks.

No, if you want firm foundations for your beliefs you will need to delve beneath the surface, beneath the level of words, beneath the level of the colours of flowers to the fundamental logic of what an idea is and how one can be created; to the very DNA of philosophy.

To my knowledge there is only one book that deals clearly with this topic and that is "The Pattern Paradigm" https://www.amazon.com/Pattern-Paradigm-Science-Philosophy/dp/1477131728 , of which I am the author.

When you have grasped the fairly straightforward ideas in the book you should have a handle on processes to evaluate other philosophical ideas. Or subsequently you could read the sequel to the book which is entitled: "Making better sense of the world".

So this is why Chamberlain said, "Democracy is the worst possible system of government, except for all the others." — god must be atheist

It was Winston Churchill who said this.

What do you mean by 'irrational'? Do you have anything more than a subjective judgement to label someone as 'irrational'?

People are actually perfectly rational.. so far as their view and experience of the world is concerned.
However when asked why a person did something they well not know the underlying rationality or they may choose to lie about their underlying reasons, which could be considered to be a perfectly rational response to the situation. So what a person says about their beliefs or their actions may not seem rational and perhaps it is not, but this does not mean that either their beliefs, their actions or what they say about their beliefs or actions are in fact irrational.

In fact one could go so far as to say that your claim that other people are irrational is itself irrational as it cannot be logically or rationally justified. However this is not to say that you yourself are irrational as it may well be that your claim is commensurate with your views and experience of the world.

I think the core of the issue is in in assuming that a line can be constructed from points on the line.

If we are talking about pure and abstract maths, and I think we are,, then there is no reason for this.

A line can be defined by an equation such as X=Y, where all numbers that satisfy that equation lie on the line. It can be considered to be a continuum as for any two points on the line another point can be identified that is between those two points.

There is no need to consider that the line is made up of points.

Yes you have a good point. It seems that most people do not understand infinity.
Infinity just means 'without end'. It is not a number and cannot be used in any calculation.

You can count the integers as far as you like and you will never reach 'infinity'. So to say that the integers are infinite is just to say that you can count them as far as you like without reaching the end.

Similarly no physical measurement can ever be 'infinite'. So to claim that time or space are 'infinite' is just to hypothesize that the end of time or space can never be reached.
To hypothesize that some things are infinite, such as hotel rooms, is to enter a fantasy world, where nothing is real.

Why do you call the categories 'primal' and 'non-primal'?

'Abstract' and 'real' would make better sense as there is a clear divide between the real world and the abstract worlds.

My girlfriend notoriously uses 3. if she is late for a date, and 4. — god must be atheist

The trouble with lies is that they not only attempt to deceive the other party but also lead to self-deception by the liar and a distorted self-image and this can lead to problems.

So my hypothesis is: non primal words can only be defined by other non primal words and primal words can only be defined by primal words.
What do you think? — khaled

Yellow is the colour of a banana.
This is not a definition, it is an understanding, you have to see a banana to understand what it means.