Whatever criticisms I have of your math ideas, I don't disparage your ability to quote from children's books.

I'm aware that with double negation we can turn any positive into a negation.

But that doesn't bear on the point I made:

We can only prove what is true. So it is always easier to prove what is true, since there is no proof of a falsehood. That applies whether it's ExP or ~ExP. — TonesInDeepFreeze

The links I provided were meant as references, not infallible sources. — TheMadFool

I'm not faulting the article. I'm pointing out that the article says explicitly the exact opposite of how you described it.

insofar as existential claims are the issue, proving the positive is much, much easier than proving the negative. — TheMadFool

We can only prove what is true. So it is always easier to prove what is true, since there is no proof of a falsehood. That applies whether it's ExP or ~ExP.

Then let's compare a true positive with a true negative.

ExP

and

~ExQ

it is not true that in all cases, ExP is easier to prove than ~ExQ. It would depend on P and Q.

you actually haven't argued your stand on the issue — TheMadFool

My point has been that your arguments are specious. That doesn't not require "taking a stand" on anything other than what I have said.

I responded adequately — TheMadFool

(1)

We don't know that P was asserted before ~P.

I assert the following statement:

It is not the case that there exists a rainbow colored kangaroo doing yoga in the White House Oval Office now.

That statement is ~P where P is:

There exists a rainbow colored kangaroo doing yoga in the White House Oval Office now..

And P was not asserted before ~P.

The best you could correctly say is that, with the language formation rules, we cannot formulate ~P without first formulating P. But it's a naked non sequitur to claim that the syntactical formation rules entail rules for discourse. Not not only is it not the case that P must be asserted first, but it is also not the case that the fact ~P cannot be syntactically formed without first forming P entails that P must be proven first. — TonesInDeepFreeze

You evaded that that is a counterexample to your claim that P must be asserted before ~P is asserted. Instead you just intoned again your non sequitur that syntactical formation entails order of proof.

(2)

Different reasons:

To assert it.

To mention that someone else asserted it.

To wonder about it.

To mention it as a topic for discussion.

To mention it as a possible topic for discussion.

To stipulate a proposition to be the subject of a formal debate.

To mention that you will use it as the antecedent for a conditional.

To enter it as the first line of proof of its negation.

Etc.

And if it is to assert it, one can assert it without proving it. People do it all the time. It's not even always reasonable to expect proof:

If I say "There is a traffic jam to avoid on that street" but not supply proof, then one may respond "Thank you for that information, I'll avoid that street" and thus grant the usefulness of my unproved assertion. — TonesInDeepFreeze

You evaded that the items in the list (except the first one) are examples answering your challenge that to state a proposition is to assert it.

You skipped completely the example of an assertion that has value without having been proven.

(3)

Suppose there are two people (two propositions, p, ~p) in a line, and both are required to pay a fee (both need proof), shouldn't the first in the line pay the fee first (prove p first) and only then the second person (prove ~p second)?
— TheMadFool

(1) I don't think so, not necessarily. There could be better, more relevant factors used

(2) It is not even an operational analogy for the matter at hand anyway. — TonesInDeepFreeze

You skipped that entirely.

(4)

Certain negations have positive equivalents.

"It is not the case that the death penalty should be continued."

is equivalent to

"The death penalty should be abolished."

And

"The death penalty should be continued."

is equivalent to

"It is not the case that the death penalty should be abolished"

So, in such an example, there wouldn't even be a way using by your rule to claim which should be proven first. — TonesInDeepFreeze

You skipped that completely.

the debate begins with "god exists" — TheMadFool

It might seem awkward for the subject of that debate to be couched in the negative, but it is not logically necessary that it be couched in the positive. It would not defy logic to start with the proposition "It is not the case that there is an omniscient, omnipotent, all-good being".

The team that starts is called the 'Affirmative' but I don't know that it is the case that the proposition itself in an academic debate must be couched in the positive.

And the conventions for academic debates don't govern controversy and discourse universally.

Also, I gave you an example where the negative has a positive equivalent and vice versa. You ignored that.

It's crystal clear that your method is to just keep insisting you're right without addressing the arguments.

Just to be clear, the reason casinos profit is the percentage payouts. People believing the gambler's fallacy helps the casino only to the extent that a person places a bet with more unfavorable payout instead of placing a bet with a payout not so unfavorable or no bet at all. For example, if a person bets on 6 because they think 6 is due then that helps the casino better than if the person bet on Pass.

