it was quasimodo and britney spears and marylin manson
like omg right>>6200651
theY baked real kike muhjoos in gulag huh
yuge pedo network discovered
https://www.cmegroup.com/company/comex.html
they talk of "jews" too
The modus tollens rule may be written in sequent notation:
P → Q , ¬ Q ⊢ ¬ P {\displaystyle P\to Q,\neg Q\vdash \neg P} P\to Q,\neg Q\vdash \neg P
where ⊢ {\displaystyle \vdash } \vdash is a metalogical symbol meaning that ¬ P {\displaystyle \neg P} \neg P is a syntactic consequence of P → Q {\displaystyle P\to Q} P\to Q and ¬ Q {\displaystyle \neg Q} \neg Q in some logical system;
or as the statement of a functional tautology or theorem of propositional logic:
( ( P → Q ) ∧ ¬ Q ) → ¬ P {\displaystyle ((P\to Q)\land \neg Q)\to \neg P} {\displaystyle ((P\to Q)\land \neg Q)\to \neg P}
where P {\displaystyle P} P and Q {\displaystyle Q} Q are propositions expressed in some formal system;
or including assumptions:
Γ ⊢ P → Q Γ ⊢ ¬ Q Γ ⊢ ¬ P {\displaystyle {\frac {\Gamma \vdash P\to Q~~~\Gamma \vdash \neg Q}{\Gamma \vdash \neg P}}} {\frac {\Gamma \vdash P\to Q~~~\Gamma \vdash \neg Q}{\Gamma \vdash \neg P}}
though since the rule does not change the set of assumptions, this is not strictly necessary.
More complex rewritings involving modus tollens are often seen, for instance in set theory:
P ⊆ Q {\displaystyle P\subseteq Q} P\subseteq Q
x ∉ Q {\displaystyle x\notin Q} x\notin Q
∴ x ∉ P {\displaystyle \therefore x\notin P} \therefore x\notin P
("P is a subset of Q. x is not in Q. Therefore, x is not in P.")
Also in first-order predicate logic:
∀ x : P ( x ) → Q ( x ) {\displaystyle \forall x:~P(x)\to Q(x)} \forall x:~P(x)\to Q(x)
¬ Q ( y ) {\displaystyle \neg Q(y)} {\displaystyle \neg Q(y)}
∴ ¬ P ( y ) {\displaystyle \therefore ~\neg P(y)} {\displaystyle \therefore ~\neg P(y)}
("For all x if x is P then x is Q. y is not Q. Therefore, y is not P.")
Strictly speaking these are not instances of modus tollens, but they may be derived from modus tollens using a few extra steps.
run real fast and try and break a wall down with your forehead
Requirements:
The argument has two premises.
The first premise is a conditional or "if-then" statement, for example that if P then Q.
The second premise is that it is not the case that Q.
From these two premises, it can be logically concluded that it is not the case that P.
Consider an example:
If the watch-dog detects an intruder, the watch-dog will bark.
The watch-dog did not bark.
Therefore, no intruder was detected by the watch-dog.
Supposing that the premises are both true (the dog will bark if it detects an intruder, and does indeed not bark), it follows that no intruder has been detected. This is a valid argument since it is not possible for the conclusion to be false if the premises are true. (It is conceivable that there may have been an intruder that the dog did not detect, but that does not invalidate the argument; the first premise is "if the watch-dog detects an intruder." The thing of importance is that the dog detects or does not detect an intruder, not whether there is one.)
Another example:
If I am the axe murderer, then I can use an axe.
I cannot use an axe.
Therefore, I am not the axe murderer.
Another example:
If Rex is a chicken, then he is a bird.
Rex is not a bird.
Therefore, Rex is not a chicken.
Relation to modus ponens
Every use of modus tollens can be converted to a use of modus ponens and one use of transposition to the premise which is a material implication. For example:
If P, then Q. (premise – material implication)
If not Q, then not P. (derived by transposition)
Not Q . (premise)
Therefore, not P. (derived by modus ponens)
Likewise, every use of modus ponens can be converted to a use of modus tollens and transposition.
