Understanding Valid and Warranted Inferences

Understanding Valid and Warranted Inferences

Inference

“Valid” and “warranted” are two concepts that are essential in understanding the different purposes of deductive and inductive arguments. The lexical definitions and connotations of these two concepts help one understand why deductive arguments aim to prove conclusions definitively, whereas inductive arguments aim to make conclusions probable. The lexical of valid, as given by Merriam-Webster, is that the term means having legal efficacy or force and being well-grounded, being at once applicable and meaningful (The Merriam-Webster Dictionary, 2022). Logically, a valid argument is one where if the premises are true, the conclusion must also be true. This definition highlights certainty and definitive proof. On the other hand, connotatively, “valid” implies solidity, certitude, and indisputability. It points toward a solid, unquestionable link between premises and deduction. This lines up with the purpose of deductive arguments, which pursue the establishment of conclusions with certainty. If a deductive argument is valid, the truth of the premises guarantees the truth of the conclusion, leaving no room for doubt.

According to Merriam-Webster, the definition of warranted is having a good reason or justification (The Merriam-Webster Dictionary, 2022). Logically, a warranted inference is one that is justified by the evidence, even though it may not be definitively proven. This is a reflection of the level of support that makes the conclusion rational but not definite. Subsequently, the term warranted connotes rationalization, reasonableness, and support without necessarily indicating certainty. It suggests that the deduction is rational given the proof but recognizes the likelihood of different conclusions. This fits with the objective of inductive arguments, whose intention is to show that a conclusion is plausible based on the premises. In inductive arguments, there is no certainty of deductive arguments; however, there is strong support that the conclusion is likely true.

Fallacies

My choice of fallacy is “Denying the Antecedent”, and I will use the Modus Tollens as a valid argument template to reveal the fallacy. The structure of the Modus Tollens is as follows:

If A, then B.

Not B.

Therefore, not A.

Here, if the consequent (B) is false, then the antecedent (A) must also be false. This form of reasoning is valid because if the initial condition (A) truly leads to the result (B), and the result (B) does not occur, it logically follows that the initial condition (A) could not have occurred.

On the other hand, the structure of Denying the Antecedent, as given by Peter and Gittens (2015), is as follows:

If A, then B.

Not A.

Therefore, not B.

Here, the argument incorrectly assumes that if the antecedent (A) is false, then the consequent (B) must also be false. This reasoning is fallacious because it ignores other possible reasons that could lead to B.

The Modus Tollens argument is valid because of the correlation that “If A, then B” asserts that A is a sufficient condition for B. When one observes “Not B,” one can confidently conclude “Not A” because A is required for B to be true. The absence of B directly indicates the absence of A due to the sufficiency of A for B. In Denying the Antecedent, one starts with the same, “If A, then B.” However, the argument is invalid because when we observe “Not A,” we incorrectly conclude “Not B.” This leap is unwarranted because the initial statement only says that A is sufficient for B, not that it is necessary. B could still occur due to other factors independent of A.

Civic Responsibility

If I were to complete the bonus exercise provided at the end of Chapter 9 of the textbook, the exercise would take up much time, but I would argue that the time would be well spent. This is because, first, the exercise would give me a better understanding of healthcare policies and their impacts, enabling me to grasp how healthcare policies are formed, the interests and stakeholders involved, and the potential consequences of different policy choices. Secondly, the exercise would provide me with a historical context, which is invaluable for informed decision-making and effective advocacy. Lastly, completing the exercise would significantly hone my critical thinking skills, research abilities, and analytical skills.

There are two issues that I believe a comparable amount of time and effort would be worth it, namely, data privacy and cybersecurity. In a rapidly evolving digital world, it is crucial to understand the impacts of these innovations on people’s lives, especially the negative ones, so that individuals can protect themselves. As a critical thinker, I believe that citizens have the duty to be informed on current issues because the only way to make a good decision is when they are well informed. Further, for input to be beneficial, one has to be well-informed; otherwise, one’s contribution will not only be ineffective but also detrimental to society.

References

Peter, F., & Gittens, C. A. (2015). Think critically.

The Merriam-Webster Dictionary. (2022). United States: Merriam-Webster, Incorporated.

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Introduction
Remember – your actual journal entry should be somewhat brief; most of your time should be spent thinking about the questions asked and the issues raised. Your thoughts should then be distilled into a mini-argument that will respond affirmatively to the four tests for evaluating arguments: truthfulness of premises, logical strength, relevance, and non-circularity.

Understanding Valid and Warranted Inferences

Instructions
For this journal assignment, briefly answer each of the following prompts:

Inference: The differing meanings of “valid inference” and “warranted inference” are closely related to the differing purposes of deductive and inductive arguments – the purpose of deductive being to prove; and the purpose of inductive being to make the conclusion most probable.
Look up the words “valid” and “warranted.” Each of these words, you will find, has what is known as a lexical definition – that is just the dictionary definition of the word. Words also have certain connotations – meanings that go beyond their lexical definitions; associated ideas and concepts – think of terms such as “fur baby” as the name for a pet.
Briefly discuss how the lexical definitions and connotations of “valid” and “warranted” can help us understand the differing purposes of deductive and inductive arguments.
Fallacies: In Section 8.2, the text states that there are “fallacious argument templates” (Facione & Gittens, p. 167) and then gives a number of examples. The authors further state: “Analysis of the meanings of the terms used and the grammatical rules of the language reveal the source of error” (p.167).
Choose one of the fallacies in this section, such as Denying the Antecedent or False Classification, and pair it with the valid argument template. For example, if you choose Denying the Antecedent, the valid argument template will be Denying the Consequent. False Classification would pair with one of the fallacies in Reasoning About Classes of Objects.
Explain, in your own words, how the fallacy is revealed through analysis of the valid argument template. Think of it this way – if you know how the heart works, you will know that certain malfunctions will prevent it from working. For example, if you know that the coronary arteries supply the heart with blood, then you can reason that a blockage will stop that vital flow. So this journal prompt asks you to explain, in your own words, how one of the valid argument templates work – and how that exposes the fallacy connected with that type of argument.
Civic Responsibility: At the end of Chapter 9 there is a Bonus Exercise that asks you to research and analyze the 2009 debate over the healthcare public option. If you were actually to complete that exercise, it would take quite a bit of time and effort.
Do you think that completing such an exercise would be time well spent or time wasted? If well-spent, why? If time wasted, why?
Is there any issue on which you think a comparable amount of time and effort would be worthwhile?
As a critical thinker, do you believe that citizens have an obligation to be informed on topics of current interest? If yes, why, if no, why not?
If you include references to outside sources (beyond the textbook), make sure you cite them properly.