Why predictions about the future have no truth value

[Dan Christensen]

It seems "intuitively obvious" to me that classical propositional logic is applicable to statements that ARE (present tense) unambiguously true or false IN THE PRESENT.

As to why it is not applicable to predictions of the future, Mark Thakkar, in his “Logic of the Future” makes an interesting point:

"It is now commonplace to treat statements about the future as logically on a par with factual claims about the present and the past....

“My principal argument for the claim that statements about the future have no truth-values is that otherwise they would have the standard entailments of propositional logic. For if ‘Brian will be in his study tomorrow’ is true, then it is true no matter what else is true.”

https://www.st-andrews.ac.uk/~mnat/files/future.pdf

Comments?

Dan

Download my DC Proof 2.0 freeware at http://www.dcproof.com
Visit my Math Blog at http://www.dcproof.wordpress.com

[Mild Shock]

You are not aware that there is something like
modal logic, arent you? How many modal sentences
that involve a future modal operator are analytically true?

What would make their analytical truth not be accepted?
That the universe collapses tomorrow? Ok, maybe thats
an assumption that can be challenged,

just like your DC Proof tool challenges even the
existence of a non-empty universe of discourse.

LoL

BTW: Here is a sentence involving future that is
analytically true:

((a→◇d) ∧ (¬a→d)) → (d∨◇d) is valid.
https://www.umsu.de/trees/#(a~5~9d)~1(~3a~5d)~5d~2~9d

It basically says,
"If you are alive then you will be dead sometimes,
and if you are not alive then you are dead,
this implies that you are dead or dead sometimes"

[Mild Shock]

The theorem, contradicts your claim about propositional logic,
being in the present. It is a simple example of a modal sentence
that doesn't need modal reasoning, its an instance of this

propositional tautology:

((a→◇d) ∧ (¬a→d)) → (d∨◇d) is valid.
https://www.umsu.de/trees/#(a~5~9d)~1(~3a~5d)~5d~2~9d

((a→e) ∧ (¬a→d)) → (d∨e) is valid.
https://www.umsu.de/trees/#(a~5e)~1(~3a~5d)~5d~2e

But I guess you can also find sentences that need a little modal
reasoning to become generally valid. But philosophers might have
a lot of additional classification than only Kantian Analytic/Synthetic

Distinction. You also find De dicto/de re discussed etc... But maybe there
exists really a group of people who reject propositional logic when it
involves future? Constructive logic can do that alreay, namely

if LEM doesn't apply, I guess you cannot prove it? But you are contra
constructive logic, but now you are nevertheless interested in
weakening propositional. Is this a new morning of Dan Christensen

becoming a hard core Anti-Latitudinarian.

[Mild Shock]

P.S.: By death I mean stone death. Not some reincarnation
dead, so that if you are dead you are not really dead,
because you are reincarnated, and then you have bullshiters

like Sadhguru, giving even more shades to death:

1008 - No Womb Will Accept Him - Sadhguru
Going Beyond Cycles Of Birth & Death
https://www.youtube.com/watch?v=1xtjy66esn4

But maybe some Non-Western Logic explains this
nonsense? Or its just some other assumptions about
words like "alive" and "death"? So what is truth then?

LoL

[Dan Christensen]

On Friday, June 16, 2023 at 5:48:55 AM UTC-4, Mild Shock wrote:

> Dan Christensen schrieb am Freitag, 16. Juni 2023 um 07:05:34 UTC+2:

> > It seems "intuitively obvious" to me that classical propositional logic <------------ Please note

> > is applicable to statements that ARE (present tense) unambiguously true or false IN THE PRESENT.
> >
> > As to why it is not applicable to predictions of the future, Mark Thakkar, in his “Logic of the Future” makes an interesting point:
> >
> > "It is now commonplace to treat statements about the future as logically on a par with factual claims about the present and the past....
> >
> > “My principal argument for the claim that statements about the future have no truth-values is that otherwise they would have the standard entailments of propositional logic. For if ‘Brian will be in his study tomorrow’ is true, then it is true no matter what else is true.”
> >
> > https://www.st-andrews.ac.uk/~mnat/files/future.pdf
> >

> You are not aware that there is something like
> modal logic, arent you? How many modal sentences
> that involve a future modal operator are analytically true?
>

[snip]

Please note that I am talking about CLASSICAL PROPOSITIONAL LOGIC. Can you comment on Mark Thakkar's analysis? I think it neatly confirms my intuition that, in classical propositional logic anyway, we cannot legitimately attach a truth value to any prediction of the future.

[Dan Christensen]

On Friday, June 16, 2023 at 1:05:34 AM UTC-4, Dan Christensen wrote:
> It seems "intuitively obvious" to me that classical propositional logic is applicable to statements that ARE (present tense) unambiguously true or false IN THE PRESENT.
>
> As to why it is not applicable to predictions of the future, Mark Thakkar, in his “Logic of the Future” makes an interesting point:
>
> "It is now commonplace to treat statements about the future as logically on a par with factual claims about the present and the past....
>
> “My principal argument for the claim that statements about the future have no truth-values is that otherwise they would have the standard entailments of propositional logic. For if ‘Brian will be in his study tomorrow’ is true, then it is true no matter what else is true.”
>
> https://www.st-andrews.ac.uk/~mnat/files/future.pdf
>

What about the past tense, e.g. "Brian WAS in this study yesterday." How do we know that? Records show (present tense) that Brian was in this his study yesterday.

[Mild Shock]

Why do you write CLASSICAL PROPOSITIONAL LOGIC in
capital letters? Because your didn't read my post, right?

This is true:

((a→◇d) ∧ (¬a→d)) → (d∨◇d) is valid.
https://www.umsu.de/trees/#(a~5~9d)~1(~3a~5d)~5d~2~9d

Because this is true:

((a→e) ∧ (¬a→d)) → (d∨e) is valid.
https://www.umsu.de/trees/#(a~5e)~1(~3a~5d)~5d~2e

If you would open a single book about modal logic,
they have usually 3 inference rules:

Rule 1: Very Long Version of Rule 1: Every CLASSICAL PROPOSITIONAL
LOGIC tautology that is around, lets call one of them A(p1,..,pn), and
instead thereof where you replace p1,..,pn by modal formulas B1,..,Bn,
then A(B1,..,Bn) is valid inference.

Rule 2: Modus Ponense
A, A -> B / B

Rule 3: Rule of Necessity
A / []A

See Definition 1.39 here:
Very Short Version of Rule 1: "all instances of propositional tautologies"
Our decision to add all propositional tautologies as axioms is an example
of axiomatic overkill; we could have chosen a small set of tautologies
capable of generating the rest via the rules of proof, but this refinement
is of little interest for our purposes.
https://www.academia.edu/2891445/Modal_Logic

And then you get Modal Logic K if you add this axiom schema:

Rule K:
[](A -> B) -> ([]A -> []B)

[Mild Shock]

The theorem I presented didn't need axiom K, or axiom N (Rule 3)
or modus ponens (Rule 2). It can be seen as a direct application
of (Rule 1), although Wolfgang Schwartz tree tool doesn't prove

this model theorem, since Wolfgang Schwartz doesn't work
as the system presented by Patrick Blackburn. But if you take
Patrick Blackburn, some next example he does in his Hilbert

Style Proof system for Modal Logik K, is this here:

([]p & []q) -> [](p & q)

This is a little bit more than only a CLASSICAL PROPOSITIONAL
LOGIC instance. His proof uses Axiom Schema K. Besides
Modal Logic K, there is a real Zoo building upon Modal Logic K,

you can add more Axiom Schemas than only K. You can also
make modal logics with temporal modal operators. So that
you could model your english sentences.

[Mild Shock]

Problem is nobody has ever heard of Mark Thakkar. Why
should somebody invest time in reading Mark Thakkar?
What is your motivational speak for him, except your

own confusion as usual? Is he famous for something? So
I don't know exactly what you should read for temporal
logic. Maybe this here:

Papers on time and tense
by Prior, A. N. (Arthur N.), 1914-1969
https://archive.org/details/papersontimetens0000prio_k3r9/page/n5/mode/2up

It has nice chapters like FUGITIVE TRUTH, etc.. etc..

LoL

[Charlie-Boo]

On Friday, June 16, 2023 at 1:05:34 AM UTC-4, Dan Christensen wrote:

What do we want? Time Travel!
When do we want it? Immaterial!

C-B

[Dan Christensen]

On Friday, June 16, 2023 at 7:10:08 PM UTC-4, Mild Shock wrote:
> Problem is nobody has ever heard of Mark Thakkar. Why
> should somebody invest time in reading Mark Thakkar?

In the immortal words of Mark Twain, "Prediction is difficult--particularly when it involves the future."

Just admit that you cannot predict the future.

If you want to reason about propositions, the truth values of which may vary over time, classical propositional logic will not suffice.

[Jim Burns]

On 6/16/2023 10:56 PM, Dan Christensen wrote:
> On Friday, June 16, 2023

> at 7:10:08 PM UTC-4, Mild Shock wrote:

>> Problem is nobody has ever heard of
>> Mark Thakkar. Why should somebody invest time
>> in reading Mark Thakkar?
>

> In the immortal words of Mark Twain,
> "Prediction is difficult--particularly
> when it involves the future."

The way I heard it, that was Yogi Berra.
Maybe Twain stole it from Berra?

> Just admit that you cannot predict
> the future.

