I've always been fascinated by the use of rhetorical devices, including informal logical fallacies, especially when they are used deliberately to mislead. Listen to any politician, religious apologist or any debate where there is real or imagined controversy (e.g. climate change) and you will always find examples of informal fallacious reasoning.
Logical reasoning is the process of using structured & rational thoughts/ideas/facts/rules/data/evidence to draw sound conclusions in the search for truth (i.e. the explanation that best describes reality). It is a form of critical thinking where one or more statements or facts (the premises) are used to reach a conclusion that is supported by the premises. The classic example is ...
Premise 1: All men are mortal
Premise 2: Socrates is a man
Conclusion: Socrates is mortal
This is an example of a syllogism (two premises and a conclusion) and the use of deductive reasoning. Logical arguments/reasoning require at least two premises (a major and a minor) but can have more; for example:
Premise 1: All humans are mortal
Premise 2: Socrates is a human
Premise 3: All mortal things eventually die
Conclusion: Therefore, Socrates will eventually die
For the conclusion to be valid, all the premises must be true. Logical fallacies can arise when either one or more premises are unsound or the conclusion does not rationally follow from the premises. For example:
Premise 1: All humans have two legs
Premise 2: I am human
Conclusion: Therefore, I have two legs
Logically, the argument is valid and I do, indeed, have two legs. However, the first premise is factually incorrect because some humans have fewer than two legs. Therefore, the conclusion will not be valid in all cases.
Here is another example of unsound logic where the premises are true but the conclusion is not valid because other types of bird (e.g. carrion crow) are also black
Premise 1: All ravens are black
Premise 2: The bird in this cage is black
Conclusion: Therefore, this caged bird is a raven
So, a sound syllogism (logical argument) must be logically valid (i.e. the conclusion follows the premises) AND have true premises. The argument is unsound if it fails either of these two conditions.
It is not uncommon in debates, discussions, arguments and everyday conversations to be presented with only the conclusion (Socrates is mortal) without any supporting premises. The premises may be innocently omitted for brevity because the speaker assumes the premises are accepted as universal truths. The alternative is that the speaker is using the omission as a rhetorical device to hide their fallacious reasoning. Do not be afraid to ask for the premises to be explicitly defined so that you can verify their truthfulness.
For example, someone who does not believe that global warming is happening might say "climate change is a hoax!"
When you ask them for evidence to support that argument, they might offer ...
Premise 1: If the earth is warming, cold nights are a thing of the past
Premise 2: It was frosty last night
Conclusion: Therefore, climate change is a hoax!
The current scientific evidence does not indicate the immediate disappearance of the winter season so we will continue to experience cold weather and snowfall at the appropriate time of the year. Premise 1 is therefore false which makes the conclusion unsound.