Affirming the consequent, evidence and probability

Affirming the consequent takes the form "P implies Q, therefore Q implies P." So you can make inferences in your day-to-day life, while being logical - as long as you assume P before you infer Q. If you assume Q, you cannot - logically - make any inferences about P.

At least, that's how it goes in theory. In practice, strict logic is completed with reason, usually in the form of empirical evidence.

Typically inferring P from Q is fallacious because Q (the output) could have many inputs (not just P). In your example, the dishes left in the sink (Q) could be the result of your family eating dinner (P), but could also be the result of them eating lunch (say, R). Thus, you couldn't say that because you observed Q, it must be because of P...

...however, there are times when P is the only input for Q, either in reality or within reason. Take this example:

"If I enter my Logically Fallacious password wrong [P], the website will say 'wrong password' [Q]. The website says 'wrong password' [Q], therefore I entered my password wrong [P]."

It seems like we affirmed the consequent, doesn't it? But remember what I said about strict logic being supported with reason. It is near-impossible that the system would show 'wrong password' for any reason other than your password being wrong. Therefore, the other hypothetical inputs are irrelevant: if you observe Q, you are within reason to suggest P was the cause.

This is now roughly equivalent to "if P, then Q" since P is the only cause of Q! This means if we assume P, Q will follow, and if we observe Q, it can only come from P.

I asked a similar question about Denying the Antecedent back in July 2020 - have a look at that conversation, it'll probably interest you.

There's a difference between a conclusion being certain and a conclusion being reasonable .  In formal logic, if A –> B and B–> C, then A –> C – (In other words, if A happens, then B has to happen and if B happens, then C has to happen so if A happens, C has to happen.)  C must be the case because of the flow of logic – there's no alternative, so we'd say it's "logical" and not fallacious.  

However, with the dirty dishes example, the statements would have to take this form:  If we've eaten, dirty dishes are likely to be in the sink.  That's a very different statement from saying If we've eaten, then there's no possibility other than dirty dishes in the sink.  I'm not sure it's correct to assume that a recent meal is the only way dirty dishes can end up in the sink.  The dirty dishes could have been washed and put back in the cupboard already; the dirty dishes could be in the dishwasher; the dirty dishes could still be on the table.  The dirty dishes example is speaking more about the likelihood of a connection between elements rather than a strict causal relationship.

I wouldn't say you're affirming the consequent ... I'd say you're selecting the most likely explanation.  That's not a fallacy, if you're clear that you're playing the odds.  If you are saying that there is no explanation for dirty dished in the sink other than that your family just ate, then you'd be moving into fallacy territory where the premise would be false.

Similarly, for the wrong password example, I would suggest that typing in the wrong password is the most likely explanation; however, it's also possible that you typed things in perfectly correctly ... with the Caps Lock on ... or ... that something in your keyboard's mechanism is sticking and not all keystrokes register ... or ... that someone else changed the password and you used the former one ... or ... .  As with the dirty dishes example, if you assume your mis-typing is the only possible cause and keep on entering the same series of characters without checking the Caps Lock and without making sure each keystroke feels normal and without checking for a changed password ... and get more and more frustrated because the password is always rejected and you "know" that the only possible explanation is your typing skills ... then, there's a fallacy in action, connected with a false premise.  If you try typing the known password a second time and still it gets rejected so you start searching for another explanation ... we'll, now you'd be working in the realm of "most likely explanation" and accepting that, in this case, the most likely explanation might not be the actual explanation.

Hi, Alex!

“This is clearly affirming the consequent, yet it’s also clear that the argument is very reasonable (at least to me.)”

Part of what makes affirming the consequent fallacious is precisely that it deceptively poses as a reasonable inference. Yet it is a mistake in reasoning, hands down. 

“Sure, there are other possible explanations, including very crazy ones like aliens having done that, but what comes to the mind first seems to be most likely correct one. So… is this still a fallacy anymore? I mean like if it is then there’s a big problem:”

There is only the illusion of a big problem. The illusion of there being a problem arises when different kinds of arguments are conflated. This is because different kinds of arguments are good or bad for different kinds of reasons. Accordingly, the three steps of separating good arguments from bad ones are as follows.

1. Identify whether an argument has been given
2. Analyze the argument 
3. Evaluate the argument 

You have identified an argument concerning the claim that your family ate dinner, per step 1. Analyzing the argument will involve determining whether the argument is deductive, inductive or other. If analysis reveals that the argument is deductive, you may then evaluate it according to the criteria that applies to deductive arguments. If the analysis reveals that the argument is inductive, you may then evaluate it according to the criteria that applies to inductive arguments. 

You see, you skipped the analysis step and went straight to the evaluation. You assumed your argument was an argument to the best explanation, but evaluated it as a deductive argument, and consequently saw that your evaluation created “big problems” for other kinds of arguments, ultimately escalating to skepticism concerning all ability to make any inferences. This highlights the importance of careful analysis. 

Here is basically how to approach the three arguments you posted about, and any argument in general:

You have identified an argument concerning your family eating dinner (step 1). It is a deductive argument (step 2). It is fallacious, according to the criteria for what makes a good or bad deductive argument (step 3.) 

You have identified an argument concerning fossils (step 1.) It is an argument to the best explanation (step 2.) It may or may not be good, depending on the criteria for those kinds of arguments (step 3.)

There is an argument concerning the existence of God (step 1.) It is a certain kind of argument (step 2.) It may be good or bad, depending on the criteria for those kinds of arguments (step 3.) 

As enjoyable as it is to spot fallacies and evaluate arguments, your post reminds us of how crucial a preceding analysis is. 

Thank you, Alex 

From, Kaiden 

In Deductive logic, Affirming The Consequent is a Fallacy.   However, in both Inductive and Abductive  logic, it is not necessarily a fallacy. A detective sees fingerprints on the murder weapon.  It is not unreasonable—in fact it is reasonable —to theorize that the person with those fingerprints used the gun. Since it’s not deductive, the conclusion doesn’t follow with certainty but it is reasonable to so theorize.  Scientists formulate theories based on conditions they see and theorize what caused them.  Inferring from an effect to a cause is a fallacy if there is either a claim that the cause followed by necessity, or if the connection to the purported cause is unreasonable (False Cause fallacies).  But everyone everyday makes reasonable conclusions based on seeing consequents and concluding the cause (antecedent).