Bertrand Russell explains that “as soon as definite knowledge concerning any subject becomes possible, the subject ceases to be called philosophy, and becomes a separate science”
We use reason to do philosophy, and logic is the study of reason.
Dialectics and Philosophical Argumentation
An argument in philosophy is a reasoned position—to argue is simply to offer a set of reasons in support of some conclusion.
A traditional dialectic is a debate or discussion between at least two people who hold differing views.
Because of the tendency of participants to appeal to emotion and prejudice in many modern popular debates, philosophers often qualify their words and refer to reasoned debate when discussing proper public discourse between people.
Dialectics usually start with a question. An interlocuter offers an answer to the question, which is then scrutinized by all participants.
Indian Dialectics and Debate
Vedas are often considered religious texts, but it is more accurate to think of them as religious and philosophical texts since they explore what it means to be a human being, discuss the purpose and function of the mind, and attempt to identify the goal of life.
The Upanishads, which are the most philosophical of the Vedic texts, often take the form of dialogues.
Buddhist philosophical texts that were part of early Indian philosophy also contain narrative dialogues (Gillon 2021)
Greek Dialectics and Debate
“Opinion” here means unjustified belief: your beliefs could be true, but they cannot count as knowledge unless you have reasons for them and can offer justifications for your beliefs when questioned by others.
Plato’s dialogues are a testament to the importance of public discourse as a form of rational inquiry in ancient Greece.
Socrates’s goal was not simply to offer people truth. Rather, through questioning, Socrates guides people to discover the truth on their own, provided they are willing to keep an open mind and admit, when necessary, that they are in the wrong.
. Aristotle’s logic is the earliest formal systematized account of inference we know of and was considered the most accurate and complete system until the late 19th century (Smith 2020). Aristotle’s system is taught in logic classes to this day.
The Use of Reason to Discover Truth
Reasoning allows us to hypothesize, work out consequences of our hypotheses, run thought experiments, assess the coherence of a set of beliefs, and generate plausible explanations of the world around us.
Because logic is the study of proper reasoning, and proper reasoning is an essential tool for discovering truth, logic is foundational to the pursuit of learning.
Testing Hypotheses
A hypothesis is a proposed explanation for an observed process or phenomenon. In testing we often formulate if–then statements:
Laws of Logic
laws of logic are construed to be laws of reality itself
Noncontradiction
a statement is a sentence with truth value, meaning that the statement must be true or false. The law of noncontradiction is a law about truth, stating that contradictory propositions cannot be true in the same sense, at the same time.
The Excluded Middle
The law of the excluded middle states that for any statement, either that statement is true, or its negation is true
Normativity in Logic
logic is normative (norm in norm and values)
Normativity is the assumption that certain actions, beliefs, or other mental states are good and ought to be pursued or realized. Normativity implies a standard (a norm) to which we ought to conform. Ethics is a normative discipline because it is the study of how we ought to act. And because we believe people ought to be logical rather than illogical, we label logic as normative.
ethics is normative in the realm of actions and behavior, logic is normative in the realm of reasoning.
Conditionals
Of particular importance is the conditional, which expresses the logical relations between two propositions Conditional statements are used to accurately describe the world or construct a theory.
A conditional is most commonly expressed as an if–then statement
- If you eat your meat, then you can have some pudding
- You can have pudding only if you eat your meat
- If you expect to graduate, then you must complete 120 credit hours
Whatever follows “if” is called the antecedent; whatever follows “then” is called the consequent
Necessary and Sufficient Conditions
those that are necessary and those that are sufficient
- If something is sufficient, it is always sufficient for something else.
- d if something is necessary, it is always necessary for something else.
Y is a necessary condition for X if and only if X cannot be true without Y being true.
- Y -> X X is a sufficient condition for Y if and only if the truth of X guarantees the truth of Y.
- X -> Y
Counterexamples
counterexamples are statements used to disprove a conditional statement
must point out a case in which the claimed necessary condition does not occur alongside the sufficient one
Counterexamples are important for testing the truth of propositions. Often people want to test the truth of statements to effectively argue against someone else, but it is also important to get into the critical thinking habit of attempting to come up with counterexamples for our own statements and propositions
Universal Statements
Universal statements are statements that assert something about every member of a set of things and are an alternative way to describe a conditional. the universal affirmative statement. Aristotle included universal affirmative statements in his system of logic, believing they were one of only a few types of meaningful logical statements (On Interpretation). Universal affirmative statements take two groups of things and claim all members of the first group are also members of the second group: “All A are B.”
These statements are called universal and affirmative because they assert something about all members of group A.
Universal Statements as Conditionals
Universal statements are logically equivalent to conditionals, which means that any conditional can be translated into a universal statement and vice versa.
Counterexamples to Universal Statements
If you wanted to prove this statement false, you would need to find just one example of a living thing that you believe does not deserve moral consideration
Arguments have two components: the conclusion and the reasons offered to support it
Getting to the Premises
The reasons offered are called premises
- “therefore” or “hence”
- Principles are also used as premises in arguments.
