Let us look at some examples just to familiarize with the terms discussed before. Following are some arguments. We shall try to find the basic blocks (paksha, hetu, vyaapti and saadhya)  of inference in them.

1.  "Whale is a mammal because it gives birth to young ones like an elephant".

Here, we want to prove that "Whale is a mammal".  Hence, the saadhya is the 'mammal' character of whale. The reason we cite to prove the whale's 'mammalness' (?!) is its character of giving birth to young ones. Hence, the nature of whale to give birth to young ones is the hetu here. If an animal gives birth to young ones, it is a mammal. For instance, elephant gives birth to young ones and is a mammal. The association of "giving birth to young ones" and "being a mammal" is the vyaapti here. The paksha under consideration is the whale itself.

2. "During Mr.X's travel on an airplane, the ink from his pen leaked out and stained his shirt. The pressure inside the pen should have been higher because, when there is a difference in pressure, a fluid flows from the high pressure region to the low pressure region as is the case of a cyclone."

In the above argument, the pen is the paksha. The argument intends to prove that "the pressure inside the pen was higher". Hence, it is the saadhya. The reason given is the flow of ink from inside the pen to outside. Hence, it is the hetu. That a fluid always flows from a high pressure region to a low pressure region is the the vyaapti. The example cited here is cyclone where air flows from high pressure region to low pressure region.

3. "Lead shots should sink in kerosene because they do so in water and as kerosene floats on water."

In this example, inference can be made in multiple stages. In each stage, an argument is given to prove the statement of that stage. The statement proved in one stage can be used in the next stage. The arguments in various stages and their building blocks are as follows:

stage 1 :    "Kerosene has less density when compared to water because it floats on water like ice. "

Here, we like to prove that "kerosene is less dense when compared to water" this nature of kerosene is the saadhya. The place of observation of kerosene and water is the paksha. The hetu is the floating of kerosene on water. The relationship that "anything  that floats on water has lesser density than water" is the vyaapti. This vyaapti is also observed in case of a stone. One may question that ship, which is made of iron, floats on water but the density of iron is greater than water. Here, though the density of iron is greater than that of water, when it is made into a ship, there is a lot of empty space which is filled by air. When the resultant density of the ship (iron + air) is considered, it is lesser than that of water. Thus, the vyaapti holds good.

 

stage 2 :    "Lead shots have greater density than water because they sink in water like a stone."

This argument is similar to the above one. We shall list the basic blocks.

Paksha - The place of observation of lead shots and water.

Hetu - The nature of lead shots to sink in water.

Saadhya - Denser nature of lead shots in comparison with water.

Vyaapti -  An object sinks in water only if it is denser than water.

 

stage 3 :    "Lead shots have greater density than kerosene because

a. density of lead shots > density of water and,

b. density of kerosene  < density   of water.

as in the case of the numbers 10, 7 and 2. 10 > 7 and 2 < 7. Also, 10 > 2."

Here, the saadhya is the denser nature of lead in comparison with kerosene. The hetu cited has two parts - greater density of lead shots in comparison with water and lesser density of kerosene in comparison with water. The paksha is the place of observation of lead shots, kerosene and water. The vyaapti governing the above conclusion is that if a > b and c < b then, a < c.  The vyaapti  is also found in the case of the numbers 10, 7 and 2.

 

stage 4 :    "Lead shots sink in kerosene because they have greater density than kerosene like a stone."

This argument is similar to arguments 1 and 2. The basic blocks are :

Paksha - The place of observation of lead shots and kerosene.

Hetu - Denser nature of lead shots in comparison with kerosene.

Saadhya - The nature of lead shots to sink in water.

Vyaapti -  An object denser than kerosene  always sinks in it.

4. "Find the next number in the series 1, 1, 2, 3, 5, 8, 13, ..."

On observing the series, we find that '2' is the sum of previous two numbers 1, 1. Similarly, '3' is the sum of previous two numbers 1 and 2. '5' is the sum of the previous two numbers 3, 2 and so on. (This series, you may know, is called the fibonacci series) Thus, one may conclude that the next term in the series should be 8 + 13 = 21. Like the above examples, here too, let us find the basic blocks of inference.

We infer that the next term in the series is 21. This is the saadhya. We reach this conclusion because the previous two numbers are 8 and 13. Hence, the hetu is "previous two numbers are 8 and 13".  The vyaapti here is interesting. We observe the numbers 1, 1 and 2. We find that '2' is the sum of previous two numbers. We also observe the numbers 1, 2 and 3. Here too, '3' is the sum of previous two numbers. By such repeated observations of a particular behaviour, we reach a general rule that "if previous two numbers are 'x' and 'y' then, the next number is 'x+y' ". This is the vyaapti. It is interesting to note that we go both from   'particular'  to 'universal' (for recognizing the vyaapti) and also from 'universal' to 'particular' (application of vyaapti and concluding that the next number is 21) in the above process of inference. Here, the paksha is the set of numbers 8, 13 and 21 (the inferred number).