Just as understanding the true nature of deductive reasoning begins with understanding the Latin verb deduco -ducere -duxi -ductum [to lead out or bring down], so too the true understanding of the nature of inductive reasoning arises out of grasping the Latin verb induco - inducere - induxi – inductum [to lead into, or up to]. This difference is more that slight and not merely semantic. As deductive arguments merely make explicit conclusions already contained inside the implications of the premises, valid deductive arguments provide certain knowledge. These ‘deduced’ conclusions are simply ‘lead out’ by logical necessity or deductive entailment. No additional premises are needed for validity. Either the conclusion is already contained in the premises or it is not. Validity, like pregnancy, has no degrees. Either a deductive aregument is valid or it is not valid. To say of a one deductive argument that it is more valid than another would be to speak falsely and ignorantly.
Such is not the case with inductive arguments and that is why they are never called valid or invalid. The factual truth of the conclusion in inductive arguments is not assured as it is in a valid deductive argument. True to the Latin root meaning, inductive arguments never claim absolutely certain knowledge. Inductive arguments 'lead up' to the likelihood that their conclusions should be accepted as factually true based on the tested truth of their premises. This 'likelihood' is referred to as 'probability' both in philosophy and in science. However, when the two most common inductive forms of reasoning are examined, analogical arguments and causal arguments it is evident that there is no universal agreement on the nature of probability.
While philosophers like to quibble about various theories of probability, scientists simply assume that future events will resemble past events sufficiently to establish some degree of 'probability' about future events. Conclusions of inductive arguments are a matter of degree ranging from 'worthless' to 'best' available. The strength of inductive arguments rests on the best testable evidence available at the time. A worthless inductive argument is one for which there is either absolutely no testable evidence for the truth of the premises, the evidence is too meager to warrant strong probability, or even worse, there is no 'logically possible evidence' that could be tested for the truth of the premises. 'Best' inductive arguments on the contrary are those for which there is not only logically possible testable evidence but also, the evidence for the premises is the very latest empirical (scientific) evidence known to researches on the topic.
1. Example of a 'worthless' inductive argument:
Tommy saw an invisible witch in the kitchen last August. Mary saw an invisible witch in the garage last week. My father saw an invisible witch on the freeway last night. Therefore, it is highly probable that I will see an invisible witch tonight after polo practice.
Assuming that 'invisible' here means something that cannot be 'seen' and that 'saw' does not here refer to a dream state of consciousness but rather a real state of consciousness this inductive argument is worthless for two reasons. First, the premises contain a logical contradiction, i.e. something is claimed to be 'seen' that by definition cannot be seen. Second, the premises are anecdotal, i.e. insufficient instances to warrant any probable conclusion.
2. Example of 'best' inductive argument from latest scientific evidence:
Analysis of all voting records kept by the City of Salem, Massachusetts for the last 300 years show that more people over the age of 25 voted in each election than people under the age of 25.
l There is an election tomorrow in the City of Salem, Massachusetts.
Therefore, it is highly probable that there will be more voters over the age of 25 voting in tomorrow’s Salem election than people under the age of 25.
Assuming that the City of Salem, Massachusetts does indeed have the voting records referred to and that they can be examined by researches, this is a 'best' evidence available inductive argument for those trying to make reliable predictions about voting patterns in the upcoming election in the City of Salem, Massachusetts. Not only is everything referred to in the argument logically possible, but also everything in the argument has a degree of empirical probability.
Notice that the 'best evidence' inductive argument does not guarantee that more people over the age of 25 will vote in the upcoming election than people under 25. It simply claims to predict with a high degree of probability that such will be the case. Unlike valid deductive arguments, the factual truth of the premises of inductive arguments does not necessitate the truth of the claim made by the conclusion.
Critical thinkers in both philosophy and science use the words ‘truth’ and ‘empirical’ with the following meanings:
• 'Truth' is either a priori or a posteriori evidence offered in support of a propositional claim.
A priori truth is evidence by reason alone or independent of immediate experience. (example of an a priori truth: All triangles in plane geometry have three sides and three angles.
A posteriori truth is evidence contingent on experience of the senses. (example of an a posteriori truth: Chico, California lies 19 miles to the east of Interstate 5 off exit 619.)
• 'Empirical' is public, testable evidence from the senses, observation or past sense experience generally.
Now is should be clear that the conclusions of inductive arguments are contingent on the empirical truth of their premises and that inductive arguments offer only probability for the truth of their conclusions.
Two popular forms of inductive arguments are:
Analogical arguments, i.e. observing that since two or more things are alike in some way that they are probably alike in some other way. This may prove to be a highly unwarranted asumption, however, due to the inherent inexactness of analogies in general.
Example: Just as a pocket watch is a very complicated thing, the universe too is a very complicated thing. And since no one supposes that a pocket watch just came into being just by some freak accident, so too we should not suppose that the universe came into being just by some freak accident especially since the universe is far more complicated than any pocket watch. Therefore, the universe most probably came into being through the work of some intelligent being.
The inherent weakness of this popular analogical argument for 'intelligent design' is quickly revealed by the observation that the universe is not a pocket watch despite the observations that both are 'complicated'.
Causal arguments, i.e. observing that whenever an event happens it correlates to certain necessary and sufficient conditions for it to happen and whenever these necessary and sufficient conditions happen again the event will probably happen again.
Example: Gas explosions occur when oxygen, fuel and a source of ignition all combine in a closed area. The gas jets in the chem. Lab are all open, the doors and windows are all closed and there is a lighted candle on the desk at the front of the lab. More than likely, an explosion will occur once enough gas fills the chem. Lab and is ignited by the candle.
Both Analogical reasoning and Casual reasoning will be examined separately in the next chapters.