Why admit it's impossible?
Because your quote says it's difficult?

Prediction is difficult and imperfect,
but, even so, it pays well to engage in it,
pays in the best coin: survival.

I heard somewhere that even bacteria
engage in a form of prediction.

In a healthy host body, a strain of
disease bacteria might be present without
much cost to the host. Call this
the "live and let live" strategy.

If the host shows signs that it won't
be around for much longer (honestly,
the details are beyond me), the bacteria
will change their strategy to
"grab what you can, while you can"
The technical term for this, from the
host perspective, is "bad".

It looks as though the change in bacterial
behavior is because of a _prediction_
that the host is going to die soon.
My guess is that the prediction is a
genetically encoded response to stress
chemicals in the environment of the bacteria.

If bacteria do that, it's because it _works_
more than it doesn't work. Otherwise, that
behavior would not have been selected for.

I like to think that humans are better at
predicting the future than bacteria, but
it's still difficult for us, and it still
yields imperfect results. But it beats
all to hell _not_ predicting the future.

> If you want to reason about propositions,
> the truth values of which may vary over

> time, propositional logic will not suffice.

Consider using predicate logic.

Predicates and variables over a domain
grant us the awesome power to describe and
reason about things, some of which we can't,
even in principle, observe.

Natural numbers. Real numbers. The core of
the Sun. The cosmos outside the observable
universe. The Big Bang. The future.

We make broad claims over the whole of some
domain. "Energy is conserved" and its ilk.
We observe some of the domain. If the claim
fails there, the broad claim fails, and
we eliminate it.
|
| When you have eliminated the impossible,
| whatever remains, however improbable,
| must be the truth.
|
-- Sherlock Holmes

It's not nearly as simple or easy as
I fear I've made it sound. But it's not
impossible. I know because we do it.

[Julio Di Egidio]

On Friday, 16 June 2023 at 07:05:34 UTC+2, Dan Christensen wrote:
> It seems "intuitively obvious" to me that classical propositional logic is applicable to statements that ARE (present tense) unambiguously true or false IN THE PRESENT.
> As to why it is not applicable to predictions of the future, Mark Thakkar, in his “Logic of the Future” makes an interesting point:
> "It is now commonplace to treat statements about the future as logically on a par with factual claims about the present and the past....
> “My principal argument for the claim that statements about the future have no truth-values is that otherwise they would have the standard entailments of propositional logic. For if ‘Brian will be in his study tomorrow’ is true, then it is true no matter what else is true.”
> <https://www.st-andrews.ac.uk/~mnat/files/future.pdf>
> Comments?

If "Brian will be in his study tomorrow’" is *stated*, besides that one should rather understand "Brian will be in his study tomorrow modulo any intervening accidents", the truth of the statement is *relative to the present knowledge* and nothing else. That is, the truth of a *proposition* indeed is about the present, it's LOGIC that you guys have no clue about.

Julio

[Julio Di Egidio]

To be clear, "knowledge" goes with that example and how one would phrase it in common speech, but it's not at all exhaustive: it's the whole (present!) "state of affairs", to say it a la Wittgenstein: the point is, truth is (of) now--and the responsibility for truth, which is what is really at stake...

Julio

[Mild Shock]

Sometimes its very easy, and its the reason why people
don't wear hats anymore. According to this video
people don't war hats anymore because we have

central heating in the office, heading in the car,
and heating at home:

Why Did Men Stop Wearing Hats?
https://www.youtube.com/watch?v=0vRvv-HUjnU

Now whats the relatively reliable prediction, that
is needed for these climat systems?

a) If I have fire = 1 in the boiler, then the
temperature of the water will go up

b) If I have fire = 0 in the boiler, then the
tenperature of the water will go down

In mathematical terms, more or less, where
this time the dependent variable y is not
a location but the temperature of the water:

y' = (2*fire-1)

Maybe dull people like Dan Christensen have
never though about the fact that calculus, and
the concept of "rate" in calculus typically

deals with the future?

[Mild Shock]

There are still situations where we might use
a hat, like a cap for sun shading etc.. so we have
a logical sentence, involving future:

[Future] Brian puts on cap iff [Present] Brian sees sun

Which is not "true no matter what else is true"
as fellow crank Mark Thakkar claims. The truth table
has two rows where the truth table would be false:

sun cap iff
T T T
T F F
F T F
T T T

[Dan Christensen]

On Saturday, June 17, 2023 at 4:53:06 AM UTC-4, Jim Burns wrote:
> On 6/16/2023 10:56 PM, Dan Christensen wrote:
> > On Friday, June 16, 2023
> > at 7:10:08 PM UTC-4, Mild Shock wrote:
> >> Problem is nobody has ever heard of
> >> Mark Thakkar. Why should somebody invest time
> >> in reading Mark Thakkar?
> >
> > In the immortal words of Mark Twain,
> > "Prediction is difficult--particularly
> > when it involves the future."
> The way I heard it, that was Yogi Berra.
> Maybe Twain stole it from Berra?
> > Just admit that you cannot predict
> > the future.
> Why admit it's impossible?
> Because your quote says it's difficult?
>
> Prediction is difficult and imperfect,
> but, even so, it pays well to engage in it,
> pays in the best coin: survival.
>

[snip]

Classical propositional logic alone is quite useless for predicting the future. To approximate it, scientists and engineers use probability theory or some time-based analysis.

[Dan Christensen]

[snip]

In other words, it is an opinion, not a fact.

[Julio Di Egidio]

On Saturday, 17 June 2023 at 13:59:40 UTC+2, Dan Christensen wrote:

> Classical propositional logic alone is quite useless for predicting the future.
> To approximate it, scientists and engineers use probability theory or some time-based analysis.

"When caught, a true charlatan goes full liar."

Julio

[Mild Shock]

As usual you are highly confused Dan-O-Matik and
you confuse the formal with the material.

Not necessarely. Every "classical" logic, first order logic,
second order logic has its foundation in "classical"
propositional logic. For example logicians do not really

say "first order logic" is not "propositional logic". They
rather say "propositional logic" is contained in "first order logic".
Whereas there is the trivial containment, namely

that you get "propositional logic" as the fragment of
"first order logic" when you restrict predicates to zero-order.
But then there is the non-trivial containment, in that

"first order logic" has the logical connectives from
"propositional logic", and therefore all instances of
"propositional logic" tautologies as theorems as well

althought these instances don't belong any more
to the "formally" to the propositional fragment, because
you replace the propositional variables by something else,

they belong "materially" to the propositional fragment.
There is no exception in modal logics, and in temporal
logics, they usually are design the same, which has

to do about some ideas of "Sense", see Frege.

[Julio Di Egidio]

On Saturday, 17 June 2023 at 14:08:49 UTC+2, Mild Shock wrote:

> As usual you are highly confused Dan-O-Matik and

And, as usual, you'll be the other side of the same coin.

Have fun...

*Plonk*

Julio

[Mild Shock]

The two viewpoints "formal" and "material" involve
two different levels, namely:

1) "formal" containtment: This basically involves the syntax.
-------------------------------------------------------------------------------------------------
Lets say L_Prop is the language of "propositional
logic", and lets say L_FOL is the language of "first order
logic", (or some modal logic, temporal logic, second order logic),

L_Prop ⊆ L_FOL

then you can say L_Prop ⊆ L_FOL, because you can
identify propositional variables with zero-order predicates.
Thats a quite trivial exercise in mathematical logic.

2) "material" containment: This basically involves semantics.
-------------------------------------------------------------------------------------------------
Lets say |=_Prop is the semantic true in all models for
propositional logic, and lets say |=_FOL is the semantic
true in all model, then you can derive the following:

|=_Prop A(p1,..,pn) => |=_FOL A(B1,..,Bn)

This is because any of the other logics first order
logic", (or some modal logic, temporal logic, second order logic),
do not only inherit part of the syntax of "propositional logic",

i.e. the connective ~, &, -> etc.. But also the semantic of
these connnectives individually and the way they are
composed. Its also an exercise in mathematical logic,

not sure whether its trivial or not. Surely its not rocket science.

[Dan Christensen]

On Saturday, June 17, 2023 at 7:11:43 AM UTC-4, Mild Shock wrote:
> There are still situations where we might use
> a hat, like a cap for sun shading etc.. so we have
> a logical sentence, involving future:
>
> [Future] Brian puts on cap iff [Present] Brian sees sun
>

There are two facts to consider in the present tense: (1) Brian is wearing a cap. (2) It is sunny where Brian is.

> Which is not "true no matter what else is true"
> as fellow crank Mark Thakkar claims. The truth table
> has two rows where the truth table would be false:
>
> sun cap iff
> T T T
> T F F
> F T F

> F F T <----- Correction

If, at present, it is cloudy where Brian is and he is wearing a cap (line 3 of your table), then your biconditional is false. That's how propositional logic works.

[Mild Shock]

I give Dan Christensen one potato, if he finds an
example from "classical" modal or temporal logic,
that breaks the "material" containment property.

|=_Prop A(p1,..,pn) => |=_FOL A(B1,..,Bn)

Namely a formula A from L_Prop and formulas
B1, ..., Bn from L_FOL (or the modal logic or the
tenporal logic or the second order logic), so that

the above is violated. Good luck. Such an example
possibly would stem from a logic that doesn't
deserve anymore the label "classical".

Which somehow also explains what the label
"classical" usually means among a wide range
of logics.