In instances of modus tollens we assume as premises that p → q is true and q is false. There is only one line of the truth table—the fourth line—which satisfies these two conditions. In this line, p is false. Therefore, in every instance in which p → q is true and q is false, p must also be false.
Modus tollens represents an instance of the law of total probability combined with Bayes' theorem expressed as:
Pr ( P ) = Pr ( P ∣ Q ) Pr ( Q ) + Pr ( P ∣ ¬ Q ) Pr ( ¬ Q ) {\displaystyle \Pr(P)=\Pr(P\mid Q)\Pr(Q)+\Pr(P\mid \lnot Q)\Pr(\lnot Q)\,} {\displaystyle \Pr(P)=\Pr(P\mid Q)\Pr(Q)+\Pr(P\mid \lnot Q)\Pr(\lnot Q)\,},
where the conditionals Pr ( P ∣ Q ) {\displaystyle \Pr(P\mid Q)} {\displaystyle \Pr(P\mid Q)} and Pr ( P ∣ ¬ Q ) {\displaystyle \Pr(P\mid \lnot Q)} {\displaystyle \Pr(P\mid \lnot Q)} are obtained with (the extended form of) Bayes' theorem expressed as:
Pr ( P ∣ Q ) = Pr ( Q ∣ P ) a ( P ) Pr ( Q ∣ P ) a ( P ) + Pr ( Q ∣ ¬ P ) a ( ¬ P ) {\displaystyle \Pr(P\mid Q)={\frac {\Pr(Q\mid P)\,a(P)}{\Pr(Q\mid P)\,a(P)+\Pr(Q\mid \lnot P)\,a(\lnot P)}}\;\;\;} {\displaystyle \Pr(P\mid Q)={\frac {\Pr(Q\mid P)\,a(P)}{\Pr(Q\mid P)\,a(P)+\Pr(Q\mid \lnot P)\,a(\lnot P)}}\;\;\;} and Pr ( P ∣ ¬ Q ) = Pr ( ¬ Q ∣ P ) a ( P ) Pr ( ¬ Q ∣ P ) a ( P ) + Pr ( ¬ Q ∣ ¬ P ) a ( ¬ P ) {\displaystyle \;\;\;\Pr(P\mid \lnot Q)={\frac {\Pr(\lnot Q\mid P)\,a(P)}{\Pr(\lnot Q\mid P)\,a(P)+\Pr(\lnot Q\mid \lnot P)\,a(\lnot P)}}} {\displaystyle \;\;\;\Pr(P\mid \lnot Q)={\frac {\Pr(\lnot Q\mid P)\,a(P)}{\Pr(\lnot Q\mid P)\,a(P)+\Pr(\lnot Q\mid \lnot P)\,a(\lnot P)}}}.