Negation is an operation. It needs a proposition i.e. before I negate p and get ~p, the proposition p has to be there. Right? Just think of it, "not cat" makes no sense if "cat" doesn't exist as an idea. I rest my case. — TheMadFool

I myself have said over and over and over that you can't form ~P without first forming P.

But, and I've said this over and over and over, that does not entail that you must first prove P.

Your "I rest my case" is empty.

And you skipped my other points, yet again.

A negative statement can't be discussed/analyzed prior to a positive statement that's subject to a similar treatment. Before negation can be performed and a negative statement obtained, there must be a preexisting positive statement that can be negated. Ergo, positive statements precede negative statements and since every statement must be proved, it follows that the burden of proof rests squarely on the shoulders of one making a positive statement. — TheMadFool

~P cannot be understood without first understanding P. But that does not entail that P must first be proved. Your "Ergo" is a non sequitur.

(1)

p was asserted first. — TheMadFool

We don't know that P was asserted before ~P.

I assert the following statement:

It is not the case that there exists a rainbow colored kangaroo doing yoga in the White House Oval Office now.

That statement is ~P where P is:

There exists a rainbow colored kangaroo doing yoga in the White House Oval Office now..

And P was not asserted before ~P.

The best you could correctly say is that, with the language formation rules, we cannot formulate ~P without first formulating P. But it's a naked non sequitur to claim that the syntactical formation rules entail rules for discourse. Not not only is it not the case that P must be asserted first, but it is also not the case that the fact ~P cannot be syntactically formed without first forming P entails that P must be proven first.

(2) Certain negations have positive equivalents.

"It is not the case that the death penalty should be continued."

is equivalent to

"The death penalty should be abolished."

And

"The death penalty should be continued."

is equivalent to

"It is not the case that the death penalty should be abolished"

So, in such an example, there wouldn't even be a way using by your rule to claim which should be proven first.

(3) You skipped my counterexample to your claim that assertion requires proof:

If I say "There is a traffic jam to avoid on that street" but not supply proof, then one may respond "Thank you for that information, I'll avoid that street" and thus grant the usefulness of my unproved assertion. — TonesInDeepFreeze

the Wikipedia page on burden of proof/can't prove a negative — TheMadFool

What page is that? The page I found says we can prove a negative.

Suppose there are two people (two propositions, p, ~p) in a line, and both are required to pay a fee (both need proof), shouldn't the first in the line pay the fee first (prove p first) and only then the second person (prove ~p second)? — TheMadFool

(1) I don't think so, not necessarily. There could be better, more relevant factors used

(2) It is not even an operational analogy for the matter at hand anyway.

(3) Also, do you get to move ahead in the line by proving things? If so, the people claiming provable positives would always get to move ahead. (I guess if you don't give a proof then you're kicked out of the line altogether and don't get inside the fancy sexy nightclub reserved for good provers.)

Whenever you declare p, you are in fact asserting p is true — TheMadFool

I didn't say 'declare P' in the sense of 'declare P to be true'.

I mean 'state P' in the sense of writing it or saying it. Not necessarily to state that it is true. I gave you examples.

A burden of proof of P does not follow from the mere fact that syntactically ~P can't be formed without first forming P.

You just skip recognizing decisive examples and arguments against you.

Why would you state a sentence p? — TheMadFool

Different reasons:

To assert it.

To mention that someone else asserted it.

To wonder about it.

To mention it as a topic for discussion.

To mention it as a possible topic for discussion.

To stipulate a proposition to be the subject of a formal debate.

To mention that you will use it as the antecedent for a conditional.

To enter it as the first line of proof of its negation.

Etc.

And if it is to assert it, one can assert it without proving it. People do it all the time. It's not even always reasonable to expect proof:

If I say "There is a traffic jam to avoid on that street" but not supply proof, then one may respond "Thank you for that information, I'll avoid that street" and thus grant the usefulness of my unproved assertion.

/

And I repeat what I just posted, but you skipped:

You are correct that in a formation sequence, P precedes ~P. But that does not entail that in a proof sequence P must precede ~P. — TonesInDeepFreeze

when you assign "2" indicating the second object, the first object is also implied — Metaphysician Undercover

I don't speak of objects being implied. What are implied are statements (or propositions). And the mathematical representation I have mentioned doesn't even need to involve such things as "it is implied that there exist [insert the members of the field of the bijection here]."

As I mentioned, there are two senses of 'count' here:

(1) A count is an instance of counting. "Do a count of the books."

(2) A count is the result of counting. "The count of the books is five."