[Mild Shock]

Maybe it needs some medieval thinking first:

Historians of logic usually classify Buridan among
the terminists or ‘moderns’, a diverse group of
thirteenth and fourteenth-century logicians who
regarded the semantic properties of terms (literally,
the ‘ends [termini]’, or subjects and predicates,
of **propositions**) as the primary unit of logical analysis.
https://plato.stanford.edu/entries/buridan/#Log

Terminist logic is a specifically medieval development.
It is named from its focus on terms as the basic unit of
logical analysis, and so it includes both **supposition**
theory, together with its ramifications, and the treatment of
syncategorematic terms.
https://www.cambridge.org/core/books/abs/cambridge-history-of-medieval-philosophy/terminist-logic/307C2B225C11FBC181C74EB0203C3BC4

Terms using "future" / "past" modifiers etc.. are
syncategorematic terms? A different conception of
"propositional" logic. Allowing "propositional" logic to
combine a wider range of terms, than only
propositional variables?

[Jim Burns]

No.
Not to approximate it.
Scientists and engineers use
propositional logic,
not an approximation of propositional logic.

Scientists and engineers don't use
propositional logic alone.
Are you claiming I've contradicted myself?

> scientists and engineers use
> probability theory or some time-based
> analysis.

Yes.
And propositional logic.

>>> Just admit that you cannot predict
>>> the future.

Or else what?

I can predict the future,
with difficulty and imperfectly.

| 'When I use a word,' Humpty Dumpty said
| in rather a scornful tone, 'it means
| just what I choose it to mean — neither
| more nor less.'
|
| 'The question is,' said Alice, 'whether
| you can make words mean so many different
| things.'

[Dan Christensen]

Referring to approximating the predication of the future.

[Mild Shock]

Well the word "approximation" has like 50 shades of
meaning. And possibly it doesn't mean what you
think it means. You can always use less than (<),

and greater or equal (>=) in analysis. For example this
here is not approximative, its exact reasoning:

/* Provable Theorem in Calculus, Right? */
ALL(t):[y'(t) > 0] => ALL(t):[y(t+k)>y(t)]

But you might not know what y'(t) is or what
y(t) is, how the function looks like.

Isn't that some kind of mathematical magic?

magic gif...
https://www.youtube.com/watch?v=X8kMlxkTlbQ

[Mild Shock]

Corr.: Typo forgot to quantify k

This direction of a proof is possibly simpler:

/* Provable Theorem in Calculus, Right? */

ALL(k):ALL(t):[y(t+k)>y(t)] => ALL(t):[y'(t) > 0]

What about the other direction?

/* Provable Theorem in Calculus, Right? */

ALL(t):[y'(t) > 0] => ALL(k):ALL(t):[y(t+k)>y(t)]

Can you prove both directions in DC Poop?

[Mild Shock]

Lets call the task, the "positive velocity and
function monotonicity theorem". LoL

[Mild Shock]

Corr. k must be possitive:

/* positive velocity and function monotonicity" */
ALL(k):ALL(t):[k > 0 => y(t+k)>y(t)] <=> ALL(t):[y'(t) > 0]

[Dan Christensen]

On Saturday, June 17, 2023 at 9:53:56 AM UTC-4, Mild Shock wrote:

> > > >> Prediction is difficult and imperfect,
> > > >> but, even so, it pays well to engage in it,
> > > >> pays in the best coin: survival.
> > > >>
> > > > [snip]
> > > >
> > > > Classical propositional logic alone is
> > > > quite useless for predicting the future.
> > > > To approximate it,
> > Referring to approximating the predication of the future.

> Well the word "approximation" has like 50 shades of
> meaning.

[snip]

Weather forecasters "approximately" predict the future when they say, for example, that there is a 40% chance of rain tomorrow. They cannot attach a truth value to the proposition, "It will rain tomorrow."

[Mild Shock]

I am this forecaster, got a request by Elon Musk for
his self driving cars, he wasn't sure whether cars
will drive forwards or whether they drive backwards:

/* positive velocity gives function monotonicity" */
ALL(t):[y'(t) > 0] => ALL(k):ALL(t):[k > 0 => y(t+k)>y(t)]

Can you prove it with DC Poop?

LMAO!

[Mild Shock]

Usually driving a car involves much more qualitative
reasoning, involving the future. If you cannot do it
as a human, then this might happen:

63-year-old woman flips car during driving test in Argentina
https://www.youtube.com/watch?v=1Y6didvqJUU

Maybe DC Poop wasn't invented for such reasoning.
Why does it even have quoted name syntax? You can
write y, y', right? Anyway this convinces me again

you stolè DC Proop, and you don't what it can do?

Bye

P.S.: Probabilistic reasoning is also exact. Its not
approximative. If you attach a probability to an event,
this doesn't make it approximative.

You surely don't know what approximative means.
The word approximative is not used in probability.
The term is usually "stochastic":

Stochastic (/stəˈkæstɪk/; from Ancient Greek στόχος
(stókhos) 'aim, guess') refers to the property of
being well described by a random probability distribution.
https://en.wikipedia.org/wiki/Stochastic

Stochastic processes etc.. etc..

[Mild Shock]

The term approximative comes from Error Calculus.
Gauss introduced it. You can use it with or without
probability. Without propability its more an interval

calculus. With propability you might have folding
some Gauss curves and things. It has a different
thinking than attaching probabilities to events:

"In the fields of science and engineering, the accuracy of a
measurement system is the degree of closeness of
measurements of a quantity to that quantity's true value."
https://en.wikipedia.org/wiki/Accuracy_and_precision#Common_technical_definition

[Mild Shock]

Last but not least you have Quantifier Disambiguiation
by Rossy Boy, thats the mathematical field when you eat
tons of cocaine and have keyboard access to google groups.

[Ross Finlayson]

Damnit I am not a head and never've had a habit.
(Also the only scrips I've _ever_ ate were antibiotics.)

What we have here is "probability theory" that according to the "philosophy of science"
there is a "philosophy of statistics" about various "laws of large numbers"
where, just like _science_, _statistics_ is only falsifiable, then that it's so
that models of probability exist and are "true" and not to be confused
with their predictions, the expected values, and "fate".

Your little classical then broken mis-use of a simple data-structure
with ambiguity of causality is a sort of effort in the objects of the
scientific method, done wrong. It's un-scientific, un-sound, ....


Then, about actually the field of probability theory and statistics
and the statistical method vis-a-vis the scientific method, and as
a "subset" of it, is it about that there are various "laws of large numbers",
and about a complement to central limit theorem in uniformization
limit theorem, in continuum limits, of continuous distributions.

You're already not doing causality, wrong, don't compound it
with misapplication of perfect and imperfect past, present, and future.

Don't worry, "truth" and "equals" is defined variously as "derived"
in various "orders of semantics, non-logical", so you can find a little
theory that says whatever you want, as long as you're not bound to
observe the logical and causality, and, the philosophies of science.

[Mild Shock]

Since both are white, you usually confuse the two.

[Mild Shock]

If you want all 3 words in one sentence. Statistics is
used to approximate probabilities out of data. So Rossy
Boy hit the jack-pot thanks to his free flowing associative

memory and usually being totally off-topic. He introduced
new term "statistics". The law of large numbers numbers
can be used to justify a derived probability by making

the error small. The easiest approximation from statistics,
is an uniform propability, lets say there is a probability
p that a fish is yellow and and probability (1-p) that a

fish is blue, then for the fish pond youre statistical
inductive reasoning gives you:

#yellow fish
p ~ ----------------------------------------------
#yellow fish + #blue fish

This is called "Statistical inference". See also:

Maximum likelihood estimator, etc...
https://en.wikipedia.org/wiki/Continuous_uniform_distribution#Statistical_inference

You might want to compute confidence intervals, to justify
the "significance" and applicability of your "estimate". The
significance propagates through error computation.

The fun begins when all this juggling doesn't practically
work, because the stochastic processes are not that
friendly and lead to very unstable results, besides that

bringing these computations numerically to
the computer can be quite hard.

[Ross Finlayson]

(Don't get me wrong, I smoke about a pack of organic tobacco cigarettes
a day, and am drinking black arabica coffee right now. I went to college
at least twice, and though not necessarily practicing or observant am
a good Rasta, Buddhist, Ninja, Christian, Muslim, Catholic, and Jew, old Irish Fish Pole.
I've already sowed my oats and my wild oats, and damn I love them oats.
In high school I had a corticosteroid inhaler but never needed it, and one quarter in
seventh grade every day after lunch I got a spoon of codeine syrup in the office.
My doctor gave me a shot of remdesivir when COVID hit, and a hepatitis vaccine.)

Anyways you hillbilly-pill popping nose-ring no-doze glue-sniffing tweaker nerds
don't know the half of it, and getting your feelings out a bottle is a bad idea.

(Don't forget that glands need exercise too, I jog about two miles a day.)

Now, if you'd like, you can always insert "f'ing" or "drogas" every other word -
I don't. (I understand that some people do.)



It's like there's this one blonde joke, working at the typewriter,
and the output's full of errors, it's like "wow, is she/he blonde
and thus stupid" and it's like "no, that's a common stereotype,
but every time there's a typo she/he keeps sniffing the white-out
and it causes dain bramage".



There really is something to be said for foundations and axiomless natural deduction -
it's a perfect sort of theory for science, and in a world of hallucinating mobs,
really is a singular sort of sanity. (And the experiential quest thereof and therefore.)