In the equations above Pr ( Q ) {\displaystyle \Pr(Q)} {\displaystyle \Pr(Q)} denotes the probability of Q {\displaystyle Q} Q, and a ( P ) {\displaystyle a(P)} {\displaystyle a(P)} denotes the base rate (aka. prior probability) of P {\displaystyle P} P. The conditional probability Pr ( Q ∣ P ) {\displaystyle \Pr(Q\mid P)} {\displaystyle \Pr(Q\mid P)} generalizes the logical statement P → Q {\displaystyle P\to Q} P\to Q, i.e. in addition to assigning TRUE or FALSE we can also assign any probability to the statement. Assume that Pr ( Q ) = 1 {\displaystyle \Pr(Q)=1} {\displaystyle \Pr(Q)=1} is equivalent to Q {\displaystyle Q} Q being TRUE, and that Pr ( Q ) = 0 {\displaystyle \Pr(Q)=0} {\displaystyle \Pr(Q)=0} is equivalent to Q {\displaystyle Q} Q being FALSE. It is then easy to see that Pr ( P ) = 0 {\displaystyle \Pr(P)=0} {\displaystyle \Pr(P)=0} when Pr ( Q ∣ P ) = 1 {\displaystyle \Pr(Q\mid P)=1} {\displaystyle \Pr(Q\mid P)=1} and Pr ( Q ) = 0 {\displaystyle \Pr(Q)=0} {\displaystyle \Pr(Q)=0}. This is because Pr ( ¬ Q ∣ P ) = 1 − Pr ( Q ∣ P ) = 0 {\displaystyle \Pr(\lnot Q\mid P)=1-\Pr(Q\mid P)=0} {\displaystyle \Pr(\lnot Q\mid P)=1-\Pr(Q\mid P)=0} so that Pr ( P ∣ ¬ Q ) = 0 {\displaystyle \Pr(P\mid \lnot Q)=0} {\displaystyle \Pr(P\mid \lnot Q)=0} in the last equation. Therefore, the product terms in the first equation always have a zero factor so that Pr ( P ) = 0 {\displaystyle \Pr(P)=0} {\displaystyle \Pr(P)=0} which is equivalent to P {\displaystyle P} P being FALSE. Hence, the law of total probability combined with Bayes' theorem represents a generalization of modus tollens [5].
Modus tollens represents an instance of the abduction operator in subjective logic expressed as:
ω P ‖ ~ Q A = ( ω Q | P A , ω Q | ¬ P A ) ⊚ ~ ( a P , ω Q A ) {\displaystyle \omega {P{\tilde {\|}}Q}^{A}=(\omega {Q|P}^{A},\omega {Q|\lnot P}^{A}){\widetilde {\circledcirc }}(a{P},\,\omega {Q}^{A})\,} {\displaystyle \omega {P{\tilde {\|}}Q}^{A}=(\omega {Q|P}^{A},\omega {Q|\lnot P}^{A}){\widetilde {\circledcirc }}(a_{P},\,\omega _{Q}^{A})\,},
where ω Q A {\displaystyle \omega {Q}^{A}} {\displaystyle \omega {Q}^{A}} denotes the subjective opinion about Q {\displaystyle Q} Q, and ( ω Q | P A , ω Q | ¬ P A ) {\displaystyle (\omega {Q|P}^{A},\omega {Q|\lnot P}^{A})} {\displaystyle (\omega {Q|P}^{A},\omega {Q|\lnot P}^{A})} denotes a pair of binomial conditional opinions, as expressed by source A {\displaystyle A} A. The parameter a P {\displaystyle a_{P}} {\displaystyle a_{P}} denotes the base rate (aka. the prior probability) of P {\displaystyle P} P. The abduced marginal opinion on P {\displaystyle P} P is denoted ω P ‖ ~ Q A {\displaystyle \omega {P{\tilde {\|}}Q}^{A}} {\displaystyle \omega {P{\tilde {\|}}Q}^{A}}. The conditional opinion ω Q | P A {\displaystyle \omega {Q|P}^{A}} {\displaystyle \omega {Q|P}^{A}} generalizes the logical statement P → Q {\displaystyle P\to Q} P\to Q, i.e. in addition to assigning TRUE or FALSE the source A {\displaystyle A} A can assign any subjective opinion to the statement. The case where ω Q A {\displaystyle \omega {Q}^{A}} {\displaystyle \omega {Q}^{A}} is an absolute TRUE opinion is equivalent to source A {\displaystyle A} A saying that Q {\displaystyle Q} Q is TRUE, and the case where ω Q A {\displaystyle \omega {Q}^{A}} {\displaystyle \omega {Q}^{A}} is an absolute FALSE opinion is equivalent to source A {\displaystyle A} A saying that Q {\displaystyle Q} Q is FALSE. The abduction operator ⊚ ~ {\displaystyle {\widetilde {\circledcirc }}} {\displaystyle {\widetilde {\circledcirc }}} of subjective logic produces an absolute FALSE abduced opinion ω P ‖ ~ Q A {\displaystyle \omega {P{\widetilde {\|}}Q}^{A}} {\displaystyle \omega {P{\widetilde {\|}}Q}^{A}} when the conditional opinion ω Q | P A {\displaystyle \omega {Q|P}^{A}} {\displaystyle \omega {Q|P}^{A}} is absolute TRUE and the consequent opinion ω Q A {\displaystyle \omega {Q}^{A}} {\displaystyle \omega {Q}^{A}} is absolute FALSE. Hence, subjective logic abduction represents a generalization of both modus tollens and of the Law of total probability combined with Bayes' theorem [6].
