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# Inference (Logic Slide 5)

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• @granadadennis in the validity of proposition and syllogism it should be materially true and formally correct. there are 10 rules in determining a valid syllogism but we are not yet sure if this is true or false. it depends in the truthfulness of material and the formality.

1) there should only 3 term and only 3.
2) each term must occur twice in the entire syllogism.
3) the minor and major term may not be universal unless it is ascertain in the premises.
4) middle term must be universal at least once
5) if both premise is positive, the conclusion must be positive
6) if 1 premise is negative, the conclusion must be negative,
7) if both premise is negative, there must be no conclusion at all.
8) at least 1 premise must be universal.
9) if 1 premise is particular, the conclusion is particular
10) minor term should be ascertain in the minor premise.

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• what are the steps in determining the validity of a propositions?
especially in categorical syllogism?

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• 1. INFERENCE - any process by which the mind proceeds from one or more propositions to other propositions seen to be implied in the former. - it signifies the operation by which the mind gets new knowledge by drawing out the implications of what it already knows. - The word inference is applied to a series of propositions so arranged that one, called the consequent flows with logical necessity from one or more others, called the antecedent . Antecedent - ( antecedo ) that which goes before. Consequent - ( consequor ) that which follows after or that which is inferred by the antecedent.
• 2. The Relation of the Antecedent and the Consequent - The truth of the antecedent entails the truth of the consequent. In other words: If the antecedent is true, the consequent is true. If the consequent is true, the antecedent is doubtful. Consequence / Sequence - the connection by virtue of which the consequent flows with logical necessity from the antecedent. It is known to be “ the heart of the inference ”. - The falsity of the consequent entails the falsity of the antecedent. If the consequent is false, the antecedent is false. If the antecedent is false, the consequent is doubtful. Consequence/Sequence is usually signified by the terms: “therefore”, “consequently”, “accordingly”, “hence”, “thus”, “and so”, “for this reason”, and so on.
• 3. Synoptic Schema INFERENCE ANTECEDENT (premises) CONSEQUENT (conclusion) SEQUENCE (connection between the antecedent and the consequent)
• 4. EXERCISE: 4. The barometer is very low and the humidity is very high; consequently, its likely to rain w/in a few hours. Determine which of the following illustrate inference. 2. He broke his leg and is therefore using crutches. 3. He’s a man and therefore mortal. 1. All men are mortal; but you are a man; therefore you are mortal. 5. I wonder how far it is from Ruano Bldg. to Beato Angelico Bldg. 6. Carrots are vegetables, dogs bark, and cows give milk. 7. His mother is sick; that’s why he did not come to school today. 8. She blushes; therefore she is guilty. 9. Smoke is pouring out of the windows; the house must be on fire. 10. Since the consequent of that syllogism is false, its antecedent must be false.
• 5. FORMAL AND MATERIAL SEQUENCE Valid sequence springs either from the from the form of the inference or from the special character of the matter or thought content. If the sequence springs from the form of inference, the sequence is FORMAL and the argument is said to be formally valid or formally correct; If the sequence springs from the special character of the thought content, the sequence is MATERIAL and the argument is said to be materially valid. Example of an inference that is formally valid: Every S is a P; therefore some P is an S If we substitute “dog” for S and “animal” for P: Every dog is an animal; therefore some animal is a dog.
• 6. If we retain the same form but substitute “dog” for “triangle” and “animal” for “plane figure bounded by three straight lines”: Every dog is an animal; therefore every animal is a dog. Example of inference that is formally invalid but materially valid: Every triangle is a plane figure bounded by three straight lines; therefore every plane figure bounded by three straight lines is a triangle. In the above example the consequent does not flow from the antecedent because of the form; but it does flow because of its special character of the thought content. “Plane figure bounded by three straight lines” is a definition of “triangle” and is therefore interchangeable with it. The above inference is obviously invalid; yet it has exactly the same form as the materially valid inference given previously: The form of which is: Every S is a P; therefore every P is an S.
• 7. Whenever we use the terms “sequence”, “inference”, “validity”, “correctness of argumentation”, and so on, without qualification, we shall understand them in their formal sense unless it is clear from the context that we are speaking of material sequence. TRUTH AND FORMAL VALIDITY Logical truth consists in the conformity of our minds with reality. A proposition, as explained, is true if things are as the proposition says they are. Logic studies reason as an instrument for acquiring truth, and the attainment of truth must ever remain the ultimate aim of the logician.
• 8. Example of technically correct though the premises and the conclusion are false: No plant is a living being; but every man is a plant; therefore, no man is a living being. This syllogism is correct formally because the conclusion really flows from the premises by virtue of the form, or structure, of the argument. IF the premise were true, the conclusion would also be true.
• 9. Every dog is an animal; but no dog is a plant ; therefore, no plant is an animal. This syllogism is not correct because the conclusion does not really flow from the premises. Its invalidity will be obvious if we retain the same form but change the matter by substituting “cow” for “plant”. The following syllogism is not correct formally although the premises and the conclusion are true: Every dog is an animal; but no dog is a cow ; therefore, no cow is an animal.
• 10. IMMEDIATE AND MEDIATE INFERENCE Inference is either Immediate or Mediate. In the stated syllogism an obviously false conclusion comes after obviously true premises; so the syllogism must be incorrect, for in a correct or valid syllogism only truth can flow from truth. Immediate Inference Consists in passing directly, without the intermediacy of a middle term or a second proposition, from one proposition to a new proposition that is a partial or complete reformulation of the very same truth expressed in the original proposition. Strictly speaking it does not involve the advancement of knowledge because the consequent is only the reformulation of the truth expressed in the antecedent.
• 11. Example : Dogs are animal; Therefore, some animals are dogs. Mediate Inference draws a conclusion from two propositions and does involve an advancement in knowledge. Example : Every animal is mortal; but every dog is an animal; therefore, every dog is mortal.
• 12. Synopsis: Immediate Inference Mediate Inference DEDUCTION AND INDUCTION - passes from two proposition - passes from one proposition - without medium - through a medium - to a new proposition but not to a new truth - not only to a new proposition but also to a new truth Deduction is the process by which our mind proceed from a more universal truth to a less universal truth. Example : All men are mortal; Peter is a man; therefore, Peter is mortal.
• 13. Induction Is the process by which our minds proceed from sufficiently enumerated instances to a universal truth. Example : This ruminant ( a cow) is cloven hoofed; A deer is cloven-hoofed; A goat, an antelope, and an elk; therefore, all ruminants are cloven hoofed. Note: Induction precedes deduction. It is principally by induction that we get the universal principles that constitute the premises of deductive arguments; it is by induction, too, that we grasp the rules governing deduction as well as the principles underlying them. Nevertheless, it is customary in logic courses to treat deduction before induction.