[Dan Christensen]

On Saturday, June 17, 2023 at 11:12:26 AM UTC-4, Mild Shock wrote:

[snip]

>
> Probabilistic reasoning is also exact. Its not
> approximative. If you attach a probability to an event,
> this doesn't make it approximative.
>
> You surely don't know what approximative means.
> The word approximative is not used in probability.
> The term is usually "stochastic":
>

[snip]

Nevertheless, you cannot attach a truth value to the prediction, "There is a 40% chance of rain tomorrow." Any outcome (rain or no rain) would be consistent with this prediction. As such, you cannot apply classical propositional logic using such predictions. Similarly, you cannot attach a truth value to the prediction, "It will rain, tomorrow." Or even, "It rains, tomorrow."

[Ross Finlayson]

If a soft MBA is too weak for you, you might be interested in "operations research".

[Ross Finlayson]

If it might rain tomorrow, maybe you should stay home.

[Jim Burns]

On 6/17/2023 10:15 AM, Dan Christensen wrote:
> On Saturday, June 17, 2023
> at 9:53:56 AM UTC-4, Mild Shock wrote:

>>> Referring to approximating
>>> the predication of the future.
>
>> Well the word "approximation" has
>> like 50 shades of meaning.

> Weather forecasters
> "approximately" predict the future
> when they say, for example, that
> there is a 40% chance of rain tomorrow.
> They cannot attach a truth value to
> the proposition, "It will rain tomorrow."

You (DC) are saying
weather forecasters are not
stating theorems about rain tomorrow.
Okay. I agree. They aren't doing that.

Have you (DC) previously thought that
weather forecasters state theorems,
but the light bulb over your head
turned on, and you wanted to share
your insight?

Did you see some poor benighted poster
claiming that weather forecasters
state theorems, and you wanted to
set them straight?

I have seen a bunch of crazy stuff,
but not that one.

> there is a 40% chance of rain tomorrow.

...which is not a theorem.

However,
there are theorems relevant to
the chance of rain tomorrow, et al.

https://plato.stanford.edu/entries/dutch-book/
| ...that an agent who violates the
| probability axioms would be vulnerable to
| having a book made against him...

General apologies for "Dutch book", which
I suspect is an old British slur.
I don't know of any other name for
this theorem.

And, of course, Bayes' Theorem.

Given evidence e
we can update the probabilities of
our hypotheses h₁,...,hₖ (∑ₖp(hₖ)=1)
from p(h₁),...,p(hₖ)
to p(h₁|e),...,p(hₖ|e)
using
p(hⱼ|e) =
p(e|hⱼ)⋅p(hⱼ)/(∑ₖp(e|hₖ)⋅p(hₖ))

p(e|hⱼ) is the probability of
evidence e given hypothesis hⱼ

p(hⱼ|e) is the probability of
hypothesis hⱼ given evidence e

...which is where predictions come from.

[Dan Christensen]

On Saturday, June 17, 2023 at 1:23:27 PM UTC-4, Jim Burns wrote:
> On 6/17/2023 10:15 AM, Dan Christensen wrote:
> > On Saturday, June 17, 2023
> > at 9:53:56 AM UTC-4, Mild Shock wrote:
>
> >>> Referring to approximating
> >>> the predication of the future.
> >
> >> Well the word "approximation" has
> >> like 50 shades of meaning.
> > Weather forecasters
> > "approximately" predict the future
> > when they say, for example, that
> > there is a 40% chance of rain tomorrow.
> > They cannot attach a truth value to
> > the proposition, "It will rain tomorrow."

> You (DC) are saying
> weather forecasters are not
> stating theorems about rain tomorrow.

[snip]

Not exactly. When weather forecasters say that it is now raining in their region, they are stating a proposition that is unambiguously either true or false. When they forecast that there is a 40% chance of rain tomorrow, they are NOT stating such a true-or-false proposition since, whatever the weather is tomorrow, it will not be inconsistent with that forecast. This would be so even if they said simply, that in their professional opinion, it will rain tomorrow.

[Ross Finlayson]

Your false antecedents and false consequents have no truth-value, and have no business in truth-tables.

[Dan Christensen]

On Saturday, June 17, 2023 at 4:16:22 PM UTC-4, Ross Finlayson wrote:
> On Saturday, June 17, 2023 at 12:23:30 PM UTC-7, Dan Christensen wrote:
> > On Saturday, June 17, 2023 at 1:23:27 PM UTC-4, Jim Burns wrote:
> > > On 6/17/2023 10:15 AM, Dan Christensen wrote:
> > > > On Saturday, June 17, 2023
> > > > at 9:53:56 AM UTC-4, Mild Shock wrote:
> > >
> > > >>> Referring to approximating
> > > >>> the predication of the future.
> > > >
> > > >> Well the word "approximation" has
> > > >> like 50 shades of meaning.
> > > > Weather forecasters
> > > > "approximately" predict the future
> > > > when they say, for example, that
> > > > there is a 40% chance of rain tomorrow.
> > > > They cannot attach a truth value to
> > > > the proposition, "It will rain tomorrow."
> >
> > > You (DC) are saying
> > > weather forecasters are not
> > > stating theorems about rain tomorrow.
> > [snip]
> >
> > Not exactly. When weather forecasters say that it is now raining in their region, they are stating a proposition that is unambiguously either true or false. When they forecast that there is a 40% chance of rain tomorrow, they are NOT stating such a true-or-false proposition since, whatever the weather is tomorrow, it will not be inconsistent with that forecast. This would be so even if they said simply, that in their professional opinion, it will rain tomorrow.

> Your false antecedents and false consequents have no truth-value, and have no business in truth-tables.

So, antecedents and consequents can only be true??? Doesn't sound very useful. Please explain.

Dan

[olcott]

On 6/16/2023 12:05 AM, Dan Christensen wrote:
> It seems "intuitively obvious" to me that classical propositional logic is applicable to statements that ARE (present tense) unambiguously true or false IN THE PRESENT.
>
> As to why it is not applicable to predictions of the future, Mark Thakkar, in his “Logic of the Future” makes an interesting point:
>
> "It is now commonplace to treat statements about the future as logically on a par with factual claims about the present and the past....
>
> “My principal argument for the claim that statements about the future have no truth-values is that otherwise they would have the standard entailments of propositional logic. For if ‘Brian will be in his study tomorrow’ is true, then it is true no matter what else is true.”
>
> https://www.st-andrews.ac.uk/~mnat/files/future.pdf
>
> Comments?

>
> Dan
>
> Download my DC Proof 2.0 freeware at http://www.dcproof.com
> Visit my Math Blog at http://www.dcproof.wordpress.com
>

Yes who knows maybe the living animal of baby kittens will become ten
story office buildings with windows and elevators at 10:00 AM tomorrow
morning. (I am not referring to a mere change of word labels).

It seems to be that you need to refresh yourself on the analytic /
synthetic distinction.

https://en.wikipedia.org/wiki/Analytic%E2%80%93synthetic_distinction#Carnap's_distinction

--
Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

[Jeffrey Rubard]

On Thursday, June 15, 2023 at 10:05:34 PM UTC-7, Dan Christensen wrote:
> It seems "intuitively obvious" to me that classical propositional logic is applicable to statements that ARE (present tense) unambiguously true or false IN THE PRESENT.
>
> As to why it is not applicable to predictions of the future, Mark Thakkar, in his “Logic of the Future” makes an interesting point:
>
> "It is now commonplace to treat statements about the future as logically on a par with factual claims about the present and the past....
>
> “My principal argument for the claim that statements about the future have no truth-values is that otherwise they would have the standard entailments of propositional logic. For if ‘Brian will be in his study tomorrow’ is true, then it is true no matter what else is true.”
>
> https://www.st-andrews.ac.uk/~mnat/files/future.pdf
>
> Comments?
>
> Dan
>
> Download my DC Proof 2.0 freeware at http://www.dcproof.com
> Visit my Math Blog at http://www.dcproof.wordpress.com

"Is this one of your traditional hobby-horses for 'the ignorant masses', guys? I can't quite remember."

[Jim Burns]

On 6/17/2023 3:14 PM, Dan Christensen wrote:
> On Saturday, June 17, 2023

> at 1:23:27 PM UTC-4, Jim Burns wrote:

>> On 6/17/2023 10:15 AM, Dan Christensen wrote:

>>> Weather forecasters
>>> "approximately" predict the future
>>> when they say, for example, that
>>> there is a 40% chance of rain tomorrow.
>>> They cannot attach a truth value to
>>> the proposition, "It will rain tomorrow."
>
>> You (DC) are saying
>> weather forecasters are not
>> stating theorems about rain tomorrow.

> Not exactly.
> When weather forecasters say that
> it is now raining in their region,
> they are stating a proposition that is
> unambiguously either true or false.
> When they forecast that
> there is a 40% chance of rain tomorrow,
> they are NOT stating such a
> true-or-false proposition since,
> whatever the weather is tomorrow,
> it will not be inconsistent with
> that forecast.

I know about two ways to read
|
| There is a 40% chance of rain tomorrow.
|
There may be more I don't know about.

1.
| In the population of tomorrows to which
| I have narrowed down the _actual_
| _occurring_ tomorrow, after a lot of
| satellite- and computer-work,
| 40% of those tomorrows will be rainy.

2.
| After a lot of satellite- and computer-
| -work, I 40% believe that the _actual_
| _occurring_ tomorrow will be rainy.

