What exactly is Anumana Pramana? Guessing the past happenings with the available evidence also come under Anumana Pramana? And how does it differ from Artapatti Pramana?
I am partially answering the question for Anumana.
As we know in Samkhya, three standards or proofs are accepted - direct perception, inference (Anumana) and Apta Vakya (or scriptures).
Drishtamanumanamaptavachanancha sarvapramanasiddhatvat |
Trividham pramanamishtam prameyasiddhih pramanAddhi ||
Pratyaksha (direct perception), anumAna (inferrence) and Apta Vakya (i.e words of the Rishis or scriptures) - these three standards are accepted in Samkhya. All other standards are accomplished/established by these three only. By using these three pramanas the propositions are established.
Samkhya Karika 4
Now, in Karika 5, Anumana is stated to be of three types:
Prativishayadhyavasayo drishtam trividhamnumanamakhyatam |
Perception is the application 1 (of the senses to special objects of sense. Three kinds of inference are declared: it (an inference or logical conclusion) is preceded by a linga (mark or sign = major premiss) and a lingi (the subject in which it inheres = minor premiss). Fit testimony is fit revelation (sruti)"
The three types of inference being talked about in the verse are - Purvavat (prior), Pashchatvat (posterior) and Samanyavat (analogous or generic).
For example, as in the inference of rain from the gathering of clouds or first we see the smoke from which infer that there is a fire somewhere as the cause (of that smoke). So, here, the cause is characterized by the Anumana.
Here, the effect is characterized instead. As an example: inference of rain (that rain has happened) upon seeing the swelling of a river or when we find out that the taste of a drop of sea water is salty we infer that the whole sea water is salty.
This is generic or analogous and it is characterized as distinct from both the cause and the effect. For example, when we infer something to be a substance when we have found it to be earthy. Or when we find that in one mango tree buds are found we infer that in all mango trees it must be the same.
In the smoke-fire example, smoke is the sign or Linga or Vyapak for (proving) the existence of fire. And fire is called the Lingi. The existence of Lingi is proved here with the help of Linga.
In all Anumanas these two - Linga and Lingi will always be there. That's why the verse 5 given mentions Anumana to be Lingalingipurvak.