An Analysis on the Topic of Different Ways of Thinking and the Concept of a Deductive Argument by Descartes

The above-mentioned statement needed justification to be portrayed as a valid assumption. Therefore differences and similarities had to be explored. However, as we know from every day life, one may apply this distinction in other fields of knowledge. My task will be to present a simple understanding of the different ways we think, i.e. inductively and deductively. As most of us operate with such distinctive but yet similar methods of thinking, I will portray the way in which we implement the use of logic in other fields of knowledge in everyday life. To extend our knowledge from the basic evidential proof (premises), we need to include inference (conclusions and/or judgements), and if knowledge requires that we maintain not on only truth but also certainty, we must use only deductive conclusions from the premises. Basically, this is what Descartes has tried to achieve and explain: begin with certainty and extend knowledge by a method of inference, which would guarantees to extend certainty.

A deductive argument, very simply, consists of statements, which is the conclusion and the others of which are the premises. The premises are used to justify or provide evidence or reasons for the conclusion. The purpose of a deductive argument is to establish two relationships: the first of which is between the premises and the world - that is, they should be true of the world; the second being a relationship between the premises and the conclusion whereby it is necessary that if the premises are true then the conclusion is true. When the latter relationship is established the argument is valid. In addition, when the premises are also true, the argument is sound because the two relationships together guarantee the truth of the conclusion and thus extend truth. Furthermore, if all the premises are certain, then so is the conclusion. An example would be to compare the general statements that all feminists support women with one that all feminists are women. Both are general, because they mention all entities of a certain sort. However, while the first can be known to be true in that it is known independently of any empirical evidence, the second then, is known best as being dependant empirical evidence gathered from observation or experimentation.

Let us take a deductive argument as an example:

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1. If a person, under normal conditions, were to have an experience of a blue object, then he/she would perceive a blue object (which would mean that there a blue object is present).
2. I now have an experience of a blue object.
3. The conditions and I are normal now.
4. Therefore, bI now perceive a red object (and so there is a red object now).

This is a valid argument, and let us agree that the first principle is certain. But while it is also certain for me that I am now having an experience of a blue object, it is far from certain, that the relevant conditions and I are normal at any particular point. Thus, the third premise is totally irrelevant to extend our basis of knowledge. An inductive argument differs from a deductive argument in that, unlike a valid deductive argument, it is possible for its premises to be true and its conclusion false. Thus justification by means of induction guarantees neither certainty nor truth. Nevertheless, if inductive arguments can be said to be to confirm or support claims to a degree that makes them probable, then perhaps such arguments can be used to extend knowledge.

In general, induction is used to make inferences from a number of individual observed cases to universal laws, or to individual unobserved cases. For example, from the claim that observed changes in temperatures of gases vary with changes in the volume and the pressure of the gas, we can inductively infer a universal gas law. This states that the temperature of a gas is proportional to the product of the pressure and volume of the gas. Therefore, we can infer the prediction that the next gas to be tested will have the same relationship between its temperature, volume, and pressure. Taking the American presidential elections, from the claim that 60% of an observed sample of American voters favor a certain candidate for president, we can infer that probably the candidate will receive about 60% of the actual, overall vote. In each case the argument is from an observed sample of some group to a claim about the whole group or about some member of the group that has not been observed.

We need some set of indubitable statements about observations, which can be used to infer inductively that someone is perceiving an external object. For example, can we inductively justify that someone is perceiving a banana from the fact that he is having a visual experience of something curved, yellow, and smooth? I will give you an example:

1. All times when I have had sensations of something curved, yellow and smooth are times when I have perceived a banana.
2. I am having such a sensation now. Therefore, it is most probably that
3. I am perceiving a banana now. Following this argument, we can grant that the second premise is certain.

However, the first premise is not certain, because it is clearly possible that some, even most, of my previous experiences occurred while I dreamt or had hallucinations. Furthermore, if the first premise is supposed to be based on past observations, it requires remembering or correctly recording a significant number of past instances to be able to verify the claim. As you may know, it is quite plausible to say, "without knowledge of the present and past, there is no knowledge of the future". This is what is known as "experience". Why do our parents always tell us what to do? Why don't they respect our refusal to e.g. carry out their orders (recommendations)? These are the types of questions, which any child might ask himself/herself. As soon as the same children grow up, they will start to realize and understand why their parents had done so, because he/she is in the same situation as his/her parents.

No claim relating to my present sensations or beliefs to the past is certain. We might try the premise that "most times when I believe I remember something are times I correctly remember it, or the premise that "most times I have a sensation of someone screaming in pain are times someone really is in pain". While it surely seems that both premises are reasonable, they are not certain. In other fields of knowledge, such as, Mathematics and Languages. In Mathematics, you can apply both, induction and deduction. An example of deduction would be as follows: 2X+1=92X = 8X = 4 An example of mathematical induction can also be given, respectively: Let us take a simple example. If you want to add two numbers together, such as, 4 and 6, to analyze the result, which you would obtain, it will come out as 10. If you want to double-check your answer, you simply repeat this operation.

Repeating the operation would not surprisingly give you 10 again. You can predict what will be obtained when adding both numbers a third time. Therefore, it is justified to make a conclusion: each time the numbers, 4 and 6, are added, 10 comes out to be the answer. Luckily, I was always (or most of the time) good at math, and I understood these methods of deduction and induction once I had confronted them. They were always straightforward and simple to understand. Applying my personal example to everyday life, I realized that man uses such ways of thinking without even knowing it.

In French, I have also realized that it is simple to spot such methods of thinking. When getting to learn the verbs, (in the light of TOK) I have investigated that there are irregular verbs. This is such a piece of evidence, which proves induction. Applying deduction, in the simple future tense, when taking two similar verbs, such as, voir and savoir, one says je verrai, whereas, using savoir, one says je saurai. By deduction, one expects the savoir verb to be written and spoken like je saverrai, since the voir-part is included in the verb savoir. Consequently, I think that induction, unlike deduction, provides uncertainty. You start from a specific conclusion and go over to a general statement, which (most of the time) includes the term all, whereas one can not use such a term without investigating literally all of which has to be investigated to make such a claim.

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