i thought finland resigned
and we all learned from revelations 3(colon)9 that jews lick nuttholes and lie about it
*buttholes
the muslims buried the last abraham in a pyramid cause it kept eating babies
du bist der Berliner mit Saurkrauter in deiner Lederhose Dorothy.
this is asstrumpet getting grounded for playing with muhjooskikes
here is grown up asstrumpet still playing with muhjooskikes
asstrumpet play nice with caprisun after getting scolded for muhjooskikeing and trannywhoreing
we believe in (you) assTrumppet
may the asstrumpet of the sepultura apocrypha larp it;s pedo handlers like a greek choir
here is asstrumpet trying to raise coaine prices for evangelicals and tax wash
zombies don;t eat
walrus
carpenter
O Oysters, come and walk with us!'
The Walrus did beseech.
A pleasant walk, a pleasant talk,
Along the briny beach:
We cannot do with more than four,
To give a hand to each.'
The eldest Oyster looked at him,
But never a word he said:
The eldest Oyster winked his eye,
And shook his heavy head —
Meaning to say he did not choose
To leave the oyster-bed.
But four young Oysters hurried up,
All eager for the treat:
Their coats were brushed, their faces washed,
Their shoes were clean and neat —
And this was odd, because, you know,
They hadn't any feet.
Four other Oysters followed them,
And yet another four;
And thick and fast they came at last,
And more, and more, and more —
All hopping through the frothy waves,
And scrambling to the shore.
The Walrus and the Carpenter
Walked on a mile or so,
And then they rested on a rock
Conveniently low:
And all the little Oysters stood
And waited in a row.
The time has come,' the Walrus said,
To talk of many things:
Of shoes — and ships — and sealing-wax —
Of cabbages — and kings —
And why the sea is boiling hot —
And whether pigs have wings.'
But wait a bit,' the Oysters cried,
Before we have our chat;
For some of us are out of breath,
And all of us are fat!'
No hurry!' said the Carpenter.
They thanked him much for that.
A loaf of bread,' the Walrus said,
Is what we chiefly need:
Pepper and vinegar besides
Are very good indeed —
Now if you're ready, Oysters dear,
We can begin to feed.'
But not on us!' the Oysters cried,
Turning a little blue.
After such kindness, that would be
A dismal thing to do!'
The night is fine,' the Walrus said.
Do you admire the view?
It was so kind of you to come!
And you are very nice!'
The Carpenter said nothing but
Cut us another slice:
I wish you were not quite so deaf —
I've had to ask you twice!'
It seems a shame,' the Walrus said,
To play them such a trick,
After we've brought them out so far,
And made them trot so quick!'
The Carpenter said nothing but
The butter's spread too thick!'
I weep for you,' the Walrus said:
I deeply sympathize.'
With sobs and tears he sorted out
Those of the largest size,
Holding his pocket-handkerchief
Before his streaming eyes.
O Oysters,' said the Carpenter,
You've had a pleasant run!
Shall we be trotting home again?'
But answer came there none —
And this was scarcely odd, because
They'd eaten every one."
book of doge and tacos and saurkrauters in dorothy's berliner
>>6194077 du bist der Berliner mit Saurkrauter in deiner Lederhose Dorothy.
canteen dues
did asstrumpet post some more?
i got filters so idk yet
#gayestshotgunwedding #ever
here is asstrumpet getting sworn in by teh cetral ass investagtors
even russian bots know how to play asstrumpet