The Difference between Truth and Logic
in philosophy logical analysis is often treated as primary.
philosophy deals with subjects in which it is difficult to determine the truth
Logical Analysis
logical analysis ascertains whether the premises of an argument support the conclusion
The argument does not contain a clear inference or evidence of reasoning
An inference is a reasoning process that leads from one idea to another, through which we formulate conclusions. So in an argument, an inference is the movement from the premises to the conclusion, where the former provide support for the latter.
Truth Analysis
Truth analysis is the determination of whether statements are correct or accurate.
If the logic in an argument seems good, you next turn to assessing the truth of the premises. If you disagree with the conclusion or think it untrue, you must look for weaknesses (untruths) in the premises.
Inferences can be deductive, inductive, or abductive. Deductive inferences are the strongest because they can guarantee the truth of their conclusions. Inductive inferences are the most widely used, but they do not guarantee the truth and instead deliver conclusions that are probably true. Abductive inferences also deal in probability.
Deductive Reasoning
A good deductive inference is called a valid inference, meaning its structure guarantees the truth of its conclusion given the truth of the premises
Valid Deductive Inferences
Validity is a property of the logical forms of arguments, and remember that logic and truth are distinct.
Disjunctive Syllogism: Modus Ponens: Modus Tollens:
Invalid Deductive Inferences
f the premises are true, the conclusion may be false.
- Affirming the Consequent
- Denying the Antecedent
Testing Deductive Inferences
Using the sample arguments given, come up with a counterexample to prove that the argument is invalid. A counterexample is a scenario in which the premises are true but the conclusion is false. Solutions are provided below.
Inductive Inferences
Inductive reasoning (induction) is also the process by which we use general beliefs we have about the world to create beliefs about our particular experiences or about what to expect in the future.
Because of the nature of experience and inductive inference, this method can
never guarantee the truth of our beliefs.
At best, inductive inference generates only probable true conclusions because it goes beyond the information contained in the premise
Based on the current science, we can reasonably conclude that the sun will rise tomorrow morning. But is this proposition certain?
Say the earth gets hit by a massive asteroid that destroys it, or the sun explodes into a supernova that encompasses the inner planets and incinerates them. These events are extremely unlikely to occur, although no contradiction arises in imagining that they could take place
while deductive reasoning can guarantee the truth of conclusions if the premises are true, many times the premises themselves of deductive arguments are inductively known.
There are several types of inductive inferences, but for the sake of brevity, this section will cover the three most common types: reasoning from specific instances to generalities, reasoning from generalities to specific instances, and reasoning from the past to the future.
Reasoning from Specific Instances to Generalities
Instance1, Instance2, Instance3 . . . Instancen --> Generalization
Reasoning from Generalities to Specific Instances
Induction can work in the opposite direction as well: reasoning from accepted generalizations to specific instances. This feature of induction relies on the fact that we are learners and that we learn from past experiences and from one another. Much of what we learn is captured in generalizations.
Reasoning from Past to Future
Based on our ample experience of the past, we have a basis for prediction
Strong Inductive Inferences
The strength of inductive inferences depends upon the reliability of premises given as evidence and their relation to the conclusions drawn. A strong inductive inference is one where, if the evidence offered is true, then the conclusion is probably true. A weak inductive inference is one where, if the evidence offered is true,
A weak inductive inference is one where, if the evidence offered is true,the conclusion is not probably true. But just how strong an inference needs to be to be considered good is context dependent. The word “probably” is vague.
Abductive Reasoning
Abductive reasoning is similar to inductive reasoning in that both forms of inference are probabilistic. In abductive reasoning, the conclusion is meant to explain the evidence offered in the premises
in abduction the conclusion explains the premises.
We start with a set of data and attempt to come up with some unifying hypothesis that can best explain the existence of those data
Detectives and forensic investigators use abduction to come up with the best explanation for how a crime was committed and by whom.
abduction as a form of reasoning used in medical diagnoses
Inference to the Best Explanation
Explanatory Virtues
Explanatory virtues are aspects of an explanation that generally make it strong.
A good hypothesis should be explanatory, simple, and conservative and must have depth.
- a hypothesis must be explanatory simply means that it must explain all the available evidence
- A good explanation is often simple
- You may have heard of Occam’s razor, formulated by William of Ockham (1287– 1347), which says that the simplest explanation is the best explanation
- conspiracy theories present the very opposite of simplicity since such explanations are by their very nature complex
- A conservative explanation maintains or conserves much of what we already believe.
- a good explanation should not raise more questions than it answers. This characteristic is the virtue of depth. A deep explanation avoids unexplained explainers, or an explanation that itself is in need of explanation.
Extraordinary Claims Require Extraordinary Evidence
In fact, the explanatory virtues are not laws but rules of thumb, none of which are supreme or necessary
Extraordinary claims will require extraordinary evidence
By the end of this section, you will be able to:
- Explain the four general categories of informal fallacies.
- Classify fallacies by general category.