I think that rational agents are supposed
to follow the well-known laws of probability
under either interpretation. I'm not sure
how the difference matters.


My own spin on probability is flavored by
a long conversation with another poster.

There are some claims we can make about
an individual in some domain, and that claim
will be true or be false _no matter which_
individual we are referring to.

We call those claims "valid" and essentially
all of our mathematics focuses on the rare
claim of that no-matter-which type.

Those no-matter-which claims are the
exceptions. When we talk about days,
_it matters which_ day we refer to when
we say "That day is(was/will be) rainy".

Probability says that the claim
"Tomorrow will be rainy"
is 40% valid -- _which is 100% crap_
I know that. "Valid" is only for all true.
But I only need a better way to say it.
The laws of probability are clear enough.


In my opinion, many "paradoxes" of
probability spring from the mismatch between
the claims we want to make, which are
almost all of the "40% valid" type, and
the rare claims we find it intuitive to
think about, which are of the "100% valid"
type.

[Dan Christensen]

On Saturday, June 17, 2023 at 6:02:02 PM UTC-4, Jim Burns wrote:
[snip]

That the "experts" think there is a good chance that it will rain tomorrow should not be entirely dismissed.

> "Valid" is only for all true.
> But I only need a better way to say it.
> The laws of probability are clear enough.
>
>
> In my opinion, many "paradoxes" of
> probability spring from the mismatch between
> the claims we want to make, which are
> almost all of the "40% valid" type, and
> the rare claims we find it intuitive to
> think about, which are of the "100% valid"
> type.

The issue here isn't so much probability as the notion that statements about the future are somehow seen by many as logically on a par with factual claims about the present and the past. "It will rain tomorrow" is no more factual than "There is a 40% chance of rain tomorrow." (100% vs. 40% probability.) Compare these statements to the factual, "It is now raining here." Or "It is now NOT raining here."

[Jim Burns]

On 6/17/2023 11:09 PM, Dan Christensen wrote:
> On Saturday, June 17, 2023
> at 6:02:02 PM UTC-4, Jim Burns wrote:

>> Probability says that the claim
>> "Tomorrow will be rainy"
>> is 40% valid -- _which is 100% crap_
>> I know that.
>
> That the "experts" think
> there is a good chance that
> it will rain tomorrow
> should not be entirely dismissed.

I didn't express myself clearly enough.

I am not dismissing any experts.
I am dismissing my own mis-use of "valid"

A _valid_ claim is true of each individual
in the domain. That's what it means.

"40% valid" is like "four-cornered
triangle", an abuse of terminology.
But maybe you will grant me just
a little poetic license.

----
You put "" around the word "experts".
I find that confusing in that particular
context.

My experience with added "" has been
of its being used to distance the writer
from what's in the quotes.
| She's gone and hired a "TV star"
| to play the part.
| [Subtext: Others may call him a TV star.
| I do not.]
Sometimes called scare quotes.

However, here

> That the "experts" think
> there is a good chance that
> it will rain tomorrow
> should not be entirely dismissed.

the rest of the sentence does NOT
doubt the expertise of "experts".
Instead, the opposite of that.
Hence, my confusion.


I have also seen scare quotes used to
emphasize. I dislike that use.
Emphasis and skepticism are very different.
It's like throwing a handful of gravel
in your bean soup. Very disagreeable.

If that's what you're doing,
I ask you to stop it,
and never do it again, anywhere.

I offer my thanks, just in case
you were doing that and
you no longer will do that,
accepting my request.

[Jim Burns]

On 6/17/2023 11:09 PM, Dan Christensen wrote:

> On Saturday, June 17, 2023
> at 6:02:02 PM UTC-4, Jim Burns wrote:

[...]

> The issue here isn't so much probability
> as the notion that
> statements about the future
> are somehow seen by many as
> logically on a par with
> factual claims about the present and
> the past.
> "It will rain tomorrow" is
> no more factual than
> "There is a 40% chance of rain tomorrow."
> (100% vs. 40% probability.)
> Compare these statements to the factual,
> "It is now raining here."
> Or "It is now NOT raining here."

Approximately a million years ago,
I took writing course in which we spent
an academic quarter defining, discussing,
writing about, arguing about a handful
of widely-used terms that smuggle a lot
of baggage into our minds, tucked safely
beneath their lovely, well-crafted surfaces.

I remember "science" was one of the terms.
"Nature" was one.
"Fact" was one.

I'm sure that it seems to you (DC) that
the distinction you are making between
fact and non-fact is simple and obvious.

I think that what you're saying by making
that distinction is a lot of things,
many of which really need to be exposed
to the light of day if this discussion
is going to have any value.


Something I have found useful to do,
when I try to pin down what I mean by
something, is to say what I said before,
only without using that term.
Whatever verbal loop-di-loops I need to
fly in order to do that, that
is my definition.


I suggest that,
if you state the difference between
a claim about the past and
a claim about the future
without using the word "fact".
you will find it useful and interesting,

I suspect it might not be easy,
but I think that you will find
the effort well-spent.

[Mild Shock]

Dan Christensen halucinated "It seems "intuitively obvious"

to me that classical propositional logic is applicable to
statements that ARE (present tense) unambiguously true or

false IN THE PRESENT." Thats his fetish, Dan Christensen. He has
a couple of fetishes, which we have already encountered when
discussing counter factuals. Which he used as an argument

against counter factuals, since he believes a fact has a fixed
truth value, therefore there can be no counter factual. He confuses
facts with logic. But most of the time logic anyway

doesn't deal with facts. For example if we reason:

Humans are Mortal
Aristotele is Human
--------------------------------------
Aristotele is Mortal

We might think, ok there are two true facts involved. But then
we can also do the following:

Humans are Mortal
Unicorn is Human
--------------------------------------
Unicorn is Mortal

So already singular expressions in the present
are fictive, don't have a truth value. The sentences is
true, if either Unicorns are Human, or if Unicorns

are non Human.

[Mild Shock]

CLASSICAL PROPOSITIONAL LOGIC already works with
what the moron Dan Christensen calls ambiguouse truth. The
below has a CLASSICAL PROPOSITIONAL LOGIC core.

Singular expressions are already "termini", i.e. end-points
with a truth value, only the truth is ambiguouse. Thats the
job of logic to deal with that. George Boole solved the problem

in using polynomial x, y, z, etc.. variables with value 0 and 1:

human(unicorn)
mortal(unicorn)

Then the non-singular expression Humans are Mortal:

∀x(human(x) -> mortal(x))

Can be viewed as a series of singular combinations:

human(aristotele) -> mortal(aristotele)
human(unicorn) -> mortal(unicorn)

Or you can cast it in modern propositional logic, the formal
requirement of only having propositional variables, as folllows:

human_unicorn -> mortal_unicorn
human_unicorn
--------------------------------------
mortal_unicorn)

The inference rule is modus ponens. As long as your logic
has modus ponens, there is nothing about unambiguously
true in the logic. The logic can perfectly well deal with

ambiguous truth, such as human(unicorn). The moron Dan
Christensen might read George Boole. He required for his
polynomial variables only:

x * (1 - x) = 0

He didn't assume that they are not varying, i.e. constants.
Thats the point of logic, to have them varying. Aristotele is
said to have introduced the concept of variable into logic.

[Mild Shock]

Modus Ponens is also available in some non-classical
logics. For example in intuitionistic logic, a proof of:

A -> B

Might be read as a function:

f : A -> B, f sends a proof x of A to a proof f(x) of B.
https://en.wikipedia.org/wiki/Brouwer%E2%80%93Heyting%E2%80%93Kolmogorov_interpretation

Modus Ponens is the shema:

A A -> B
--------------------
B

Which can be viewed in BHK:

x : A f : A -> B
------------------------------
f(x) : B

So the justification for Modus Ponens is basically a form
of function application. This works perfectly well if A is
ambigious, there might be many x1,..,xn that justify A,

and the job of the implication is to send them to f(x1),..,f(xn)
that then justify B. Gentzen Cut Eliminiation studies some
effects of Modus Ponens on Proofs. Because Modus

Ponens is function application, and if f is itself composite,
then we can find that the justifictation x1,..,xn can pushed
down a proof tree, in the components of the composite f.

But nobody assumes that a justification of A needs to
be associated with an unambigious truth value of A. Thats
just nonsense and would lower the value of logic in mathematics

and rehtorics to practically zero. The prosition A could be some
varying empirical data. Or just some assumption which is
part of some discourse.

[Dan Christensen]

On Sunday, June 18, 2023 at 9:10:23 AM UTC-4, Mild Shock (aka Mr. Collapse) wrote:
> Dan Christensen halucinated "It seems "intuitively obvious"
> to me that classical propositional logic is applicable to
> statements that ARE (present tense) unambiguously true or
> false IN THE PRESENT."

If you want to talk about logical propositions, the truth-values of which may vary over time, classical propositional logic will not suffice. It's that simple, Mr. Collapse. Some form of temporal logic, e.g. predicate logic with a variable for time would then be required for consistency.

In classical propositional logic, we say, for example, that proposition P _is_ true, or that proposition Q _is_ false (both in the present tense). When we say that P implies Q, we mean only that it _is_ false that both P _is_ true and Q _is_ false. Or equivalently, that P _is_ false or Q _is_ true. There is no passage of time or chronological record of events or predictions of future events. In classical propositional logic, there is only that which _is_ true, and that which _is_ false.

I hope this helps.