In order not to have to continually specify which sense I mean, I'll use 'count' in sense (1) and 'result' for sense (2).


Again, here is the mathematical representation I have told you about:

A (non-empty) count is a bijection form a set onto a set of natural numbers (where 1 is in the set and there are no gaps). The result is the greatest number in the range of the count.


Here is a count:

{<'War And Peace' 1> <'Portnoy's Complaint' 2>}

The result of that count is 2.

The ordinary order induced by that count is <'War And Peace' 'Portnoy's Complaint'>


Here is another count:

{<'Portnoy's Complaint' 1> <'War And Peace' 2> }

The result of that count is 2.

The ordinary order induced by that count is <'Portnoy's Complaint' 'War And Peace''>


This involves nothing about "implying objects" or "signifying objects".

Of course, though, it is already assumed that there are objects (books on a shelf in this case) named 'War And Peace' and 'Portnoy's Complaint'. But that's not a mathematical concern. It's just a given from the physical world example.

by what principle do we say that "2" refers to one object, the number 2? — Metaphysician Undercover

By the principle of stipulative definition. Anyway, your question doesn't weigh on the mathematical notion of counting.

If this is the case, then "2" refers to the two objects counted, and a third object, the number 2. — Metaphysician Undercover

You are using 'refer' without specifying in what you sense of the word you mean. Here is what obtains:

2 is the cardinality of a set of two objects.

'2' names 2.

'2' names the cardinality of a set of two objects.

2 is the cardinality of {'War And Peace' 'Portnoy's Complaint'}.

'2' names the cardinality of {'War And Peace' 'Portnoy's Complaint'}.

In the bijection, 'Portnoy's Complaint' is mapped to 2.

'2' names the number that 'Portnoy's Complaint' is mapped to in the bijection.

The result of the count is 2.

'2' names the result of the count.

There is no equivocation or contradiction in any of that.

the numbers are simply not countable. They are infinite and this renders them as not countable — Metaphysician Undercover

Setting aside your other confusions, I will address the term 'countable' as used in a mathematics, to prevent misunderstanding that might arise:

'countable' is a technical term in mathematics that does not adhere to the way 'countable' is often used in non-mathematical contexts.

In non-mathematical contexts, people might use 'countable' in the sense that that a set can be counted as in a finite human count.

But in mathematics 'countable' doesn't have that meaning. Instead, in mathematics the definition of 'countable' is given by:

x is countable iff (there is a bijection between x and a natural number or there is a bijection between x and the set of natural numbers).

I can't state p unless I have proof. — TheMadFool

Wrong. Just to merely state a sentence does not require proving the sentence.

You are correct that in a formation sequence, P precedes ~P. But that does not entail that in a proof sequence P must precede ~P.

you can't prove a negative — TheMadFool

Not true.

proof of Is (p) has precedence over proof of Is not (~p) — TheMadFool

So you assert.

It's like being uncertain whether there's a burglar in the house; the best course of action is to assume there is one. — TheMadFool

That's a good example against your argument. We don't assume there is a burglar in the house, since we don't want to be constantly running to the front door to escape or constantly taking whatever defensive measures one would take against a burglar.

Sure, always nice work to get others to paint the white fence for you.

If an angel now rolls the dice and the 6 appears, then everyone knows that in the next 5 rolls no more 6 will come. — spirit-salamander

Wrong.

But how would it like with Laplace's Demon? — spirit-salamander

I don't know.

In the case of the dice, one would say that it is quite evenly shaped, without one side having more weight than another. — spirit-salamander

Of course, in the physical world, dice are not perfect. We don't claim that the mathematical framework corresponds to every physical pair of dice. The mathematical framework is an "ideal" that is still useful even though such things as physical dice are not ideal.

The 1/6 seem to be the mathematical expression for it (laws of nature and the absence of the manipulation). — spirit-salamander

Perhaps some people think in terms of laws of nature in this regard. But personally I think of it just as I described it - an ideal event space and ideal events

our probability formula is empty and meaningless [?] — spirit-salamander

If you thought probability is meaningless, wouldn't you be just as happy if the doctor told you that the chance of surgery survival is 1% as if he told you it was 90%?

if I rolled 6 on the first roll, the probability of a 6 appearing again on the second roll would be minimally lower. Lower in the sense of something like 0.0000000000000000000001. This is not meant to be mathematically correct. — spirit-salamander

It's not mathematically correct and there's no reason to think it's empirically correct.

