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So I'm not sure whether the following statement is a logical fallacy but it seems to me like it is.

If statement A is true then statement B must be true as well.

Not sure if I properly constructed the logical reasoning here very well. I'm new to the study of logic and arguments but it seems very fun.

The following reasoning is one of the most common ones that i find on the web and in everyday social settings

Ex:

"I'm going to use a proxy for all web activities"
"Oh you are using proxies, you must be hiding something."

that guy dyed his hair red
gay guys dye their hair
so that guy must be gay

let's assume person x has no military background or interest in joining.
Person x decides to buy guns and research military tactical techniques.
Person y says : oh he must be violent and plans to do something crazy.

Please tell me if all set of statements I proposed fall under the same logical fallacy--if of course they can be considered as such.

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For starters:
An argument is valid if and only if when all the premises are true, then the conclusion is true.
An argument is sound if and only if it is valid and all its premises are true

As for the logical form of your example arguments, you could formulate them as syllogisms - where a conclusion is made from two premises, each sharing a term in the conclusion and a term not in the conclusion.

Argument #1a)
Premise #1) Person X uses a proxy for their web activities.
Premise #2) All people who use a proxy for their web activities are hiding something.
Conclusion) Person X is hiding something.

This is a valid and sound argument, but, only trivially in the sense that proxy servers hide the users ip addy. Note tho that language use (and definition of terms) can be ambiguous. For example, in a trivial sense it does follow that using proxies necessarily entails that you are actually hiding something because the use of a proxy hides your i.p. addy. The implication that you are being deceitful, however, does not necessarily follow from the use of a proxy. Using "hiding something" to conclude deceit as a result of this reasoning would be a deductive fallacy:

Argument #1b)
Premise #1) Person X uses a proxy for their web activities.
Premise #2) All people who use a proxy for their web activities are hiding something.
Conclusion) Person X is deceitfully hiding something.

And this would be unsound:

Argument #1c)
Premise #1) Person X uses a proxy for their web activities.
Premise #2) All people who use a proxy for their web activities are deceitfully hiding something.
Conclusion) Person X is deceitfully hiding something.

Argument #2)
Premise #1) Person X dyed their hair red.
Premise #2) Some people that dye their hair red have trait Y.
Conclusion) Person X has trait Y.

The argument is not valid as only some and not all people with dyed red hair have trait Y - i.e. it does not follow that "dyeing hair red" entails "trait Y".

Note the distinctive uses of "some" and "all" in these two examples.

Lastly, I think we can also squeeze your third example argument into a syllogistic form to demonstrate its truth or fallacy:

Argument #3a)
Premise #1) Person X bought a gun.
Premise #2) Some people who buy guns plan crazy violence.
Conclusion) Person X is planning crazy violence.

Like the second example, it does not follow that Person X necessarily intends crazy violence. If however, premise #2 were true in this reformulation:

Argument #3b)
Premise #1) Person X bought a gun.
Premise #2) All people who buy guns plan crazy violence.
Conclusion) Person X is planning crazy violence.

...then the argument would be valid and sound.

As for interpreting the combination of Person X's lack of military background, lack of interest in joining the military and interest in researching military tactics... well, I'd recommend studying logistics instead of tactics ;)

Hope that helps. If you enjoy this kinda stuff, you might dig Harry J. Gensler's website: http://www.harryhiker.com/lc/

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In the second example (red hair), the middle term of the syllogism is not distributed. The absence of distribution prevents a link between the two premises. Thus the reasoning fails.

The general form is the syllogism AAA in the second figure: All S are M; All P are M; Thus All S are P. The A statement distributes only the subject, not the predicate, so AAA-2 never distributes the middle term M.

In the example, the major premise is: If gay guy, then dyes hair. The minor premise is: If a person is this guy, then dyes hair. The premises fail to distribute the middle term (hair).

Syllogism AAA in the second figure is probably the only syllogism with an informal name in common use. This fallacy produces guilt by association.

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This is called causality. Systems have inputs and outputs (called also action and reaction). When we know that an input WILL cause an output, we recognize causality. We know all the systems we live with. So we know the planet system, the action and the reaction of the environment when we jump. If we jump, we always fall down. Causality proves true again. But if you jump and you start floating, causality is probably broken. Causality never breaks on our visible environment. But causality is broken on quantum physics. We can prove several times that particles disappear and appear on distant places, and those are not the causality laws we know. You can get crazy if you see an object disappear in front of your eyes: causality is our most elementary reasoning element.

But you seem to refer also to the rhetoric of the affirmation, that can be just garbage. I can say "If I jump, I will fly until venus". But that does not mean it is true. Does not mean that it will force causality to behave in a different way.

If you know that one input through a systems SOMETIMES cause an output, that is not called causality, but probability.

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