[Mild Shock]

The proposition itself can express some future:

mortal_dan_christensen

To what time frame relative to now
does „mortal“ reference in your opinion?

[Mild Shock]

dead and mortal are two different words.
mortal means subject to death. hence these
two propositions have two different truth values.

/* I guess the truth value is currently FALSE */
dead_dan_christensen

/* I guess the truth value is TRUE */
mortal_dan_christensen

But I agree the truth value mortal Dan Christensen
could be controversal. Maybe Dan Christensen is
immortal? Who knows, or as Thomas Aquinas had it:

„Future contingents cannot be certain to us,
because we know them as such. They can be
certain only to God whose understanding is in
eternity above time. Just as a man going along
a road does not see those who come after him;
but the man who sees the whole road from a height
sees all those who are going along the road
at the same time.“

Dimitri finds out about his paper
https://m.youtube.com/watch?v=-9gBOuoqLRs

[Mild Shock]

So whats Dan Christensens choke point? He believes
his own nonsense, namely that „If you want to talk about

logical propositions, the truth-values of which may vary

over time, classical propositional logic will not suffice.“
He doesn’t know that propositions are not that restricted.
He confuses facts with propositions. But propositions

only refers to parts of sentence that can have true or
false value. The are nowhere restricted to present time
facts. Accordingly to his limited knowledge about

what the term proposition means. But he can read here
that propositons are not facts or events:

„Mit dem Ausdruck Proposition bezeichnet man in
der Linguistik, genauer gesagt in der linguistischen
Semantik, den Inhalt, der mit einem Satz (in einem
Kontext) ausgesagt wird. Propositionen haben als
wichtigste Eigenschaft, dass sie einen Wahrheitswert
annehmen, d. h. wahr oder falsch sein können[1] (im
Unterschied zu Fakten oder zu Ereignissen).
https://de.m.wikipedia.org/wiki/Proposition_(Linguistik)

So we can say Dan Christensen is a quite unprepared
crank, which can be easily ambushed. He didnt
take these lessons:

US Army Evasive Driving Training Video (1988)
https://m.youtube.com/watch?v=8u-XIjXS98Q

[Dan Christensen]

On Sunday, June 18, 2023 at 12:10:57 PM UTC-4, Mild Shock wrote:

> Dan Christensen schrieb am Sonntag, 18. Juni 2023 um 17:03:20 UTC+2:
> > On Sunday, June 18, 2023 at 9:10:23 AM UTC-4, Mild Shock (aka Mr. Collapse) wrote:
> > > Dan Christensen halucinated "It seems "intuitively obvious"
> > > to me that classical propositional logic is applicable to
> > > statements that ARE (present tense) unambiguously true or
> > > false IN THE PRESENT."
> > If you want to talk about logical propositions, the truth-values of which may vary over time, classical propositional logic will not suffice. It's that simple, Mr. Collapse. Some form of temporal logic, e.g. predicate logic with a variable for time would then be required for consistency.
> >
> > In classical propositional logic, we say, for example, that proposition P _is_ true, or that proposition Q _is_ false (both in the present tense). When we say that P implies Q, we mean only that it _is_ false that both P _is_ true and Q _is_ false. Or equivalently, that P _is_ false or Q _is_ true. There is no passage of time or chronological record of events or predictions of future events. In classical propositional logic, there is only that which _is_ true, and that which _is_ false.
> >

> The proposition itself can express some future:
>
> mortal_dan_christensen
>
> To what time frame relative to now
> does „mortal“ reference in your opinion?

Formalizing that most famous syllogism of antiquity using modern notation:

1 ALL(a):[Man(a) => Mortal(a)]
Axiom

2 Man(aristotle)
Axiom

3 Man(aristotle) => Mortal(aristotle)
U Spec, 1

4 Mortal(aristotle)
Detach, 3, 2

I don't think it can be stated in PROPOSITIONAL logic alone, i.e. without variables and a quantifier. In any case, no timeframe is specified here for the predicate Mortal. A variable for time might be introduced in a more detailed formalism with time of birth/death, etc.

[Mild Shock]

You can state it in propositional logic:

human_aristotele -> mortal_aristotele
human_aristotele
--------------------------------------
mortal_aristotele

Its just modus ponens.

[Mild Shock]

https://en.wikipedia.org/wiki/Modus_ponens

You might also have it in DC Proof? Don't you?

[Ross Finlayson]

It means several things.

Mostly what it means is that "ex falso quodlibet" results _not_ a proof. It's a mistake.

It's like whenever you make a stipulation, it's not "this is true", it's "this is stipulated".
Truth what follows is _only contingent_.

And, when it's mistaken, it's not "that wasn't true" it's "that stipulation was wrong".
(In closed theories, where for example incomplete theories reflect "tertium datur"
not "tertium non datur".)

Also there's "contradiction in a variable implies _nothing_ about an independent variable".

So, a false antecedent, when it's posed implication of a true positive antecedent, implies _nothing_,
and a true positive antecedent, does not imply _any_ false positive consequents.

That "~p v q" is an expression in Boolean values, is positively determinate in neither.

Most people's impressions of "truth tables" is the Boolean algebra determinately about them,
in terms of relations the ordered pairs of antecedents and consequents, called implication.
(The "causal".)

[Mild Shock]

Wrong thread Rossy Boy. Put some blinker fluid
into your car, so that you take the right turns.
The ex falso thread was another thread.

LoL

[Mild Shock]

Rossy Boy, thats quite irresponsible to drive without
blinker fluid. People might not be able to predict the
future which turn you will take. Now I used predict

and future, maybe we should make a car blinker example?
Also modus ponens is effectively irrelevant. Most likely
Dan Christensen denies that this is a proposition:

mortal_aristotele

But it has all the properties of a proposition as defined here:

/* Bablefish Translation */
In linguistics, more precisely in linguistic semantics,
the term proposition is used to describe the content that
is stated with a sentence (in a context). The most important
property of propositions is that they assume a truth value, i. H.
can be true or false[1] (as distinct from facts or events)

/* German Wikipedia */

„Mit dem Ausdruck Proposition bezeichnet man in
der Linguistik, genauer gesagt in der linguistischen
Semantik, den Inhalt, der mit einem Satz (in einem
Kontext) ausgesagt wird. Propositionen haben als
wichtigste Eigenschaft, dass sie einen Wahrheitswert
annehmen, d. h. wahr oder falsch sein können[1] (im
Unterschied zu Fakten oder zu Ereignissen).
https://de.m.wikipedia.org/wiki/Proposition_(Linguistik)

[Mild Shock]

You could also read Aristotle himself, to judge whether
the general consensus is that expressions that intensionally
refer to the future can be also proposition. He basically founded

already 2000 years ago modal logic, when he wrote:

t1 = “Tomorrow there will be a sea-battle”

t2 = “Tomorrow there will not be a sea-battle”

You can can make t1 v t2 true, in Modal Logik K, using
the possibility operator <> for "there will be", and the seriality
assumption, to assure that "there will be a tomorrow":

◇b ∨ ◇¬b
https://www.umsu.de/trees/#~9b~2~9~3b||seriality

[Mild Shock]

Wolfgang Schwartz tree tool gives me:

◇b ∨ ◇¬b is valid.
https://www.umsu.de/trees/#~9b~2~9~3b||seriality

If you model the two sentences like this, you even don't need seriality:

◇b ∨ □¬b is valid.
https://www.umsu.de/trees/#~9b~2~8~3b

Because ◇b is defined as ¬□¬b you could derive
it purely with propositional logic.

[Dan Christensen]

> You can state it in propositional logic:
>
> human_aristotele -> mortal_aristotele
> human_aristotele
> --------------------------------------
> mortal_aristotele
>

You seem to have missed the point. You might as well have said "bald" instead of "mortal." The quality in question is supposed to apply to ALL men.

The syllogism is usually stated:

All men are mortal. <-------- You missed this key assumption about men and mortality.
Socrates is a man.
__________________________________________
Therefore, Socrates is mortal.

[Mild Shock]

You are changing the topic. I don't want to discuss ALL =>.
The implication is irrelevant. Also the universal
quantifier. Because the topic is, what is a "proposition".

So I don't need this to discuss what is a "proposition".

1 ALL(a):[Man(a) => Mortal(a)]
Axiom

I want to discuss "closed formulas" such as:

Man(aristotle)
Mortal(aristotle)

Do they have the status of a parameterless "proposition"?
Where we assume they have either true or false value? If
something has either true or false, we can for example prove:

((A => B) & (~A => B) => B)

Now you have in the same formula A refering to a "proposition"
being true. And ~A refering to a "proposition" being false.
Is the same still valid if we replace A by Mortal(DanChristensen)

and B by Sun(Hot). Do you need FOL to prove the following?

((Mortal(DanChristensen) => Sun(Hot)) &
(~Mortal(DanChristensen) => Sun(Hot)) => Sun(Hot))

You seem to claim that it is impossible to apply propositional
logic reasoning to propositions that have not strictly the
syntactic shape "p". Whereas every logician will not hesitate

to confirm, that propositional logic reasoning applies
also to other shapes, like FOL shapes, i.e. "p(t1,..,tn)"
or to modal formulas, i.e. "[]p" where Box is a modal operator.

But you might not yet be ready for such insights.