In an empirical situation, if you suspect that one side of the coin has an advantage, then after a side comes up, one would expect that the probability of it coming up next is higher not lower.

What is the 1 here, what is the 6 and what / and how do they relate to the real world? — spirit-salamander

6 is the cardinality of the set of possible outcomes; that set is the event space. 1 is the particular outcome, which is one of the members of the event space. Division expresses the ratio of the particular outcome to the possible outcomes.

In actual rolls of the die, we would have an expectation, that in the long run, six comes up in close to 16 and 2/3 percent of the rolls, and we expect that it comes closer and closer to 16 and 2/3 percent as we do more and more rolls. That is an expectation but it is not ensured.

one must always add an imaginary closed overall context — spirit-salamander

Any given experiment would be a finite number of events. But there there are always longer and longer experiments - more events - than any given finite number of events.

possible worlds — spirit-salamander

That seems fine.

we could set the machine so that it always alternates the conditions. First like this, then like that, and so on. Surely here we could say that there is a 50% probability? — spirit-salamander

Of course, if we don't know which alternate the machine is about to produce, then we expect 1/2 probability of heads.

But in talking about probability in greatest generality, we don't have in mind a machine that alternates like that. We consider an abstract "framework" where results can't be predicted but only expectations can be given, based on the sheer mathematics that there are two equally likely possible outcomes and one of them is heads, so the probability of heads is 1/2. But probability does not ensure outcomes. Of course, there will be experiments in which heads comes up less than half among the flips and experiments in which heads comes up more than half among the flips.

Following up on tim wood:

Given the assumption that there were 5 sixes, then what is the probability that the 6 roll sequence will be 6 sixes? That probability is 1/6, which is exactly the probability of any single roll having a six.

That is different from not having the assumption that there were 5 sixes, where the probability of 6 sixes is 1/(6^6).

If you think that, if you roll 5 sixes, then the payout on rolling a six on the next roll should be proportionate to 1/(6^6), then I'd love to play with you and bet on a six not being rolled on your 6th roll on a day when you happened first to roll 5 sixes.

When we use "2" within the act of counting, do you agree that it signifies that a quantity of two objects have been counted. or do you believe that the numeral pairs with one particular object as "the second"? — Metaphysician Undercover

Both. That is entailed by remarks in an earlier post of mine.

equivocation — Metaphysician Undercover

There is no equivocation. The second book is mapped to 2. And 2 is also the greatest element in the range of the mapping,

Depends on the situation.

positive statements precede negative statements and since every statement must be proved, it follows that the burden of proof rests squarely on the shoulders of one making a positive statement. — TheMadFool

That's a non sequitur. Yes, to have a negation there is first a statement to be negated. But that doesn't entail anything about burden of proof.

So, as you understand that by 'count' I mean in the sense of 'successive numbering', you may see that my mathematical representation of it is correct and that indeed an ordering is induced. That is not question begging. I am telling you the sense of the word 'count' I mean, then going on to provide a mathematical representation, then showing how, in both the everyday context and in the formal mathematical context, an ordering is induced.

This tangent on counting arose from my response to your comment:

There is a fundamental problem with the concept of numbers. The numeral "1" represents a basic unity. an individual. The "2" represents two of those individuals together, and "3" represents three, etc. But then we want "2" and "3", each to represent a distinct unity as well. So we have to allow that "1" represents a different type of unity than "2" does, or else we'd have the contradiction of "2" representing both one and also two of the same type of unity. — Metaphysician Undercover

And later you have said:

To have a true count, "1" must refer to the first book, "2" refers to the first and second together, "3" refers to those two with a third, etc. — Metaphysician Undercover

Count the books on the shelf for example. "Book" signifies the type of unity being counted, "1" signifies that a unity called "a book" has been identified, and a first one has been counted , "2" signifies two of these units, etc.. — Metaphysician Undercover

Numerals are used fundamentally for counting things, objects like chairs, cars, etc.. There is no such thing as "the count", without things that are counted. So in that situation "1" signifies the existence of one object counted, "2" signifies two, etc. — Metaphysician Undercover

To have a true count, "1" must refer to the first book, "2" refers to the first and second together, "3" refers to those two with a third, etc.. — Metaphysician Undercover

Ordinarily, when someone says "I counted the books on the shelf", we understand that he used numbers (indeed as the positive natural numbers are sometimes called 'the counting numbers'), numbering in increasing order as he looked individually at each book, and not that just that he immediately perceived a quantity. That is the ordinary sense of counting I have been talking about.

