Contrast Between a System of Logic and the Foundation of Arithmetic

When considering the nature of certainty, there are several ways to approach the subject. The two main viewpoints on this issue (at least in the abstract) are scientific realism and phenomenalism. What separates the two concepts is the validity of human perception on anything. However, both ideas are not invalid with the closest approximation of an answer to the question lying somewhere in between them. Evaluating the various aspects that determine certainty will require determining the validity of the following statement: Absence of evidence is not evidence of absence.

Inductions, a series of examples, can be used to verify a major premise, which can then be the framework for deductions, by applying it to a specific case (minor premise). Deductive reasoning can be structured as a syllogism, a “logical structure that uses the major premise and minor premise to reach a necessary conclusion.” In this case, if the major and minor premise are true, then the conclusion is logically valid. In Elizabeth Cady Stanton’s The Declaration of Sentiments, both induction and deduction are used.

A deductive argument is an argument that is intended by the user to be valid and to guarantee the truth of the conclusion given that premises are true. An inductive argument is an argument that is intended by the user to be strong or good enough that, if the premises were to be true, then it would be unlikely that the conclusion itself is false. An example of a deductive argument would be; Socrates was a man. All men are mortal. Therefore, Socrates was mortal. An example of an inductive argument would be; Socrates was Greek. Most Greeks ate fish. Socrates at fish.

Inductive reasoning stands for the arguments that do not preserve the truth, unlike the deductive reasoning. There is no guarantee in inductive reasoning even if the premises are true that the conclusion will be true. The premises bring forth the probability most in life situations. In inductive reasoning, the premises are described to be weak, implausible or cogent, and they form the basis for the drawn conclusion as the evidence available determines whether the argument is strong or weak.

4) Inductive Reasoning- Reasoning in which ideas come at the end. Global commentary and periodic sentences are inductive.

Induction is a form of reasoning where the premises support the conclusion, but do not confirm that the conclusion is true. To justify induction, we are required to justify that we can infer that experiences we have never experienced will resemble those that we have experienced. Making inductive inferences is necessary for everyday life as well as in science. It is rational to rely on inductive arguments in everyday life for claims such as “the sun will rise tomorrow.” But inductive arguments require that nature is uniform. For example, tomorrow the laws of physics will continue to work the same as how they have in the past, so the world will continue spinning and the sun will rise. This perceived uniformity (the principle of uniformity of nature) allows claims like the one previously outlined to be easily understood. Although inductive arguments are useful, whether or not they can be justified is a topic of debate. In James Van Cleve’s “Reliability, Justification and the Problem of Induction,” he uses an inductive argument to attempt to justify induction. In his justification he claims that his method of argument is not circular. I argue that his reasoning is problematic because an inductive argument is not able to justify induction, mainly because inductive arguments presuppose the Principle of the Uniformity of Nature.

Throughout his work Mill explains his principles and what he believes our laws should look like. In Mill’s harm principle he states

David Hume, a philosopher who raised radical doubts about the rationality of the scientific enterprise. Hume believed that “experience can only assure us of what we are actually observing at present, or can remember having observed in the past” (Cottingham, 2008). In this paper I will show that David Hume’s claim on induction that when there is real knowledge of an event, it cannot correctly justify inductive assumptions.

Induction and deduction will be codependent on each other in order to make an argument stronger. Induction lends itself to making conclusions based on several pieces of information gathered, whereas deduction uses syllogisms and enthymemes to make a straightforward conclusion. Writers can use these powerful tools to develop arguments and explanations that would make sense to the reader and proof how failsafe their argument is on

The reason induction originated as a concept of reasoning did not come from its ability to result in proofs, but the usefulness in predicting future occurrences which it allows. As an example of this principle, we can bring into the light the supposed laws of nature which provide constants to our physical world. For any number of the infinite reasons at any instantaneous point of time exceptions to the laws of nature can emerge. Due to this fact, and the fact that the laws of nature are based on a finite number of circumstances of which permanence is assumed, laws of nature cannot be fully proven. However, without the human assumption of the existence of laws of nature, the progress of science would be halted. The laws of nature serve as an exceptional example of how even without a definite proof, inductive reasoning enables leaps in knowledge and

As a teen, I often thought mathematics was primarily a subject you take in school and it wouldn’t affect any aspect of my daily life. However, mathematics I have learned throughout this course is in every aspect of my life, personal and professional. For instance, if I were to conclude a decision I made in my personal and professional life, there are two types of reasoning I might use, inductive or deductive reasoning. Inductive reasoning is the process of arriving at a general conclusion based on observations of specific examples and deductive reasoning, is the process of proving a specific conclusion from one or more general statements. (Blitzer, 2014, pgs. 3 & 8). I have applied inductive reason, when deciding which way would be best to take, either the highway or the main roads, to arrive at work on time. I took the highway for several weeks and the main roads. Each time on the highway I would arrive 10 to 15 minutes late for work and on the main road, I would arrive 5 to 10 minutes

Philosophers create new thesis all the time. Many times these thesis are challenged by other ideas. The Problem of induction was introduced by David Hume in the 18th century. He questioned how past observation could be the same observation in the future. We can assume that past events can occur again, and this was not the problem. The problem is Hume does not believe that past experiences can lead to the future. It is beneficial to completely understand Hume’s stand point therefore I will explain the difference between inductive and deductive reasoning. Inductive reasoning is multiple premises that are believed to be true or at least true most of the time. Deductive reasoning is a theory that claims truth. If the premise is true the conclusion is true. Hume first separated human reasoning in two different ways. The first way is relations of ideas. These are the sciences of geometry, algebra and

In his work “Conjectures and Refutations,” Popper discussed several aspects of induction including the topics of conjectures (opinions or conclusions formed on the basis of incomplete information) or tentative theories and refutations (ways to refute an argument, opinion, testimony, doctrine, or theory, through contradicting evidence) or the acts of disproving arguments through counterexamples (Oxford).

Karl Popper was critical of inductive methods used in science. He argued that there is a chain of justifying arguments that could never be complete, therefore an original statement that is made can never receives the justification that it needs (Popper 505-506). He was a firm believer in the concept of falsification, emphasizing that we can never be sure that a theory is true but we can be sure that a theory is false. He continues to explain that all inductive evidence is limited: we do not observe the universe at all times and in all places. Popper identifies that no matter how many observations are made which confirm a theory there is always potential for future observations to refute the claim (Popper 426). For example, if millions of white swans were observed, using inductive reasoning, we could come up with a theory that all swans are white. However, no matter how many instances of white swans we may have observed, this information does not provide us with justification for the conclusion that all swans are white (Popper 426). Therefore induction cannot yield certainty. For scientists to continue to rely on inductive reasoning to

Human beings are inherently flawed creatures. Through faults in reason and sense perception we interpret the world not as it truly is. Both the Human and Natural Sciences are tools to understand the world and are a lens in which to comprehend ideas not readily available to us purely through common sense logic and sense perception. The implications made in the title are that the inductive scientific method, when removed from error and bias, provides unequivocal and unobjectionable objective truth. The