Dan Christensen schrieb:

[Mild Shock]

Here is a proof of:

Mortal(danChristensen) => Hot(sun)
~Mortal(danChristensen) => Hot(sun)
---------------------------------------------------------------
Hot(sun)

I don't think it uses some FOL specific inference rules,
these are all inference rules also available in propositional
logic, i.e. Or Not, Join and Cases:

1 Mortal(danChristensen) => Hot(sun)
Axiom

2 ~Mortal(danChristensen) => Hot(sun)
Axiom

3 Mortal(danChristensen) | ~Mortal(danChristensen)
Or Not

4 [Mortal(danChristensen) => Hot(sun)]
& [~Mortal(danChristensen) => Hot(sun)]
Join, 1, 2

5 Hot(sun)
Cases, 3, 4

So don't worry. In case the sun is hot if you are mortal
or immortal, the sun is still hot.

[Dan Christensen]

> You are changing the topic. I don't want to discuss ALL =>.
> The implication is irrelevant.

> quantifier. Because the topic is, what is a "proposition".
>
> So I don't need this to discuss what is a "proposition".
> 1 ALL(a):[Man(a) => Mortal(a)]
> Axiom
> I want to discuss "closed formulas" such as:
>
> Man(aristotle)
> Mortal(aristotle)
>

OK, so you don't want to talk about Aristotle's famous mortality syllogism. (BTW the subject was Socrates, not Aristotle.)

Maybe you can explain how your "closed formulas" here allow us to attach truth values in the present to events that have yet to occur, i.e. to predict the future. Again, if you want to reason about propositions, the truth values of which may vary over time (e.g. whether or not it is raining at given time), you really should consider introducing a variable for time.

[Mild Shock]

You don't attach truth values permanently to closed formulas.
You assume truth values true or false, make it a supposition.
Thats why you have the inference rule Or Not in DC Poop.

What would Mark Thakkar say to the below DC Poop proof?
You cited “My principal argument for the claim that statements

about the future have no truth-values is that otherwise they

would have the standard entailments of propositional logic."

Is the below proof illegal? What does he mean by "would have"?
Does he completely exclude propositional entailment?

Or does he have certain forms of propositional entailment in mind?
For example there are certain modal logics where |- doesn't
behave like =>. Its not clear what Mark Thakkar quote means

for the below proof. And I doubt Dan Christensen knows either?

--------------------------------------- begin DC Proof --------------------------------------

1 Mortal(danChristensen) => Hot(sun)
Axiom

2 ~Mortal(danChristensen) => Hot(sun)
Axiom

3 Mortal(danChristensen) | ~Mortal(danChristensen)
Or Not

4 [Mortal(danChristensen) => Hot(sun)]
& [~Mortal(danChristensen) => Hot(sun)]
Join, 1, 2

5 Hot(sun)
Cases, 3, 4

--------------------------------------- end DC Proof --------------------------------------

[Mild Shock]

Well "Or Not" in DC Poop is not the best indicator that closed
formulas don't have permantly attached truth values. A good
example is maybe the drinker paradox:

∃x(Dx → ∀yDy) is valid.
https://www.umsu.de/trees/#~7x(Dx~5~6yDy)

If you had the false value attached to the closed formula
∀yDy, then you would have ¬∀yDy, and therefore ∃y¬Dy
as in your application of Russell Paradox. And then you

can make ∀yDy irrelevant. i.e. both provable ∃x(Dx → ∀yDy)
and ∃x(Dx → ∀yDy), namely the nonsense your
Generalized Drinker Paradox produces:

∃y¬Dy → ∃x(Dx → ¬∀yDy) is valid.
https://www.umsu.de/trees/#~7y~3Dy~5~7x(Dx~5~3~6yDy)

So maybe a logical test about "not permantly" attached,
would be some independence.

[Dan Christensen]

What about this "formalism" of yours suggests anything to do with the passage of time? It needs to be fleshed out a bit. I see nothing, for example, that might be a variable for time.

[Mild Shock]

For example normally you cannot prove:

p→¬p is invalid.
https://www.umsu.de/trees/#p~5~3p

But you can prove:

p→p is valid.
https://www.umsu.de/trees/#p~5p

If you attach the value false to p, suddently p→¬p becomes
also provable. As is seen here:

¬p → (p→¬p) is valid.
https://www.umsu.de/trees/#~3p~5(p~5~3p)

[Mild Shock]

Now you can make a drinker paradox, about a guy
sitting alone at home, and drinking at home. The home
drinking paradox deals with weekdays and the future.

Lets say D(x) doesn't stand that the drinker x drinks,
but it stands that the home alone drinker drinks on
weekday x. Is this generally valid:

/* There exists a weekday so that the home alone
drinker drinks all weekdays? */
∃x(Dx → ∀yDy)

[Mild Shock]

Now there are 7 weekdays, and therefore 128 possible
combinations, of weekdays drinking and not drinking.
Now if you are at the beginning of the week,

you nevertheless know that this formula is true,
without knowning the future, which pattern of the
128 possible combinations will consist the concrete

week just before you!

[Mild Shock]

I think there is a saying among mathematicians/physicists
that runs counter Mark Thakkar skepticism about reasoning
with the future. They say we live in a fourth dimensional

continuum, the 3 dimensions of space, and then there is
the 4th dimension of time. But its all the same geometry.
Unless you are from the projective geometry camp,

then you might even work with more dimensions.

[Mild Shock]

Some processes are even time reversible:
https://en.wikipedia.org/wiki/Time_reversibility

[Dan Christensen]

On Sunday, June 18, 2023 at 6:59:40 PM UTC-4, Mild Shock wrote:
> I think there is a saying among mathematicians/physicists
> that runs counter Mark Thakkar skepticism about reasoning
> with the future. They say we live in a fourth dimensional
> continuum, the 3 dimensions of space, and then there is
> the 4th dimension of time.

I'm fairly certain that when talking about quantities that vary over time, scientists are going to introduce a variable for time in their analysis. It's unavoidable.

[Mild Shock]

Yes, and they build expressions about the future.
Whereas Mark Thakkar claims, such expressions
cannot have a truth value, cannot be propositions,

and cannot have entailments of propositional logic.
Whereas usual mathematicians/physicists think
that each dimension, space or time, more or less

has the same logical rules. Right of you (x+1) and
Ahead of You (t+1), is just an adjacency relation.
For example you can use Peano Axioms for both

the location successor and the time successor.
Whereas according to Mark Thakkar the future is
so so so special, that (t+1) would not be Peano,

whereas (x+1) would be Peano?

[Mild Shock]

You literally cited Mark Thakkar "“My principal argument for

the claim that statements about the future have no truth-values
is that otherwise they would have the standard entailments

of propositional logic. "Take Peano, it has also "entailments of
propositional logic" for example the induction schema:

P(0) & ALL(a):[P(a) => P(a+1)] => ALL(b):P(b)

It obeys this truth table:

P(0) & ALL(b):P(b) P(0) & => ALL(b):P(b)
ALL(a):[P(a) => P(a+1)] ALL(a):[P(a) => P(a+1)]
F F T
F T T
T F F
T T T

According to Mark Thakkar , what is exactly the difference
between induction accross space, and induction accross time?
Does somebody know? Whats the difference between these two:

"If here it is sunny, and whenever it is sunny at some
location, it is also sunny to the left of this location, then its everywhere
sunny to the whole of the left"

"If here it is sunny, and whenever it is sunny at some
time, it is also sunny ahead of this time, then its everywhere
sunny to the whole of the future"

[Mild Shock]

Dan Christensen probably lacks the sensory to smell
whats behind Mark Thakkar vote. He still bounces back
and forth between some propositional logic versus FOL

syntactic viewpoint. But Mark Thakkar point of departure is
probably something totally different, most likely some
medieval or antique world view, which doesn't match the

modern world view, of time-space continuum. You can
read about the modern world view, for example here, this
was an attempt to give it a philosophical footing:

Whitehead's Process and Reality
"Process and Reality is a book by Alfred North Whitehead,
in which the author propounds a philosophy of organism,
also called process philosophy.

The book, published in 1929, is a revision of the
Gifford Lectures he gave in 1927–28."
https://en.wikipedia.org/wiki/Process_and_Reality

Process philosophy
"Process philosophy, also ontology of becoming, or processism,
is an approach in philosophy that identifies processes, changes,
or shifting relationships as the only real experience of everyday living.

In opposition to the classical view of change as illusory (as argued
by Parmenides) or accidental (as argued by Aristotle), process
philosophy posits transient occasions of change or becoming as the
only fundamental things of the ordinary everyday real world."
https://en.wikipedia.org/wiki/Process_philosophy

Most mathematics/physics today, what you find in math textbooks,
and what you claim to be able to formalize with DC Poop, of
course is based on process philosophy. Calculus with its idea

of a rate is of course based on a process philosophy as well, if
I am not totally mistaken.

[Dan Christensen]

On Monday, June 19, 2023 at 4:20:58 AM UTC-4, Mild Shock wrote:

> Dan Christensen schrieb am Montag, 19. Juni 2023 um 03:53:23 UTC+2:
> > On Sunday, June 18, 2023 at 6:59:40 PM UTC-4, Mild Shock wrote:
> > > I think there is a saying among mathematicians/physicists
> > > that runs counter Mark Thakkar skepticism about reasoning
> > > with the future. They say we live in a fourth dimensional
> > > continuum, the 3 dimensions of space, and then there is
> > > the 4th dimension of time.

> > I'm fairly certain that when talking about quantities that vary over time, scientists are going to introduce a variable for time in their analysis. It's unavoidable.

