The kids blamed the dog
for the footprints.
Given Y, then X.
Given X, then certainly/probably/possibly/maybe/hopefully Y.
A sign is a thing the presence or absence of which indicates the presence or absence of some other thing: a shadow, a reflection, an imprint, a sound, a hound not barking in the night. Signs are important forms of evidence because they enable inference with varying degrees of certainty.
Forensic rhetoric, Arsitotle said in Rhetoric there are three genres of rhetoric:
forensic -- (aka judicial) deals with determining if an event did or did not take place and the justice of it's having or not having taken place
deliberative -- (aka political) deals with the future, rather than the past, and is concerend with deciding the best course of action, where best is defined as the most expient thing to do
epideictic -- (aka ceremonial or ritualistic) deals with the current situation and is focused on amplifying the audiences existing beliefs and is focused on gaining praise for the speaker's efforts.
the kind of thinking and speaking relevant when accusing someone of wrong-doing our defending yourself against someone else's accusation, supplied our ancient predecessors with an endless source of material to practice arguments from signs. See for example Greek Declamation, DA Russell or "Schoolroom and Courtroom" , Michael Winterbottom. Think CSI or Sherlock Holmes or Agatha Christie, to name a couple of relatively contemporary creative examples of how forensic signs are still used.
Signs also play a part in deliberative rhetoric via forecasting -- in deciding what to do based on what one thinks current conditions indicate about what will happen in the near future. In ancient Greece, some people believed that the entrails of animals or the shape of clouds indicated the course of future events. While augury and divination are no longer credible, we still look to the clouds, if only to predict the weather. The news is full of "leading indicators." And you can get a degree in the field of predictive analytics, the practice of sifting oceans of data to locate purchases certain kinds of people have made in the past that suggest a plausible bet on what similar kinds of people are likely to buy in the future see for example Predictive Analytics, Eric Siegel or The Signal and the Noise, Nate Silver.
Aristotle offered two categories of signs: infallible and fallible.
An infallible sign is one where the connection between two events is causal -- a shadow indisputably indicates the presence of a physical body. One may infer with certainty from the cause to the effect or backward from the effect to the cause because the first always produces the second. The fallacy of post hoc, ergo propter hoc occurs when temporality is confused with causality: just because two things happen in sequence does not mean that the first caused the second or that the two are related in any way at all.
Fallible signs are the most common. They only suggest the presence (or likelihood) of a prior (or future) event.
We might refine Aristotle's heading of infallible signs by adding probable, improbable, prejudicial, superstitious, and absurd fallible signs.
A probable sign (Eoikos resemblance) is one where the connection between two events is strong enough that we will feel pretty secure in inferring the presence of one from the other.
An improbable sign is one where the connection between two events is unlikely but possible.
Is there a less wished for and therefore more likely explanation?
A prejudicial sign is one where an inference is drawn about a person based on the presence of a stereotypical characteristic.
Is this sign an accident or an intentional signifier? Is there a chance you are being played?
A superstitious sign is one where the link between two events is purely associative.
Most people engage in ritualistic behavior of some kind, often knowing what they are doing has only a psychological effect but doing it anyway.
An absurd sign is one where two events are linked by imagination alone.
Does adding individual signs up lead to an increase in likelihood? If a person who has been accused of a crime had means, motive, and opportunity, are they more likely guilty than someone who had means and motive alone? If all three conditions need to be met in order to have a viable suspect, that is a person who might be convicted and hopefully also have done the crime, then the person who was on a cruise when the crime was committed is a less viable suspect. But a person could have motive, means, and opportunity and still not have done it. They might have been framed, or been really unlucky, or they might not really have motive but fit the profile (stereotype) of one who does. Our many police procedural and mystery TV shows and movies exploit signs and how audiences tend to decode them. But we use inferences from signs to navigate the world in general, not always to our advantage.
Consider "The Linda problem."
Linda is 31 years old, single, outspoken, and very bright. She majored in philosophy. As a student, she was deeply concerned with issues of discrimination and social justice, and also participated in anti-nuclear demonstrations. Which is more probable? Linda is a bank teller. Linda is a bank teller and is active in the feminist movement. The majority of those asked chose option 2. However, the probability of two events occurring together (in "conjunction") is always less than or equal to the probability of either one occurring alone(link)
In other words, the thicker the description, the more persuasive the argument even though the probability of its being valid may actually be decreasing.
While today we have probability as an arithmetic discipline, a 17th century invention, (as well as its digitally enabled descendants demographics and psychometrics) the ancient Greeks (and the Romans) had eikos, "probable" in the sense of an expectation created by repeated observation of a common phenomenon or vivid examples from shared experience or literary memory and occasionally a surprising result vivid enough to revise expectations. Thus to be persuasive required knowing how to exploit your audience's expectations and beliefs (and prejudices) about human behavior. That's still true today, as the "Linda problem" indicates. Most of us don't understand probability very well and are more easily persuaded by anything that is consistant with our expectations and prejudices. Educated people like to think they are above "mere rhetoric." They aren't. Even rhetoricians aren't. Educated people, rhetoricians among them, have the intellectual tools to make more carefully informed opinions, but most of the time we don't because we think "fast" is the same thing is smart.See Thinking Fast and Slow
During the Hellenistic period, this collective understanding of how people behave was transmitted around the Mediterranean and from generation to generation via paideia, the Greek word for education. See for example Paideia: The Ideals of Greek Culture, Werner Jaeger or A History of Education in Antiquity, Henri Marrou.