- Identify fallacies in ordinary language.
When the form of an argument is problematic, it is called a formal fallacy a problem in the relationship between the evidence given in the premises and the conclusion
There are many specific types of informal fallacies, but most can be sorted into four general categories according to how the reasoning fails. These categories show how reasoning can go wrong and serve as warnings for what to watch out for in arguments. They are (1) fallacies of relevance, (2) fallacies of weak induction, (3) fallacies of unwarranted assumption, and (4) fallacies of diversion.
Fallacies of Relevance
In fallacies of relevance, the arguer presents evidence that is not relevant for logically establishing their conclusion. nothing that’s relevant to the conclusion
Appeal to Emotion
Emotional appeals can target any number of emotions—from fear to pity and from love and compassion to hate and aversion.
Ad Hominem Attacks
It is so named because when someone commits this fallacy, the reasons they give for their conclusion concern the characteristics of the person they are arguing against rather than that person’s position Why?
- we problematically assume that characteristics held by an arguer will be transferred to their argument.
- we allow ourselves to be ruled by emotion rather than reason
When someone commits a tu quoque ad hominem fallacy, they attempt to undermine a person’s argument by pointing to real or perceived hypocrisy on the part of the person.
They assert or imply that their opponent, in the past or currently, has done or said things that are inconsistent with their current argument.
Fallacies of Weak Induction
The fallacies of weak induction are mistakes in reasoning in which a person’s evidence or reasons are too weak to firmly establish a conclusion.
Earlier in the chapter I used a generalization about the return of the red-winged blackbirds in March. But what if I based my generalization on just two years of experience? Now my conclusion—that the blackbirds return every mid- March— seems much weaker.
Hasty Generalization
A hasty generalization is a fallacy of weak induction in which a person draws a conclusion using too little evidence to support the conclusion.
not a large enough sample size to draw predictive conclusions about an election. .
Biased Sample
In a biased sample, the problem is that the evidence used is biased in some way.
Appeal to Ignorance
because we do not have evidence or sufficient arguments for God’s existence, then God cannot exist
False Cause Attribution
The fallacy of false cause occurs when a causal relation is assumed to exist between two events or things when it is unlikely that such a causal relationship exists
correlation does not equal causation
Fallacies of Unwarranted Assumption
an argument relies on a piece of information or belief that requires further justificatio
False Dichotomy
False dichotomy, or “false dilemma,” occurs in an argument when a limited number of possibilities are assumed to be the only available option
A false dichotomy is an informal fallacy, and such errors depend upon the content of arguments (their meaning and relation to the world) rather than the form
Begging the Question
Begging the question occurs when an arguer either assumes the truth of the conclusion they aim to prove in the course of trying to prove it or when an arguer assumes the truth of a contentious claim in their argument.
circular reasoning.
To “beg” the question means to assume you already know the answer
Fallacies of Diversion
Fallacy of diversion, which usually occurs in contexts where there is an opponent or an audience.
Strawman
a strawman occurs when an arguer presents a weaker version of the position they are arguing against to make the position easier to defeat
The arguer takes their opponent’s argument, repackages it, and defeats this new version of the argument rather than their opponent’s actual position.
Red Herring
A red herring is a smelly smoked fish that was used to train hunting dogs to track
smells by dragging this fish along a path as practice. So the fallacy gets its name because it means to trick people into following a different path of reasoning than the one at hand.
Ch 5 Review Questions — Logic and Reasoning
5.1 Philosophical Methods for Discovering Truth
1. What is the general structure of a dialectic?
2. What is a statement?
3. Offer an example of a statement and its negation.
4. How does the law of noncontradiction logically imply the law of the excluded middle?
5.2 Logical Statements
5. Offer an example of a conditional, then identify the necessary and sufficient conditions expressed by it.
6. What is a counterexample?
7. Consider the following conditional: "If you walk in the rain, your shirt will get wet." What is a possible counterexample to this statement?
8. Consider the following universal affirmative statement: "All games involve a winner and a loser." What is a counterexample to this statement?
5.3 Arguments
9. What is an argument?
10. What are the key components of an argument?
11. Consider the following argument: "Since Jori is allergic to cats and her apartment complex does not allow dogs, it must be the case that Jori does not have a pet." What are the premises of this argument, and what is the conclusion? What words in the argument indicate the premises and conclusion?
12. Explain the difference between a logical analysis and a truth analysis of an argument.
5.4 Types of Inferences
13. What makes a deductive argument valid, and how can you test for validity?
14. Explain inductive inference, and describe how it is different from an abductive inference.
15. How is reasoning from specific instances to generalizations similar to reasoning from the past to the future?
16. Explain abductive inference and describe how it is similar to an inductive inference.
5.5 Informal Fallacies
17. What are the four general categories of informal fallacies?
18. What is the difference between fallacies of relevance and fallacies of weak induction?
19. What is problematic with appealing to emotion in an argument, and how does this qualify it as a fallacy of relevance?
20. Explain what a fallacy of unwarranted assumption is, and offer an example of one.