Logic is the study of abstract symbolic reasoning. It resembles mathematics in that it works from axioms and seeks to prove theorems, but it differs in that it does not involve numbers. It is also self-reflective in a way that mathematics tends not to be. Namely, it questions the truth of its own axioms.
OR (as paraphrased and quoted from philosophicalsociety.com)
Logic is the study of reasoning --- the nature of good (correct) reasoning and of bad (incorrect) reasoning. Its focus is the method or process by which an argument unfolds, not whether any arbitrary statement or series of statements is "true" or accurate. Logicians study and analyze arguments, premises, inferences, propositions, conditional statements, and symbolic forms. As a "branch" of philosophy, logic is often broken down into many subsets: for instance, modal logic, many-valued logic, modern logic, symbolic logic, formal and informal logic, deductive and inductive logic.
Aristotle was the founder of logic. Later research has not superseded his work, but expanded it.
From the beginning, with Aristotle, there have been certain presuppositions (accepted truths).
They are the law of identity: whatever is, is (A is A); the law of contradiction: a thing cannot both be and not be (A cannot be B and not-B); the law of the excluded middle: a thing must either be or not be (A is either B or not-B).
This leads us to 4 statements. For any two categories (S and P) at least one of these is true:
All S are P.
Some S are P.
No S is P.
Some S are not P.
For logic to work there must be axioms. These are rule, or basic assumptions we agree are true. Then we will take one step as leading to the next.
For an argument to establish its conclusion, it must be built on true premises. But a deduction can be valid, even if one or more premises are false. And a conclusion may be true, even if the premises are false.
Premise: All canoes are refrigerators. FALSE.
Premise: All refrigerators are watercraft. FALSE.
Conclusion: So all canoes are watercraft. TRUE.
YET THE FINAL LINE WOULD HAVE TO BE TRUE, IF THE FIRST TWO LINES ARE TRUE.
Deductive thinking is largely reducible to a form such as: All men are mortal. Socrates is a man, therefore Socrates is mortal (all S is P, M is S, therefore M is P); or more exactly: If all men are mortal, and if Socrates is a man, Socrates must then be mortal. Such a form is known as a syllogism.
Induction is the process by which general propositions are established: a general induction is made by discovering apparent uniformities which afford the basis of generalizations. It can achieve only probability, never mathematical certainty.
John Stuart Mill's writings on method sought to formulate the principles of experimental procedure. The theory of probability belongs to induction as well as to mathematics, along with Euclidean geometry. The process of induction has been the great method of modern science, and by it many of the most notable of scientific achievements have been made. The theories of gravity (Newton), and evolution (Darwin) were proposed using induction.
Some metaphysicians have held that the law of contradiction may not be true at all times, that A may be both B and not-B. Similarly some claimed that, though it is true, it is not strictly capable of syllogistic statement that: if A is to the right of B and C is to the right of A, then C is to the right of B.
Enthymeme - a syllogism or other argument in which a premise or the conclusion is unexpressed. It’s implied!!!
•Example: “I live in Wisconsin, so I am probably a Green Bay Packer Fan”
•What is the missing premise?
•“Most people from Wisconsin are Green Bay Packer Fans.” •“a syllogism or other argument in which a premise or the conclusion is unexpressed.”
•Meaning- it’s implied!!!
•Example: “I live in Wisconsin, so I am probably a Green Bay Packer Fan”
•What is the missing premise?
•“Most people from Wisconsin are Green Bay Packer Fans.”
Inference - A mental movement from premises to a conclusion.
Justification - Evidence or reasons that are presented in support of the truth of a belief or statement.
Inductive Reasoning - an inference from many particular claims, toward a general claim.
Example: This snail eats lettuce, that snail eats lettuce, this other snail eats lettuce, this one too, etc. Therefore, all snails eat lettuce.
Induction moves from many specific statements toward a generality.
Conflicts / Discussions: David Hume and Nelson Goodman.
Deductive Reasoning - An inference from a general claim, leading to a particular conclusion.
Example: All snails eat lettuce, and this thing is a snail, therefore this thing eats lettuce.
Circular Argument - Consisting of premises offered in support of a conclusion, where the conclusion is not just one of the premises. Here is a famous example: It should be okay to destroy property when you are angry because angry people destroy things.