Also, for example, if I see an 8 oz glass and that it's full of water, then I may say that the quantity of water is 8 ounces, without counting in the sense of numbering each ounce one by one. But that's not what people ordinarily mean by 'counting'.

Again, if you mean some wider sense, then of course certain of my remarks would not pertain.

to see that there are two chairs in front of me, does not require that I associate a number to each of them. — Metaphysician Undercover

That's the case where there is immediate recognition of the number of objects, but when immediate recognition is not possible, then we count with numbers. Counting in the sense of numbering is what would be understood in the context of this discussion.

Do you accept the OED definition, that to count is to determine the number? — Metaphysician Undercover

I don't doubt that you quoted part of an OED definition:

"determine the total number or amount of, esp. by assigning successive numbers". — Metaphysician Undercover

And the sense I have been using is indeed the one that is relevant - assigning successive numbers. You are only retroactively saying that the sense we should use is the widest sense. That widest sense is not what one would ordinarily and fairly understand by "count the books on the shelf".

I suggest, going forward, that if you wish to use 'count' in the wider sense, you would say 'count(wide)'.

The logic of Troy — Trestone

An analogy so attenuated in connection with logic that it's ridiculous.

Our logic is not only two thousand years old,
it is also the basis of all science and only those who are stupid
and not suitable for true science cannot understand it, because it is very easy. — Trestone

That's not an argument logicians would give for the worthiness of logic.

the arithmetic showed
that most true sentences could not be proven — Trestone

What logician ever said that?

There is no sentence that can't be proven in some system. However for any system (of a certain kind), there are sentences not proven in that system.

Why don't you at least learn to properly identify that which you falsely comment on?

They did not want to show any nakedness and emphasized the universal validity and unquestionable truth of the new logic. — Trestone

Fear of not being accepted is not a basis on which logicians endorse work in the field of study. Or, if you claim it is, then please point to a logician of whom it is true.

it doesn't work! — Trestone

It's question begging just to claim that it doesn't work. Actually, logicians prove it does work in the sense of (1) proving soundness, (3) proving completeness, (3) displaying the development of mathematics from axioms.

We prove negations often.

You mentions bears. I'll mention termites. If you call an inspector to your house, and he reports "No termites", then you may say, "What's your basis? What's your proof?" And you shouldn't have to pay him if he just says, "Well, I can't be expected to prove a negative, now can I?" No, he may show you photos of the areas and surfaces or whatever. Or he may give as evidence his attestation that he examined the areas.

So there are instances where the burden of proof does go to person who claims a negation.

The way gambling against the house works is you give the house x amount of money. If you lose the bet then the house keeps your money. If you win the bet then the house gives you x+y amount of money, where y>0. But when you win, the x+y that you get is less than what a "fair" payout would be. For example, if the chances of winning are only 1/10, then a "fair" payout on a one dollar bet would be ten dollars (x=1 and y=9), but the house doesn't pay "fair" so you only get, say, nine dollars (x=1 and y=8). So the house has a percentage advantage (here it's a 10% advantage). Sucker games are those where the house has really great advantage.

If the game is "fair" (so there's no house making a profit) then there's no reason to expect you'll do better or worse, no matter how you bet. For example, if you bet a dollar ten times on an outcome that has a 1/10 chance, then you would expect to lose nine times, thus lose nine dollars, but you also expect to win once with a payout of ten dollars, which is a nine dollar profit on that particular bet (since you spent a dollar on that tenth bet). So expect that your losses will equal your profits.

The gambler's fallacy is thinking that the chance of an outcome is less because that outcome has recently occurred (or that the chance of an outcome is more because that outcome has not recently occurred). The fallacy is in not understanding that each outcome is independent, not affected by previous outcomes. But if the game is "fair" then, even though it is a fallacy to think the chance of an outcome is affected by previous outcomes, we would not expect that it would hurt to bet per the gambler's fallacy, since there's not an expectation of better advantages among bets anyway.

But if the game is against a house that does not pay "fair", then the gambler's fallacy is not a wise basis for placing bets. Why is it not wise? Because instead of placing bets where the house has not a very great percentage advantage, instead you're distracted by a fallacy into placing bets you ordinarily wouldn't place where the house does have a great percentage advantage. If the house takes a great percentage on a certain kind of bet, but you take that bet because you think your hoped for outcome has a better chance than it actually has, then we would expect that you're on a course to lose more money than you would if you played without the gambler's fallacy.

