One doesn't need the missing evidence which cannot be produced for one reason or the other, when it exists, one can reason it into existence using what is known in relation to what is claimed.
By the same mode one can reason out of existence what is claimed to exist by means of what is known of the thing claimed: IPIU's; Invisible Pink Internet Unicorns, The Easter Bunny, Sqeaky Clean Clergymen. The Tooth Fairy, Honest Politicians, Santa Claus ... you name it.
The way to do this is by means of deductive arguments that are valid and sound. They are considered to be proof when they cannot, logically, be refuted.
(There exist exceptions, but exceptions are not the rule; the rule is)
A claim, usually in the form of a conclusion, is meant to be a definite proposition. Hopefully it is derived through valid (correct) inference (deduction) using sound (true) premises and the truth of the conclusion then, necessarily follows from the premises which necessarily follow from each other. Quite often this is not the case.
A deductive argument provides in true premises to establish a definite proposition; the conclusion. When the premises are true, the conclusion, derived from the true premises, must also be true. Deductive arguments are conclusive.
A sound argument is defined as an deductive argument whose premises are (shown) sound and are logically connected to each other through valid inference. A sound argument therefore, always arrives at a true conclusion; the definite proposition.
What matters in the end is whether the evidence is sound; justifying the premises of an argument, and whether the argument form is valid; proper inference. When a deductive argument is valid and sound, its conclusion is true - no matter how disturbing that conclusion, no matter how counter-intuitive or emotionally unsatisfying it may be.
When none of this applies, chances are, those involved are philosophizing, i.e., discussing possibilities/probabilities.
Discussion has no real rules, except common courtesy. In discussion, parties involved might be trying to establish some sort of consensus, i.e., whether they agree or disagree - (dis)agreement however, doesn't render anything less or more true/false.
The problem that often arises is that when discussion gets heated, it turns debate. That's where the tricky parts comes in. Since the line between discussion and debate no longer appears to exists, participants then often say "I agree", meaning "that is true" and vice versa or "I disagree", meaning "that is false" and vice versa. Those involved are now operating two modes simultaniously, often without realizing it. Miscommunications galore occur. "Reasoning 101" might be handy then.
Not convinced yet? See below.
When evidence is empirical in nature,
anecdotal evidence is not really needed.
The vice versa however, is not equally true,
no matter how popular that opinion seems to be.
Thinking, Reasoning, Evidence, Inference, Logic, Proof ... and Stuff
An argument is a form of reasoning whereby one gives a reason or reasons in support of some claim. The reasons are called premises and the claim one tries to support with them is called the conclusion.
In logic, an argument is a set of declarative sentences known as premises along with another declarative sentence known as the conclusion.
A deductive argument asserts that the truth of the conclusion is a logical consequence of the premises that are non-ambiguous.
An inductive argument asserts that the truth of the conclusion is supported by the premises since they are ambiguous.
Since deductive arguments are considered the most rigorous and convincing, each premise and conclusion of a deductive argument are only either true or false, not ambiguous.
The statements comprising a deductive argument are referred to as being either true or false, not as being valid or invalid. Arguments are referred to as being either valid or invalid, not as being true or false. Whichever term is used, each premise and conclusion of a deductive argument must be capable of being true or false and nothing else; they are the truthbearers.
A deductive argument postulates, as a maxim or axiom, the truth of the conclusion as a logical consequence of sound premises.
An argument is a set of declarative sentences known as the premises and the conclusion.
An argument is referred to as being valid or invalid
The premises comprising a deductive argument are referred to as being true or false.
A valid argument with sound premises is considered to be logically correct reasoning.
"An argument is a connected series of statements to establish a definite proposition". -- Monty Python
The building blocks of an argument are propositions, also called statements. A proposition (not to be confused with preposition) is a statement which is either believed, doubted or denied or is either true or false. To produce a valid argument however, a few things are imperative:
Firstly - One or more propositions are necessary for an argument to continue. Propositions therefore, must be stated explicitly. They are called the premises of an argument. They are the evidence (or reasons) for accepting arguments and their conclusions. Premises (assertions) are often indicated by phrases such as "because", "since", "obviously"(*) and so on.
Secondly - The premises of the argument are used to obtain further propositions. This process is known as inference. In inference, we start with one or more propositions which have been accepted. We then derive a new proposition. The propositions arrived at by inference can then be used in further inference. Inference is often denoted by phrases such as "implies that", "thus", "therefore" and so on.
Thirdly - We arrive at the conclusion of the argument, another proposition. The conclusion is often stated as the final stage of inference. It is affirmed on the basis of the accepted premises and the valid inference from them. Conclusions are often indicated by phrases such as "therefore", "it follows", "hence" and so on.
A conclusion is meant to be a definite proposition derived through a deduction that is valid using sound premises. The truth of the conclusion necessarily follows from sound premises which necessarily follow from each other through valid inference.
"When you have eliminated the impossible, whatever remains, however improbable, must be the truth." -- Arthur Conan Doyle (Sherlock Holmes)
Not all arguments follow the mode described above. Arguments known as 'universal truth' often state only one premise and a conclusion: "when you don't breath, you die"; or only the conclusion: "water is wet", "pain hurts". This is perfectly valid. These kind of arguments, where the stated (explicit) necessarily implies the non-stated (implicit), are used for conveniece sake; "stating the obvious" to cut long stories short or to emphasize a point.
Also, arguments do not per se follow the order described above. Quite often the conclusion is stated first and the premises in support of the conclusion afterwards. This is perfectly valid as well, although somewhat confusing at times.
There are two traditional types of argument, deductive and inductive.
A deductive argument provides in true premises to establish a definite proposition; the conclusion. When the premises are true, the conclusion, derived from the premises through valid inference, must also be true.
Deductive arguments are conclusive since its premises are non-ambiguous.
An inductive argument provides in premises with some evidence for the truth of the conclusion. Inductive arguments are not valid or invalid, they are better or worse than other arguments depending on how probable their premises are.
Inductive arguments are generalizations since its premises are ambiguous.
There is one very important thing to keep in mind: the fact that a deductive argument is technically valid does not imply its conclusion holds.
However, when a technically valid and deductive argument is also logically sound, the one thing we cannot do is reach a false conclusion (through valid inference) from premises that are true. The argument is then sound.
A sound argument is defined as a valid argument whose premises are (shown) true and logically connected to each other through valid inference. A sound argument therefore, always arrives at a true conclusion; the definite proposition.
What matters in the end is whether the evidence is sound, justifying the premises of an argument, and whether the argument form is valid. When a deductive argument is valid and sound, its conclusion is true - no matter how disturbing that conclusion, no matter how counter-intuitive or emotionally unsatisfying it may be.
May all your deductive arguments be sound.
Incredulity is not an argument against, rather an argument for
(*) The phrase "obviously" is often viewed with suspicion, as it can be used to intimidate others into accepting dubious premises. If something doesn't seem obvious, don't be afraid to question it. You can always say "Oh, yes, you're right, it is obvious" when you've heard the explanation. Also, faulty, or fallacious, arguments can arrive at true conclusions.
Fallacious arguments can arrive at true conclusions.
Arguing therefore, that a proposition is false merely on the grounds that it has been presented as the conclusion of a fallacious argument is a fallacy fallacy.
Other sorts of logic obey different rules. When people talk of sound reasoning, logical valid arguments etc., they (mean to) refer to reasoning as described above. See: 'Socrates', Plato, Aristotle etc..