Relativism - A collection of views that claim that one sort of thing (e.g. morality) depends on something else (e.g. cultural values), which varies. Since there is no set of standards that stand out (all cultural values are equal to each other), there is nothing to choose between various accounts of one sort of thing (hence, morality is relative).
Scepticism - The view that knowledge in some domains is not possible. This can be specific in nature (belief in miracles) or general (about all of our alleged knowledge).
Syllogism - a logical argument composed of three components: major premise, minor premise, and conclusion inferred from the premises. Syllogisms make statements that are generally true in a particular situation. In doing so, syllogisms often provide irrefutable argumentation. Syllogisms are an integral component of the formal study of logic, and are commonly featured in aptitude tests meant to assess logical reasoning abilities.
Thought Experiment - An imagined case, designed to put pressure on our intuitions and clarify the way we think of something. For philosophers, thought experiments are like test tubes, for testing our beliefs, and knowledge.
Logical Fallicies - A full list and explanation can be found here.
SO... Since logic is the study of reasoning -- the nature of good (correct) reasoning and of bad (incorrect) reasoning. Its focus is the method by which an argument unfolds, not whether any arbitrary statement is true or accurate. Thus, an argument can be both deductively valid and perfectly absurd, as in 1. All telephone poles are elephants. 2. Sally is a telephone pole. 3. Therefore, Sally is an elephant. The conclusion is valid because it conforms to a correct syllogistic pattern -- in this case, affirmation of the antecedent -- but is ludicrous at the same time. That doesn't matter. What matters is, does it make sense as it is represented, and not necessarily in a real world context.
Websites for Research:
The God/Stone Paradox
Great Moments in Logic - consequently.org
List of famous Logicians - Ranker
THE BOOK OF BAD ARGUMENTS
6 Short Videos to teach High Schoolers Logic
Philosophy Learning and Teaching Organization - Current Issues Articles.
What is a valid argument? (consistency, logic, reason, contradiction, deduction, induction, validity)
What is a logical fallacy?
What is truth?
What is falsity?
Can something be both true and false? Or neither?
What is nonsense?
Section 8 of the Charter of Rights and Freedoms
8. Everyone has the right to be secure against unreasonable search or seizure.
REASONABLE GROUNDS as discussed in CriminalNotebook.ca
"The legal standard of "reasonable and probable grounds" is employed in many aspects of law enforcement. It is the threshold that a peace officer must satisfy before certain powers can be employed including arrest and searches.
This level of proof is the point where "the state’s interest in detecting and preventing crime begins to prevail over the individual’s interest in being left alone at the point where credibly-based probability replaces suspicion".
Reasonable and probable grounds is the “the point where credibly-based probability replaces suspicion". It is the reasonable belief that "an event not unlikely to occur for reasons that rise above mere suspicion. "Reasonableness" concerns the legitimate expectations in the existence of certain facts. It can then be said that the belief in certain facts can be "reasonable" without being "probable".
The standard of reasonable grounds to believe is greater than mere suspicion but less than on a balance of probabilities when the totality of the circumstances are considered.It is also greater than "[m]ere suspicion, conjecture, hypothesis or ‘fishing expeditions’".
The purpose of emphasizing the "totality of the circumstances" is to "avoid concentrating on individual pieces of evidence".
It is a standard of reasonable probability and is credibility based. It must be more than mere possibility or suspicion. It is a standard of "credibly-based probability" 
The reasonableness requires that the grounds be justifiable from an objective point of view. A reasonable person placed in the position of the officer must be able to find that the grounds exist."
Controlled Drug and Substances Act, Part 2: Enforcement
Search, Seizure and DetentionMarginal note:Information for search warrant
- 11 (1) A justice who, on ex parte application, is satisfied by information on oath that there are reasonable grounds to believe that
- (a) a controlled substance or precursor in respect of which this Act has been contravened,
- (b) any thing in which a controlled substance or precursor referred to in paragraph (a) is contained or concealed,
- (c) offence-related property, or
- (d) any thing that will afford evidence in respect of an offence under this Act or an offence, in whole or in part in relation to a contravention of this Act, under section 354 or 462.31 of the Criminal Code
Where warrant not necessary
(7) A peace officer may exercise any of the powers described in subsection (1), (5) or (6) without a warrant if the conditions for obtaining a warrant exist but by reason of exigent circumstances it would be impracticable to obtain one.