So irrespective of betting against a profit-taking house, or even irrespective of gambling at all, the gambler's fallacy is thinking that chances of a single event are affected by previous outcomes. And with regard to betting against a profit-taking house, the danger of the gambler's fallacy is this: Instead of making bets on games where the house doesn't have such a great percentage advantage, you think you can beat the house at games it does have a very great percentage advantage as you incorrectly expect that you will ameliorate the effect of that advantage because your chances on an outcome are 1/n when they're really 1/(n+k).

I know what you said. You said "A count (1) implies an ordering". — Metaphysician Undercover

And you don't understand what that means.

There is more than one way to carry out that action which is counting, and not all ways require ordering. — Metaphysician Undercover

Whatever you have in mind, I didn't say that one first declares an ordering. I said that the count itself implies an ordering. The ordering I have in mind is the ordering by the number associated to each item.

You may pick up 'War And Peace' and say (or think) '1', then 'Portnoy's Complaint' and say '2' etc. The ordering implied by that count is {<'War And Peace' 'Portnoy's Complaint'>} because 1<2.

or

You may pick up 'Portnoy's Complaint' and say '1', then 'War And Peace' and say '2'. The ordering implied by that count is {<'Portnoy's Complaint' 'War And Peace'>} again because 1<2.

You can see that there are five books on the shelf without ordering them at all, just like I can see that there are two chairs in front of me right now, without ordering them at all. — Metaphysician Undercover

You see my response in this post about ordering. And in my previous post I refuted the argument about seeing things at a glance. But you skip what I said. Again, immediate instantaneous impression of a quantity is not at stake in a discussion about counting. Counting is different from immediate instantaneous impression of a quantity. You really make yourself look like a dishonest interlocutor with such a grasping at straws argument.

Why does the action of counting have to be a human count? — Metaphysician Undercover

It doesn't. Indeed I mentioned a purely mathematical formulation of counting that doesn't require consideration of human features. But when you get into certain kinds of measurements of quantities, it may be murky whether it's what we mean by 'count'. By 'count' in this context, we mean consideration of discrete objects that are recognized each one at a time, one after another, just as your original example of books on a shelf.

the essence of counting (what is necessary to the act), is to determine the quantity, no matter how this is done — Metaphysician Undercover

"determine the total number or amount of, esp. by assigning successive numbers". Notice that it says "esp.", which means mostly, or more often than not — Metaphysician Undercover

But this is how you started this tangent on counting:

Count the books on the shelf for example. "Book" signifies the type of unity being counted, "1" signifies that a unity called "a book" has been identified, and a first one has been counted , "2" signifies two of these units, etc.. — Metaphysician Undercover

That's talk about "a first" and "units". That sets a context that is a far cry from the far broader "determine the total number". You can't blame me for addressing the kind of counting that you mentioned yourself (counting chairs, one after another, or books, one after another) and then switch the context to something far wider.

Either you are being intentionally sneaky or you just forgot the context that you set up yourself.

Right, I don't understand how what fishfry was saying is relevant. — Metaphysician Undercover

Right, it is common that you lose your place in the discussion.

What should you commit? A bet? Or what? What is the payout? If the payout is proportionate to the odds, then mathematically it doesn't matter whether you bet on six or not-six (where 'not-six' means any number other than six wins) or whether you even play at all.

The gambler's fallacy would be to think that because there were 5 sixes then for the next throw the probability of a six is less than 1/6. Recognizing that the probability of a six is 1/6 is not fallacious. it doesn't matter what happened on the previous throws.

A common misuse of "I call fallacy" occurs sometimes when a person cites ad hominem. One can pile all kinds of insult on another but alongside give a good argument for one's position on an issue. Insulting someone is not necessarily the ad hominem fallacy. It's only the ad hominem fallacy when the insult is supposed to be part of supporting the argument on the matter under contention. Saying "ad hominem" sometimes itself is a fallacy - the strawman - when it is meant to discredit an argument that does not rely on ad hominem but that was accompanied by insults. Also, sometimes a person's character is itself the matter under contention.

I think many of the arguments identified as logical fallacies are legitimate arguments. Example - appeal to authority. I believe that the general relativity is a correct method for describing gravity because Einstein and many other physicists say so. — T Clark

They're informal fallacies, so there's wiggle room. Sometimes citing authority is reasonable in argument and other times not very reasonable, depending on context and specifics.

Gambler's fallacy?? — TheMadFool

No. It's more probable not to roll a six than to roll a six, in any circumstance - no matter what was rolled before. That's not the gambler's fallacy.