T5.3 2 of 5

>I

Well, this "making an assumption" talk and "what if?" thinking will become clear if it's not already. For now, we turn to the technical side of SD and turn the informal derivation just presented into a formal SD derivation. Once you get used to doing derivations with assumptions, it will be much easier to see that they make sense.

Here again is that table:

Premise (from the definition of "sound"): 1. S>V  
Premise (from the definition of "valid"): 2. V>~(T&F)  
Assumption (we ask "what if" the argument is sound): 3. what if..... S
1,3 >E 4. then........ V
2,4 >E 5. then........ ~(T&F)
Conclusion from our assumption 3. and the argument through 5 6. S>~(T&F)  

We will call lines 3-5 a subderivation. And the conclusion at 6 we will say is justified by means of >I. Here's what our derivation will look like from now on:

 
  1.
  2.
  3.
  4.
  5.
  6.

Notice that this is just a briefer version of what is given above in blue. And it introduces our rule of conditional introduction: >I.

Whenever you need to prove a conditional in SD, you need to cite a whole subderivation (like 3-5 in this example)

>I

input:



output:
P


Q
P>Q

Here the bar indicates a subderivation with P as assumption and Q as final line.

Now, we need to say more about the concept of a subderiation.