POLICE POWERS AND DRUG-RELATED OFFENCES
The power of search incidental to an arrest has since been held to extend to the search of a vehicle for the purposes of obtaining evidence against a driver arrested for possession of narcotics. In a four-to-three majority of the Supreme Court of Canada in R. v. Caslake,() the principles governing the common law power of search incidental to an arrest were once again reviewed. In this case, the accused was arrested in his car after a police officer discovered a bag of marijuana in the grass near the roadway. Approximately six hours after the arrest, a police officer searched the car where it had been towed and found cocaine. The officer did not have a warrant or the person’s consent to do so. He testified that the search was conducted pursuant to a police policy that required that an inventory be taken of the condition and contents of a vehicle that had been impounded during the course of an investigation. The purpose of the policy was to safeguard the valuables belonging to the owner of the vehicle and to note the general condition of the vehicle. The accused challenged his conviction for possession of cocaine stating that the search of the car was unreasonable.
Prepared For The Senate Special Committee On Illegal Drugs by Gérald Lafrenière, Law and Government Division,6 March 2001
Search, Seizure & Detention Under the Charter
"In Collins v. The Queen, the Supreme Court of Canada said that the Crown has the burden of establishing that a warrantless search is reasonable; a search will be reasonable if it is authorized by a law that is reasonable and is carried out in a reasonable manner. Section 10 of the Narcotic Control Act authorizes police officers to search without warrant a place other than a dwelling-house, if they have reasonable grounds to believe that it contains a narcotic in respect of which an offence has been committed."
In R. v. Grant, the court held that "warrantless searches pursuant to section 10 of the Narcotic Control Act must be limited to situations in which exigent circumstances render obtaining a warrant impracticable," in order to avoid violation of section 8 of the Charter. Exigent circumstances would include "imminent danger of the loss, removal, destruction or disappearance of the evidence," should the search be delayed to obtain a warrant.
With respect to other forms of warrantless search, the Supreme Court of Canada has further held that "sniffing" for marijuana at the door of a suspect’s house constituted an unreasonable search. Thus, a warrant supported by the "evidence" thereby obtained was found to be invalid. Writing for the majority in R. v Evans, Mr. Justice Sopinka acknowledged an "implied invitation" extending to members of the public, including the police, to knock in order to communicate with the occupants of a dwelling. The police had approached with the intention of securing evidence against the occupant; thus, they were engaging in a search, which the lack of any prior authorization rendered unreasonable and in violation of section 8 of the Charter. Because, however, the police had acted in good faith, the impugned real evidence (in the form of marijuana plants) existed irrespective of the Charter violation, and the violation was not particularly grave, the Supreme Court of Canada held that the evidence was admissible since exclusion would have been more harmful to the administration of justice.
6. Plain View Doctrine
In Shea, the Ontario High Court followed the "plain view" doctrine cases in the United States in deciding that, once a police officer is lawfully in residential premises, he has the right to seize articles such as narcotics that are in plain view.
In Heisler, a random search of people entering a rock concert disclosed a large quantity of drugs in the accused’s possession. The evidence revealed, however, that there had been no grounds upon which to base the search. The Alberta Provincial Court determined that the accused had been subjected to an unreasonable search that went beyond the bounds of mere bad taste and impropriety. The evidence was excluded on the grounds that to admit it would bring the administration of justice into disrepute. In the Roy case, however, the Ontario High Court held that where posted signs declare that entry to a rock concert is conditional on submitting to a search, such a search is not in violation of section 8.
In Debot, the police received a tip from an informant that the appellant was going to take delivery of a substantial quantity of the amphetamine "speed." He was stopped, ordered from his car, and told to assume a "spread eagle" position and to empty his pockets; speed was found. Although the search was carried out without a warrant, the Supreme Court of Canada held that the police had acted reasonably and that the evidence should not have been excluded as the trial judge had ordered. Chief Justice Dickson said that, although a detainee must be informed of the right to retain and instruct counsel immediately upon detention - a requirement the police had observed in this case - and although the "spread eagle" direction amounted to a detention, the police are not obligated to suspend a search as an incident to an arrest until the detainee has had the opportunity to retain counsel.
- Marilyn Pilon
Law and Government Division
Revised 15 February 2000