> Yes, and they build expressions about the future.

Yes, they can, for example, predict the time and place of solar eclipses with amazing accuracy. Such calculations, however, would be impossible using only classical propositional logic which has no variables such time and place.

> Whereas Mark Thakkar claims, such expressions
> cannot have a truth value, cannot be propositions,
>

[snip]

The truth value of the proposition, "A solar eclipse is occurring in London" varies over time. It's truth value tomorrow at noon cannot be determined with certainty until tomorrow at noon. As such, no truth value can currently be attached with certainty to the proposition that a solar eclipse is occurring in London tomorrow at noon.

[Mild Shock]

You are highly confused. Where do you see even the mention of
your concept "propositional variable", in Mark Thakkar quote?

“My principal argument for the claim that statements about the
future have no truth-values is that otherwise they would have the
standard entailments of propositional logic."

- Mark Thakkar

He refers to "standard entailments of propositional logic", which
means implication =>. His example here, which he thinks doesn't
have =>, is also not purely propositional variables:

‘Brian will be in his study tomorrow’

Whats wrong with you?
Nobody knows what you are talking about.
You surely not talking about Mark Thakkar quote.

[Mild Shock]

You can try and prove, a lot of future and standard entailments
of propositional logic, an impossibility according to Mark Thakkar:

If it rains John takes an umbrella
If John takes an umbrella he doesn’t get wet
If it doesn’t rain then John doesn’t get wet
------------------------------------------------------------------------------
John doesn’t get wet.

Here is a proof in DC Proof, the example is similar to what
I already did, i.e. ((A => B) & (~A=>B) => B).

R: It rains
U: John takes an umbrella
W: John gets wet.

---------------------------- begin proof --------------------------------

1 R => U
Axiom

2 U => ~W
Axiom

3 ~R => ~W
Axiom

4 R
Premise

5 U
Detach, 1, 4

6 ~W
Detach, 2, 5

7 R => ~W
Conclusion, 4

8 R | ~R
Or Not

9 [R => ~W] & [~R => ~W]
Join, 7, 3

10 ~W
Cases, 8, 9

---------------------------- end Proof --------------------------------

See also:
https://www2.cs.sfu.ca/CourseCentral/411/jim/

[Dan Christensen]

On Monday, June 19, 2023 at 10:35:56 AM UTC-4, Mild Shock wrote:
> You can try and prove, a lot of future and standard entailments
> of propositional logic, an impossibility according to Mark Thakkar:
>
> If it rains John takes an umbrella
> If John takes an umbrella he doesn’t get wet
> If it doesn’t rain then John doesn’t get wet
> ------------------------------------------------------------------------------
> John doesn’t get wet.
>
> Here is a proof in DC Proof, the example is similar to what
> I already did, i.e. ((A => B) & (~A=>B) => B).
>
> R: It rains
> U: John takes an umbrella
> W: John gets wet.
>

[snip]

Where does your prediction of the future come in? The daily weather forecast with its % chance of rain on the day in question? It will still be the forecast regardless of the actual weather.

[Jim Burns]

On 6/19/2023 4:31 AM, Mild Shock wrote:

> Whats the difference between these two:
>
> "If here it is sunny, and
> whenever it is sunny at some location,
> it is also sunny to the left of this location,
> then its everywhere sunny to
> the whole of the left"
>
> "If here it is sunny, and
> whenever it is sunny at some time,
> it is also sunny ahead of this time,
> then its everywhere sunny to
> the whole of the future"

The questions have embedded within them
certain assumptions about "left" and
"future" which are only true for
close and slow-moving agents.

Let us suppose that I stand on a planet
with a circumference of 24,901 miles.
24,900 miles to my left is 1 mile to
my right.

Let us suppose that I jog past you
on the street at 3 meters/second.
There is a galaxy 10⁹ light-years
from here for which 1 second of its
worldline is in my past and in your future.

Is the original point of
| Why predictions about the future
| have no truth value
|
to promote those assumption from
very good physical approximations to
logical truths?

----

> "If here it is sunny, and
> whenever it is sunny at some location,
> it is also sunny to the left of this location,
> then its everywhere sunny to
> the whole of the left"

My preference is to think of this as

| If here it is sunny, and

| there is no sunny/not-sunny edge,
| then it's everywhere sunny.

There are no points-at-infinity,
implicit or explicit, in this formulation.

[Mild Shock]

When rain drop falls from the sky it takes some
to arrive at Dan Christensense skull. It then makes
a hollow sound, because it falls on a void.

[Mild Shock]

So we are in the mists of the Sorites paradox

The sorites paradox (/soʊˈraɪtiːz/;[1] sometimes known as the
paradox of the heap) is a paradox that results from vague predicates.
https://en.wikipedia.org/wiki/Sorites_paradox

When is John wet? How long does it take? Can
propositional logic deal with sentences like "John get's wet".
Not only when is John wet, but also how long does it

take until "John get's wet" is true. What if he only gets
a little wet, and then the rain stops, and he drys up?
Maybe its easier to build a turing machine for a SAT

solver and run this here through it:

(R => U)&(U => ~W)&(~R=>~W) => ~W

Than to think whether we might need some angels or
devils help us to assign truth values to "John get's wet".
Maybe "John get's wet" even doesn't have truth values

at all? Maybe it has some gradual truth?

[Dan Christensen]

On Monday, June 19, 2023 at 6:08:07 PM UTC-4, Mild Shock wrote:
> So we are in the mists of the Sorites paradox
>
> The sorites paradox (/soʊˈraɪtiːz/;[1] sometimes known as the
> paradox of the heap) is a paradox that results from vague predicates.
> https://en.wikipedia.org/wiki/Sorites_paradox
>
> When is John wet? How long does it take? Can
> propositional logic deal with sentences like "John get's wet".
> Not only when is John wet, but also how long does it
>
> take until "John get's wet" is true. What if he only gets
> a little wet, and then the rain stops, and he drys up?
> Maybe its easier to build a turing machine for a SAT
>

Consider the conditional sentence: "If it is raining (R), then it is cloudy(C)." Here is the truth table:

R C R=>C
T T T
T F F
F T T
F F T

Now, the truth values of R and C will vary over time. The truth value of R=>C at time t can be determined only if the values of both R and C are know at time t. If, for example, we know only that both R(0) and C(0) are true, then the conditional R(0)=>C(0) will be true at time 0. On the other hand, if we know only that both R(0) and C(1) are true, we cannot determine the truth value of R(0)=>C(1).

[Ross Finlayson]

T T

[Mild Shock]

The example is from here, see lecture about propositional logic:

Knowledge Representation and Reasoning - Fall 2019
https://www2.cs.sfu.ca/CourseCentral/411/jim/

We can determine the truth value (for any now, like just now,
in the past now, or in the future now):

(R(now) => U(little_later))&(U(little_later) => ~W(later))&(~R(now)=>~W(later)) => ~W(later)

or for short of this propositional sentence:

(R => U)&(U => ~W)&(~R=>~W) => ~W

DC Proof tells me its a tautology. This doesn't say that R is
always true. It only says that the implication is always true,
i.e. the entailment as Mark Thakkar calls it.

But R can be true or false. Although the sentence is
always true as a whole supposedly that R(now), U(little_later)
and W(later) are bivalent, by the very definition of a tautology,

it is a sentence that is true, for all possible truth assignments
to the involved propositional variables. The term "tautology"
basically indicates that the truth functional of the formula

amounts to a constant function that always yields true.

--------------------------- begin proof --------------------------------

1 R => U
Axiom

2 U => ~W
Axiom

3 ~R => ~W
Axiom

4 R
Premise

5 U
Detach, 1, 4

6 ~W
Detach, 2, 5

7 R => ~W
Conclusion, 4

8 R | ~R
Or Not

9 [R => ~W] & [~R => ~W]
Join, 7, 3

10 ~W
Cases, 8, 9

---------------------------- end Proof --------------------------------

[Mild Shock]

You can also manually see that it is a tautology, i.e. all
rows are true, using the truth table technique. If you
assign probabilities not much changes, you could weight

each row of the truth table by some probability, you will
still have each row giving truth. Probability is interesting
if it would exclude a row, so that you have a probabilistic

tautology i.e. P(A) = 1, although its not a propositional
tautology, i.e. A is not generally valid. A probabilistic
tautology is for example:

P(~A) = 1, if we assume P(A)=0

But ~A is not a propositional tautology.

https://web.stanford.edu/class/cs103/tools/truth-table-tool/
R U W (((R → U) ∧ ((U → ¬W) ∧ (¬R → ¬W))) → ¬W)
F F F T
F F T T
F T F T
F T T T
T F F T
T F T T
T T F T
T T T T

[Mild Shock]

You can prove:

P(~A) = 1, if we assume P(A)=0

Using the second and third axiom of probability:

assumption of unit measure
https://en.wikipedia.org/wiki/Probability_axioms#Second_axiom

additivity of mutually exclusive event
https://en.wikipedia.org/wiki/Probability_axioms#Third_axiom

Since A and ~A are mutually exclusive,
we have P(~A) + P(A) = P(A v ~A) = P(Ω)
Now plugging in P(A) = 0 and P(Ω) = 1, gives:

P(~A) + 0 = 1

Solving for P(~A) gives P(~A)=1.

[Dan Christensen]

If we restrict our attention to propositions in the present tense, we can safely ignore the complications of temporal logic. See: https://en.wikipedia.org/wiki/Temporal_logic