Can an Inductive inference be Deductively valid?
no. 4 properties are opposite to each other.
- Pigs are winged animals
- All winged animals can fly
- therefore, pigs can fly
- unacceptable
- unacceptable
- conclusion is still inductively valid
ARG conditions vs Inductive arguments
Always fails the A condition.
but satisfies the R condition.
Inductive Reasoning
trend –> generalization.
Taking experience from the past and applying it to estimate the future. Don’t know 100% that it will be true.
ex: cereal was good on Tuesday, so it will be good tomorrow.
Inductive Arguments
Arguments that provide probable support for the conclusion. Can’t 100% guarantee tho.
Different types: Inductive Generalization, Analogy, Inference to the Best Explanation(IBE)
4 properties of Inductive Arguments
- Ampliative: the conclusion may not contain everything that is said in the premises.
- Non truth preserving: conclusion may be false if premises are all true.
- Erodible by future evidence
- They come in degrees of confidence: some premises support the conclusion more strongly then others.
Inductive Generalization
(Inductive Argument)
uses evidence. uses a certain amount of things to make a claim about ALL or most things of that type.
ex: I’ve dated 5 men form Texas that wear cowboy hats. therefore, all men from Texas wear cowboy hats.
Retrodiction
(Inductive Argument)
uses evidence from the present to make a claim about the past.
ex: We dug about dinosaur bones that are 65 million years old. Therefore, dinosaurs used to live on earth 65 million years ago.
sample
a certain amount of participants who represent a broader group. less then 50 = weak. greater then 1000 = strong.
- has to be random sample
- has to be representative of broader group
- not biased sample
Target population
using the number of samples we have to make a conclusion about the broader group (target population)
ex: We interviewed 50 uni students about their opinions on the quality of the food who represented the opinions of the whole university population.
50 = sample
university = target population.
random sample
sample in which every member of the population has an equal chance of participating. True random sample is hard to obtain. Race, gender, sexual orientation, rich/poor etc.
Representatives
more crucial then sample size. Trying to accurately reflect the sample size to the broader target population.
Stratified sampling
A sample selected in such a way that significant characteristics within the population are (approximately) proportionately represented within it.
Guidelines for Evaluating Inductive Generalization
- Determine sample size and target population. (if not stated, try best to guess relying on the context for cues)
- if size is less then 50 = weak.
- Reflect on variety of the population with regard to the property, x.
- Is there sample bias?
- samples based on volunteers, college students, pr persons of a single gender, race, or social class are NOT representative.
- what’s the representative. If it’s a good reason = strong. if not = weak.
Problems of Induction
Doesn’t provide same certainty as deductive reasoning. But can’t get by in life without inductive reasoning.
What’s more crucial, Representativeness or sample size?
representativeness.
Sample bias
A sample that misrepresents the target population.
ex: surveys about camping via e-mail.. e-mail you won’t get the true campers since they probably don’t like using technology.
Hasty Generalization
(fallacy of false generalization)
Drawing a conclusion based on a whole group from a small sample.
ex: all 3 of my professors are bald, therefore, every professor is bald.
